POLITECHNIKA WARSZAWSKA

POLITECHNIKA
WARSZAWSKA
WARSAW UNIVERSITY OF TECHNOLOGY
Faculty of Electrical Engineering
ROZPRAWA DOKTORSKA
Ph.D. Thesis
Dariusz L. Sobczuk, M. Sc.
Application of ANN for Control of PWM
Inverter Fed Induction Motor Drives
WARSZAWA
1999

Warsaw University of Technology
Faculty of Electrical Engineering
Institute of Control and Industrial Electronics
Ph.D. Thesis
M.Sc. Dariusz L. Sobczuk
Application of ANN for Control of PWM
Inverter Fed Induction Motor Drives
Thesis supervisor
Prof. dr hab. Marian P. Kaźmierkowski
Warsaw – Poland, 1999

Contents
1. Introduction 4
2. Mathematical description of induction motor 7
2.1. Introduction 7
2.2. Basics of induction motor model 7
2.2.1. Space vectors 7
2.2.2. Vector Equilibrium equations 9
2.2.3. Vector Equilibrium equations in per unit system 11
2.2.4. Orientation of the model 11
3. Basics of Artificial Neural Networks (ANN) 14
3.1. Introduction 14
3.2. Artificial neuron model 15
3.2.1. Activation function 16
3.3. ANN topologies 18
3.3.1. The layer of neurons 18
3.3.2. Linear filter 19
3.3.3. Multilayer Neural Networks (MNN) 20
3.4. Learning and training of ANN 21
3.4.1. Introduction 21
3.4.2. Learning algorithms for feedforward neural networks 22
3.5. Structures of Neuromorphic controllers 32
3.5.1. Introduction 32
3.5.2. Inverse control 34
3.5.3. Adaptive neurocontrol 38
4. ANN based current controllers (CC) 40
4.1. Introduction 40
4.2. Basics of CC in three-phase PWM converters 41
4.2.1. General requirements and performance criteria 41
4.2.2. Nonlinear current controllers 43
4.2.3. Linear current controllers 49
4.3. Off line trained neural comparator 54
4.3.1. Introduction 54
4.3.2. NN controller in three-phase ABC coordinates 54
4.3.3. NN controller in α-β coordinates 63
4.3.4. Results 64
4.3.5. Current controller based on single layer perceptron model 79
4.4. Optimal mode ANN CC 85
4.4.1. Optimal mode CC 85
4.4.2. Three layers NN controller trained by optimal PWM pattern 89

Contents
5. Speed estimation of induction motor 97
5.1. Introduction 97
5.2. Basic techniques of speed estimation 97
5.2.1. Open loop estimators 99
5.2.2. Closed loop estimators – observers 102
5.2.3. Model Reference Adaptive Systems 107
5.2.4. Estimator based on Artificial Intelligence 109
5.3. ANN based speed estimators 113
5.3.1. Speed estimation with on-line ANN 113
6. ANN sensorless field oriented control of IM 120
6.1. Principle of field oriented control (FOC) 120
6.2. Block scheme description 125
6.2.1. General description 125
6.2.2. Description of block scheme implemented in practice 127
6.3. Design of current controller 130
6.3.1. Introduction 130
6.3.2. Decoupled current regulators 130
6.3.3. Controllers design for field oriented IM 131
6.3.4. Internal model control 133
6.4. Design of speed controller 136
6.4.1. Introduction 136
6.4.2. Design methods 137
6.5. Rotor and stator resistance adaptation 139
6.5.1. Introduction 139
6.5.2. Stator resistance adaptation 140
6.5.3. Rotor resistance adaptation 142
7. Simulation and experimental results 145
7.1. Introduction 145
7.2. The choice of the learning rate 145
7.3. Steady state behaviour 147
7.4. Dynamic behaviour 158
8. Conclusions 168
References 155
Appendices 170
A1. Description of the simulation program 170
A2. Laboratory setup 194
A3. Motor parameters 202
A4. Notation 203

1. Introduction
1. INTRODUCTION
The induction motor thanks to its well known advantages as simply construction,
reliability, raggedness and low cost has found very wide industrial applications.
Furthermore, in contrast to the commutator dc motor, it can also be used in aggressive
or volatile environments since there is no problems with spark and corrosion. These
advantages, however, are occupied by control problems when using induction motor
in speed regulated industrial drives. This is due primarily three reasons:
(a) - the induction motor is high order nonlinear dynamic system with internal
coupling,
(b) - some state variables, rotor currents and fluxes, are directly not measurable,
(c) - rotor resistance (due to heating) and magnetising inductance (due to saturation)
varies considerably with a significant impact on the system dynamics.
Therefore in the early 70s besides the simple scalar u/f=const control method, the
more complicated vector approaches have been developed. The field oriented control
(FOC) has been proposed almost in the same time by Hasse and Blaschke. In this
method the motor equations are transformed in the field coordinates system (which
rotates with the rotor flux vector). This transformation corresponds to the decoupled
torque production in separately excited DC motor. The disadvantage of this method is
its complicity. It is necessary to design the flux, torque, and two current controllers,
and of course make signals transformation to the field-oriented coordinate system.
Current Control (CC) technique of the Voltage Source (VS) Pulse Width Modulated
(PWM) inverters is the key problem in the FOC systems. There are many possibilities
to design CC, but only few are based on artificial neural network (ANN) approach.
Among the main advantages of the ANN controllers are fast signal processing,
learning and generalisation abilities, robustness and insensitivity to the load parameter
changes.
Currently, thanks to digital processor based control implementation induction motor
drives have reached the status of modern technology in a wide range applications
from low-cost to high performance systems. Recently, a very intensive research is
concentrated on the elimination of the mechanical speed sensor without distortion the
4

1. Introduction
dynamic performance of the speed control loop. The advantages of such sensorless
speed control drive can be summarized as follows:
- lower cost,
- reduced size of the drive motor,
- elimination of the sensor cable,
- higher reliability.
In recent years a lot of methods have been developed which allows to eliminate speed
sensors, because in many industrial applications it is neither possible nor desirable to
use a mechanical sensors. These methods can be generally divided in two groups:
closed loop sensorless speed control where the motor speed is estimated from other
measurable quantities as stator voltage and currents and open loop speed control with
slip compensation where the motor synchronous speed is controlled and the effect of
load torque changes on motor shaft speed is only compensated. For speed estimation
very often advanced observer technique or neural networks are applied. Slip
compensation methods, in contrast, are usually much simpler but cannot guarantee
good dynamic performances.
Among published papers only one is based on Neural Networks (NN) approach.
Therefore, the author has formulated the following tasks of the thesis:
• Basing on the Artificial Neural Network approach, development of the current
controllers in field oriented controlled PWM voltage source inverter fed
induction motor,
• Basing on the Artificial Neural Network theory, estimate the mechanical speed of
the induction motor, with the measuring of the stator currents and voltages.
In the both groups of problems the new original solutions have been proposed (the
author is the co-author of the patent no. P310512). To carry out this tasks at first the
simulation investigation have been performed, and after that the experimental set-up
has been design and the laboratory experiments have been done. Note that the
sensorless FOC of induction motor, described in this thesis, could be used in the high
performance motor drives of the electrical vehicles (for example hybrid cars) and in
the factories, in which the measurement of the mechanical speed is expensive or even
impossible.
5

1. Introduction
In the author’s opinion the following results of the thesis are his original achievements:
• Development in C language of simulation packet DSIM for the investigation
of PWM voltage source inverter fed induction motors control,
• Development of the two types of the Artificial Neural Network Current
Controllers. The simulation study and experimental verification of these
approaches,
• Development of the new Artificial Neural Network based induction motor
speed estimator. The simulation study and experimental verification of this
approach
• Implementation of the closed loop field oriented control (FOC) with the
neural network based speed estimator (instead of the tachogenerator,
encoder or resolver) on experimental set up with floating point DSP –
TMS320C31.
The thesis consists of eight chapters. Chapter 1 is an introduction. Chapter two is
devoted to the mathematical model of the induction motor. Chapter 3 is the simple
introduction to the Artificial Neural Network theory, which is used, in the further part
of this thesis. Chapter 4 describes the Current Controllers design methods. In the same
chapter two ANN based current controller design approaches are presented and the
simulation and experimental results are shown. In Chapter 5 the speed estimation
methods are described and discussed. The new ANN based speed estimator is shown
and compared with other methods. In Chapter 6 in turn the Field Oriented Control
(FOC) and its implementation is described and discussed in details. Finally in
Chapter 7 the simulation and experimental results in closed loop FOC with the neural
network based speed estimator are presented and studied. Chapter 8 includes
conclusions. Description of the simulation program and the laboratory set-up is given
in Appendix.
6

2. Mathematical description of induction motor
2. MATHEMATICAL DESCRIPTION OF INDUCTION MOTOR
2.1. Introduction
In this chapter the continuous model of induction motor will be presented and, in the
further part of this thesis, used as the controlled plant. This mathematical description
is based on the complex space vector in per unit (p.u.) notation [12]. The
mathematical model in the coordinates, which rotate with angular speed (ω K ), is
presented. Finally some special cases, i.e. α-β and x-y coordinates are considered.
2.2. Basics of induction motor model
2.2.1. Space vectors
The induction motor model will be presented in space vector notation. Therefore, in
this subsection we introduce the short description of this approach.
A three-phase symmetric system can be replaced by one resultant space vector
represented as the complex number.
Let us:
A
B
C
T
k = [k , k , k ]
(2.1)
and the elements of this vector satisfy the condition:
k k + = 0
(2.2)
A + B kC
then a space vector is defined as
2
[ 1k
+ ak + a k ]
2
k = A B C
(2.3)
3
where a and a 2 are calculated using following formula:
7

2. Mathematical description of induction motor
j2π
/ 3 1
a = e = − + j
2
2 j4π
/ 3 1
a = e = − − j
2
3
2
3
2
(2.4)
It is obviously that space vector k is divided into real and imaginary parts:
k = k α + jk β
(2.5)
Using eq. 1.2, eq.1.3 we can obtain
kα
= k A
kB
− k
k = C
β
3
(2.6)
and
k A = kα
1
kB
= − kα
+
2
kC
1
= − kα
−
2
3
kβ
2
3
kβ
2
(2.7)
These equations describe transformations from ABC to αβ and from αβ to ABC
respectively.
8

2. Mathematical description of induction motor
2.2.2. Vector equilibrium equations
The following simplifying assumptions are made when deriving the set of equation
describing induction motor [12]:
1. the motor under consideration is a symmetrical three-phase one;
2. only the basic harmonic is considered, while the higher harmonics of
the spatial field distribution and of the magnetomotive force (MMF)
in the air gap are disregarded;
3. the distributed stator and rotor windings are replaced by a specially
formed so-called concentrated coil;
4. the effects of anisotropy, magnetic saturation, iron losses and eddy
currents are neglected;
5. the coil resistances and reactances are taken to be constant.
Using above assumptions one can obtain the following equation of the motor [12]:
d Ψ
U = + sK
sK Rs
I sK + jΩK
ΨsK
dt
d Ψ′
U ′ = ′ + rK
rK Rr
I rK + j(
ΩK
− pbΩm
) Ψ′ rK
dt
ΨsK
= Ls
I sK + LM
I ′ rK
Ψ′ rK = Lr′
I ′ rK + LM
I sK
dΩm
1 ⎡ m
⎤
=
⎢
− p s *
b LM
Im( I sK I ′ rK ) − M L
dt J
⎥
⎣ 2
⎦
(2.8)
where:
• Ω m denotes the rotor angular speed,
• Ω K denotes the angular speed of reference frame K,
9

2. Mathematical description of induction motor
• Ψ sK denotes the the stator flux space vector in K frame,
• I sK denotes the stator current space vector in K frame,
• U sK denotes the stator voltage space vector in K frame,
• Ψ ’ r denotes the rotor flux space vector in K frame referred to the stator circuit,
• I ’ rK denotes the rotor current space vector in K frame referred to the stator circuit,
• U ’ rK denotes the rotor voltage space vector in K frame referred to the stator circuit,
• M L denotes the external torque on the motor shaft.
Motor parameters:
• R s is stator winding self-resistance,
• R ’ r is rotor resistance referred to the stator circuit,
• L s is stator winding self-inductance,
• L ’ r is rotor winding self-inductance referred to the stator circuit,
• L M is main, magnetizing inductance,
• p b is number of pole pairs,
• m s is number of phase windings,
• J is the moment of inertia.
2.2.3. Vector equilibrium equations in per unit system
Per unit (p.u.) systems are defined in terms of base units which most frequently
correspond to rated motor parameters (U b , I b , Ω mb ).
It is a standard procedure to use capital letters to denote the absolute physical
quantities and to represent the relevant quantities expressed in relative units by small
letters.
Thus, for instance, if
U
u = (2.9)
U b
then U is an absolute physical value (in volts), U b the base quantity (in volts), and u
the dimensionless relative value. Using per unit system equations eq. 2.8 can be
rewritten in the following form
10

2. Mathematical description of induction motor
d
u
sK
sK = rs
isK
+ TN
+ jωKψ
dt
sK
dψ
u
rK
rK = rr
irK
+ TN
+ j(
ωK
−ωm
)
dt
= x
sK s isK
+ xM
irK
= x
rK r irK
+ xM
isK
dωm
1 *
= [ Im( ψ isK
) − mL
]
dt T sK
M
ψ
ψ
ψ
ψ
rK
(2.10)
Note, that:
• time t, T M and T N are expressed in absolute units,
• l = x, the inductances in the flux-current equation are replaced by the reactances
corresponding to them,
• the rotor quantities recalculated to the stator side are referred to the same base
units - for that reason the prime index is omitted.
2.2.4. Orientation of the model
When resolving vector equations, one can adopt an arbitrary coordinate reference
frame. The main applied coordinate systems are chosen as follows:
• stator-fixed system of coordinates (α-β) (ω K = 0),
• rotor-fixed system of coordinates (d-q) (ω K = ω m ),
• synchronous-rotating system of coordinates (x-y);
In the last case the coordinate system is oriented along one of the space vectors in the
motor. This vector could be:
• the space vector for the stator currents
• the space vector for the stator voltages
• the space vector for the rotor currents
• the space vector for the rotor flux linkages
Some of these possibilities will be presented.
11

2. Mathematical description of induction motor
2.2.4.1. Stator oriented model α - β
In this case ω K = 0 and the set of induction motor vector equation may be written as:
d
u
s
s = rs
is
+ TN
dt
dψ
u
r
r = rr
ir
+ TN
− j
dt
= x
s s is
+ xM
ir
= x
r r ir
+ xM
is
dωm
1 *
=
s s
dt TM
ψ
ψ
ψ
ω
m
ψ
[ Im( ψ i ) − m ]
L
r
(2.11)
We can rewrite the above equations in the α-β coordinates as:
u
u
u
u
ψ
ψ
ψ
ψ
sα
sβ
rα
rβ
sα
sβ
rα
rβ
dω
dt
= r i
= r i
m
= x
= x
= x
= x
s sα
s sβ
= r i
= r i
r rα
r rβ
i
s sα
i
s sβ
i
r rα
i
r rβ
1
=
T
M
+ T
+ T
+ T
+ T
N
N
N
N
+ x
+ x
+ x
+ x
dψ
dt
dψ
dt
i
M rα
i
M rβ
i
M sα
i
M sβ
[(
ψ i −ψ
i ) − m ]
sα
sβ
sα
sβ
dt
dψ
dt
dψ
rα
rβ
+ ω ψ
m
−ω
ψ
m
sβ
sα
rβ
rα
L
(2.12)
In the case of a cage rotor machine, we have additionally u r = 0 i.e. u rα = u rβ = 0.
State variables could be chosen as follows:
12

2. Mathematical description of induction motor
13
T
m
s
s
r
r
i
i ]
,
,
,
,
[ ω
ψ
ψ
β
α
β
α
=
x (2.13)
then the above equations may be rewritten in the following manner:
where
r
s
M
x
x
x 2
= 1−
σ (2.15)
L
s
r
s
r
r
M
m
M
s
s
s
r
s
r
M
s
r
r
r
s
r
M
r
m
r
s
M
s
N
s
s
s
r
s
r
M
s
r
r
m
r
s
M
r
r
s
r
M
s
N
s
M
r
r
r
r
r
r
m
r
N
s
M
r
r
r
m
r
r
r
r
N
m
i
i
x
x
dt
d
T
u
x
i
x
x
r
x
r
x
x
x
r
x
x
x
x
dt
di
T
u
x
i
x
x
r
x
r
x
x
x
x
x
x
r
x
dt
di
T
i
x
x
r
x
r
dt
d
T
i
x
x
r
x
r
dt
d
T
−
−
=
+
+
−
+
+
= −
+
+
−
+
=
+
−
=
+
−
= −
)
(
1
1
2
2
2
2
2
2
2
2
α
β
β
α
β
β
β
α
β
α
α
β
α
α
β
β
α
β
α
β
α
α
ψ
ψ
ω
σ
ο
ψ
σ
ψ
ω
σ
σ
ο
ψ
ω
σ
ψ
σ
ψ
ψ
ω
ψ
ψ
ω
ψ
ψ
(2.14)

3. Basics of Artificial Neural Network (ANN)
3. BASICS OF ARTIFICIAL NEURAL NETWORK (ANN)
3.1. Introduction
Recently parallel distributed processing such as Artificial Neural Networks (ANN)
have received wide attentions in processing a complex data in very short time. ANN
models are composed of many linear or nonlinear computational elements (neurons or
nodes) operating in parallel. Parallelism, robustness, and learning ability are among
the main features, which determined wide applications for ANN to control of
industrial processes.
This Chapter is intended to provide a general introduction to neural networks.
Concepts of Artificial Neural Networks (ANN) are introduced, and their attributes are
described. Many types of ANN exist and the configuration that are most applicable to
the context of control problems are overviewed. The special interest from this point of
view has Multilayer Neural Network (MNN) with backpropagation learning
algorithm. Finally some structures of neuromorfic control will be presented.
Artificial Neural Networks have several important characteristics, which are of
interest to control engineers:
• Modeling. Because of their ability to be trained using data records for the
particular system of interest.
• Nonlinear systems. The nonlinear networks have the ability to learn
nonlinear relationship.
• Multivariable systems. Artificial Neural Networks, by their nature, have
many inputs and many outputs and so can be easy applied to multivariable
systems.
• Parallel structure. This feature implies very fast parallel processing, fault
tolerance and robustness.
14

3. Basics of Artificial Neural Network (ANN)
The above features are the main reason for the interest, which is currently being
concentrated in this field.
3.2. Artificial neuron model
The elementary computational elements, which create neural network, have many
inputs and only one output. These elements are inspired by biological neurons systems
and, therefore, are call neurons (or by analogy with directed graphs - nodes).
Inputs Weights Output
x 1
w 1
x 2
w 2 Σ F
y
w 0
w N
x N Bias
Fig. 3.1. Neuron model
The individual inputs x j weighted by elements w j are summed to form the weighted
output signal:
e = ∑
N
w j⋅
x j
(3.1)
j = 0
and
x 0 = 1
(3.2)
15

3. Basics of Artificial Neural Network (ANN)
where elements w j , are called synapse weights, can be modified during the learning
process.
The output of the neuron unit is defined as follows:
y = F(e) (3.3)
Note, that w 0 - is adjustable bias and F – is activation function (also called transfer
function). Thus, the output, y, is obtained by summing the weighted inputs and
passing the results through a nonlinear (or linear) activation function F.
The activation function F map, a weighted sum's e (possibly) infinite domain
to a prespecified range. Although the number of F functions is possibly infinite, six
types are regularly applied in the majority of ANN: linear, step, bipolar, sigmoid,
hyperbolic tangent. With the exception of the linear F function, all of these functions
introduce a nonlinearity in the network by bounding the output within a fixed range.
In the next subsection some examples of commonly used activation functions are
briefly presented.
3.2.1. Activation functions
The linear F function (Fig. 3.2) produces a linearly modulated output from the input e
as described by equation
F(e) = ξ e (3.3)
F (e)
F (e)
1
1
0
e
0
e
-1
-1
-1 0 1
-1 0 1
Fig. 3.2. Linear activation function
16

3. Basics of Artificial Neural Network (ANN)
where e ranges over the real numbers and ξ is a positive scalar. If ξ = 1, it is
equivalent to removing the F function completely. In this case:
y = ∑
N
w j⋅
x j
(3.4)
j = 0
The step F function (Fig. 3.3a) produces only two, typically, a binary value in
response to the sign of the input, emitting +1 if e is positive and 0 if it is not. This
function can be described as:
⎧1
if e ≥ 0
F (e) = ⎨
(3.5)
⎩0
otherwise
One small variation of Eq. 3.5 is the bipolar F function (see Fig. 3.3b)
⎧1
if e ≥ 0
F (e) = ⎨
(3.6)
⎩-1
otherwise
which replaces the 0 output value with a~-1.
F (e)
a) b)
F (e)
1
1
0 0
e
e
-1
-1
-1 0 1 -1 0 1
Fig. 3.3. Step activation function
The sigmoid F function is a continuous, bounded, monotonic, nondecreasing function
that provides a graded, nonlinear response within a prespecified range. The most
common function is the logistic function:
17

3. Basics of Artificial Neural Network (ANN)
1
F (e) =
(3.7)
1+
exp( −βe)
where β > 0 (usually β=1), which provides an output value from 0 to 1.
The alternative to the logistic sigmoid function is the hyperbolic tangent:
F ( e) = tanh( βe)
(3.8)
which ranges from -1 to 1.
3.3. ANN topologies
In the biological brain, a large number of neurons are interconnected to form the
network and perform advanced intelligent activities. Artificial Neural Network is built
by neuron models and in most cases consists of neurons layers interconnected by
weighted connections. The arrangement of the neurons, connections, and patterns into
a neural network is referred to as a topology (or architecture).
3.3.1. The layer of neurons
Neural networks are organized into layers of neurons. Within a layer, neurons are
similar in two respects:
• the connection that feed the layer of neurons are from the same source;
• the neurons in each layer utilize the same type of connections and activation F
function.
A one-layer network with N inputs and M neurons is shown in Fig. 3.4.
18

3. Basics of Artificial Neural Network (ANN)
Inputs Neuron Layer Outputs
x 1
Σ F
x 2
Σ F
x N
w 11
w NM
Σ F
y 1
y 2
y M
Fig. 3.4. One layer network
In this topology, each element of the input vector X is connected to each
neuron input through the weight matrix W. The sum of the appropriate weighted
network inputs W*X is the argument of the activation F function. Finally, the neuron
layer outputs form a column vector Y. Note, that it is common for the number of
inputs to be different from the number of neurons, i.e. N ≠M.
3.3.2. Linear filter
For the linear activation F function, with ξ=1, the output of the neuron layer can be
described by the following matrix equation:
Y = W k X (3.9)
where
⎡w
11 w21
L wN1
⎤
W =
⎢
⎥
k M M M
(3.10)
⎢
⎥
⎢⎣
w1M
w2M
L wNM
⎥⎦
19

3. Basics of Artificial Neural Network (ANN)
is the weight matrix.
Such a simple network can recognize M different class of patterns. The matrix W k
define linear transformation of the input signals X ∈ R N into output signals Y ∈ R M .
This linear transformation can have an arbitrary form (for example Fourier transform).
Therefore, such a network can be viewed as a linear filter.
3.3.3. Multilayer Neural Networks (MNN)
A neural network can have several layers. There are two types of connections applied
in MNN:
• Intralayer connections are connections between neurons in the same layer.
• Interlayer connections are connections between neurons in different layers.
It is possible to build ANN that consist of one, or both, types of connections.
Organization of the MNN is classified largely into two types:
• a feedforward network,
• a feedback (also called recurrent) network.
When the MNN has connections that feed information in only one direction (e.g.,
input to output) without any feedback pathways in the network, it is a feedforward
MNN. But if the network has any feedback paths, where feedback is defined as any
path through the network that would allow the same neurons to be visited twice, then
it is call a feedback MNN.
An example of multilayer feedforward network is shown in Fig. 3.5.
Each layer has a weight matrix W (l) k , a weighted input E (l) , and an output vector Y (l) ,
where l is the layer number. The layers of a multilayer ANN play different roles.
Layers whose output is the network output are called output layers. All other layers
are called hidden layers. In many publications additional layer so called input layer is
introduced. This layer consists of input vector to the whole MNN (in this layer input
vector is equal to output vector).
Note that the output of each layer is the input of the next one.
20

3. Basics of Artificial Neural Network (ANN)
Layer 1 Layer 2 Layer 3
w 11
1
e 1 1
y 1 1
x 2
e 1 e2
2
y 1 2 2
Σ F
2
y
2
Σ F Σ
e 3 2
x 1 Σ F Σ F Σ
e 3 1
e 2 1
y
1
2
F
F
y 1
3
y 2
3
x N
1
w NM
Σ
e 1 M
F
y 1 M
Σ
e M
2
F
y M
2
Σ
e M
3
F
y M
3
Fig. 3.5. Multilayer feedforward ANN.
Feedback ANN has all possible connections between neurons. Some of the weight can
be set to zero to create layers within the feedback network if that is desired. The
feedback network are quite powerful because they are sequential rather than
combinational like the feedforward networks. The output of such networks, because
of the existing feedback, can either oscillate or converge.
Finally we can note, that the Multilayer Linear Neural Network is equivalent to
Neural Network with one layer. So, it is senseless to use linear ANN with multiple
layers.
3.4. Learning and training of ANN
3.4.1. Introduction
One of the most important qualities of ANN is their ability to learn. Learning is
defined as a change of connection weight values that result in the capture of
information that can later be recalled. Several algorithms are available for a learning
process. Generally, the learning methods can be classified into two categories:
supervised and unsupervized learning.
21

3. Basics of Artificial Neural Network (ANN)
Supervized learning is a process that incorporates an external teacher and (or) global
information. The supervized learning algorithms include: error correction learning,
reinforcement learning, stochastic learning, etc.
Unsupervized learning, also referred to as self-organization, is a process that incorporates
no external teacher and relies upon only local information during the entire
learning process. Examples of unsupervized learning include: Hebbian learning,
principal component learning, differential Hebbian learning, min-max learning and
competitive learning.
Most learning techniques utilize off-line learning. When the entire pattern set
is used to condition the connections prior to the use of the network, it is called off-line
learning. For example, the backpropagation training algorithm is used to adjust
connections in multilayer feedforward ANN, but it requires thousands of cycles
through all the pattern pairs until the desired performance of the network is achieved.
Once the network is performing adequately, the weight are stored and the resulting
network is used in recall mode thereafter. Off-line learning systems have the inherent
requirement that all the patterns have to be resident for training.
Not all networks perform off-line learning . Some networks can add new information
"on the fly" nondestructively. If a new pattern needs to be incorporated into the
network's connections, it can be done immediately without any loss of prior stored
information. The advantage of off-line learning networks is that they usually provide
superior solutions in difficult problems such as nonlinear classification, but on-line
learning allows ANN to learn during the system operation.
In this Section only the supervized learning algorithms based on error
correction for feedforward ANN will be described. This is because in control systems
mostly the feedforward ANN are applied.
3.4.2. Learning algorithms for feedforward neural networks
In the 1986 Rumelheart et. al. proposed a learning algorithm with the teacher of the
feedforward ANN to solve this problem by multilayering using a back-propagation
algorithm [149]. The back-propagation is a generalization of the Least Mean Squares
(LMS) algorithm. In this algorithm, an error function is defined and equal to the mean
22

3. Basics of Artificial Neural Network (ANN)
square difference between the desired output and the actual output of the feedforward
ANN. In order to minimize this error function, the backpropagation algorithm uses a
gradient search technique.
3.4.2.1. The Widrow-Hoff (standard delta) learning rule
Learning rule for one linear neuron
Let us consider the simplest case of ANN. It means, that the Neural Network consists
of one linear neuron with N inputs. We will study supervized learning process of this
network. So, it is convenient to introduce so-called teaching sequence. We can define
this sequence as follows:
T
( 1) (1) (2) (2) ( P)
( P)
= {{ X , z },{ X , z }, K ,{ X , z }} (3.11)
( j)
( j)
where each element { X , z }, consists of input vector X in the j-th step of learning
process, and appropriate desired output signal z.
In order to show the learning algorithm, we define the error function as:
Q =
1
2
P
( j)
( j)
2
∑(
z − y )
j=
1
(3.12)
We can rewrite this equation in the following form:
Q =
P
( j)
∑Q
j=
1
(3.13)
where:
23

3. Basics of Artificial Neural Network (ANN)
( j)
Q
1 ( j)
( ) 2
= ( z − y
j )
(3.14)
2
Since Q is a function of W, the minimum of Q can be found by using the gradient
descent method:
wi
= −
∂Q
∂wi
∆ η (3.15)
where η - is proportionality constant called learning rate.
For the j-th step of the learning process we can obtain:
( j+
1) ( j)
wi
− wi
= ∆wi
( j)
∂Q
= −η (3.16)
∂wi
and using the chain rule:
( j)
∂Q
∂wi
( j)
∂Q
=
( j)
∂y
( j)
∂y
∂wi
(3.17)
The first part shows the error changes in the j-th step of the learning process with the
output of the neuron and the second parts how much changing w i changes that output.
From Eq. 3.14 is:
( j)
∂Q
( j)
∂y
( j)
( j)
= −(
z − y )
= −δ
( j)
(3.18)
Since the linear network output is defined as:
N
( j)
( j)
( j)
y = ∑wk
⋅ xk
k = 1
(3.19)
24

3. Basics of Artificial Neural Network (ANN)
than
( j)
∂y
∂w
i
= x
( j)
(3.20)
Substituting Eq. 3.18 and Eq. 3.20 back into Eq. 3.17 one obtains
( j)
∂Q
( j)
( j)
− = δ ⋅ x
(3.21)
∂wi
Thus, the rule for changing weights Eq. 3.16 is given by:
( j)
( j)
( j)
∆wi
= ηδ ⋅ xi
(3.22)
or in vector form:
( j)
( j)
( j)
∆ = ηδ ⋅
(3.23)
W
X
Finally, the algorithm for new values of the weight vector W can be written as:
W
( j+
1) ( j)
( j)
( j)
= + ηδ ⋅
(3.24)
W
X
Learning rule for linear ANN
In the case of the linear ANN with M outputs and N inputs, we can introduce the
learning algorithm by results generalization of the previous paragraph. In this
paragraph the teaching sequence is define as follows:
( 1) (1) (2) (2) ( P)
( P)
T = {{ X , Z },{ X , Z }, K,{
X , Z }} (3.25)
25

3. Basics of Artificial Neural Network (ANN)
( j)
( j)
where each element { X , Z } consists of input vector X in the j-th step of learning
process, and appropriate desired output vector Z.
One can obtain on the analogy of Eq. 6.24 the following learning algorithm:
W
( j+
1) ( j)
(j) ( j)
( j)
T
k
= Wk
+ η ( Z − Y ) ⋅(
X )
(3.26)
One can define error vector:
D
( j)
(j) ( j)
= Z − Y
(3.27)
this vector consists of the following elements:
( j)
( j)
( j)
( j)
T
D = [ δ1
, δ
2
, K,
δ
M
]
(3.28)
where
( j)
( j)
( j)
δ
i
= zi
− yi
(3.29)
is the difference between desired and actual i-th output in the j-th step of learning
process.
Finally substituting Eq. 3.27 to Eq. 3.26, the algorithm for new values of the weight
vector W can be rewritten as:
W
( j+
1) ( j)
(j) ( j)
T
k
= Wk
+ η D ⋅(
X )
(3.30)
where:
• Y (j) - network output vector M × 1 in the j-th step of learning process,
• Z (j) - target vector M × 1 in the j-th step of learning process,
• X (j) - input vector N × 1 in the j-th step of learning process,
26

3. Basics of Artificial Neural Network (ANN)
• D (j) - error vector M × 1 in the j-th step of learning process,
( j 1) ( j)
• W + k
, Wk
- weights matrix M × N in the j+1-th and j-th step of learning
process,
• N - number of neurons,
• M - number of inputs,
• P - number of learning steps,
• η - learning rate.
The algorithm given by Eq. 3.30 is called the Widrow-Hoff learning rule [149]. Also,
because the amount of learning is proportional to the difference D (j) - or delta -
between the target and actual network output, the algorithm is often called the
standard delta rule [149].
The delta rule is the basis for most applied learning algorithms. As shown the standard
delta rule essentially implements gradient descent in a sum-squared error for linear
functions. In this case, without hidden layers, the error surface is shaped like a bowl
with only one minimum, so that the gradient descent is guaranteed to find the best set
of weights with hidden layers, however, it is not so obvious how to compute the
derivatives, and the error surface is not concave upward, so there is the danger of
getting stuck in local minima. Note, that the same algorithm (Eq. 3.32) one can use to
adapt weights in single layer perceptron with nonlinearity described by Eq. 6.6 or
Eq. 6.5.
Acceleration of the learning process
The algorithm described by Eq. 3.30 is a generalization of the Least Mean Squares
(LMS) algorithm using gradient search technique. In this case the learning process is
convergent, but this convergence is very slowly. However, we can have an effect on
the some features of the learning algorithm to improve learning convergence:
• Selection of the initial value of the weight matrix
(1)
W
k . In the most cases, one can
assume that the initial values of this matrix should be selected at random and
27

3. Basics of Artificial Neural Network (ANN)
rather small. Very important condition is to avoid the same values of any pairs of
elements, i.e.
• Selection of the learning rate coefficient η. It is possible to change this value
during the time of the learning process. But in the many applications, it is enough
to assume a typical constant value of η = 0.6.
• Modification of the standard delta rule algorithm. One can improve the learning
process by adding the additional term to Eq. 3.30 proportional to momentum.
Momentum is defined by:
( j)
( j)
( j−1)
M = Wk
− Wk
(3.31)
Thus, the algorithm for new values of the weight vector can be written as:
( j+
1)
k
( j)
k
( j)
T
W = W + η D ⋅(
X ) + µ M
(j)
( j)
(3.32)
The good results of the learning process are obtained with η = 0.9 and µ = 0.6.
3.4.2.2. The generalized delta learning rule - backpropagation
Generalized delta rule has been developed for learning the layered feedforward ANN
with hidden layers [149]. In the first paragraph, we will derive a learning formula for
one nonlinear neuron using the consideration described in the previous section. In the
second paragraph, the actual generalized delta learning rule will be derived.
Learning rule for one nonlinear neuron
In the case of one nonlinear neuron the output in the j-th step can be expressed as:
( j)
( j)
y = F(
e )
(3.33)
28

3. Basics of Artificial Neural Network (ANN)
where
(j)
e
= ∑
N ( j)
( j)
w
i
⋅ x
i
i = 0
(3.34)
and F(.) is activation function.
We can use sigmoidal activation F function, which is continuous, nondecreasing and
differentiable function.
The derivative in Eq. 3.16 is product of two parts:
∂
( j)
Q
∂wi
∂
=
∂
( j)
Q
( j)
e
( j)
e
wi
∂
∂
(3.35)
From Eq. 3.34 we see that the second factor is:
( j)
∂e
∂wi
=
∂
∂
wi
N
∑wk
xk
k =1
= xi
(3.36)
The first part of Eq. 3.35 can be written as:
( j)
( j)
( j)
( j)
∂Q
∂Q
∂y
δ = − = −
(3.37)
( j)
( j)
( j)
∂e
∂y
∂e
By Eq. 3.33 we see that
( j)
∂y
( j)
∂e
=
d
de
F(
e)
(3.38)
is derivative of the activation function. In case of the sigmoid function this derivative
is very easy to calculate:
29

3. Basics of Artificial Neural Network (ANN)
d
de
( j)
( j)
F(
e)
= y (1 − y )
(3.39)
The first factor in Eq. 3.37 we can calculate as:
( j)
∂Q
( j)
∂y
( j)
( j)
= −(
z − y )
(3.40)
and substituting for the two factors in Eq. 3.37 we get:
( j)
( j)
( j)
d
δ = ( z − y ) ⋅ F(
e)
(3.41)
de
Finally Eq. 3.41 and Eq. 3.22 give us the description of the algorithm in the form:
( j+
1) ( j)
( j)
( j)
dF(
e)
( j)
wi
= wi
+ η ( z − y ) ⋅ xi
(3.42)
de
For the sigmoid activation function, we can rewrite Eq. 3.42 using Eq. 3.39 as:
w
( j+
1)
i
= w
( j)
i
+
( j)
( j)
( j)
( j)
( j)
η ( z − y )(1 − y ) y xi
(3.43)
Learning rule for nonlinear multilayer ANN
In the case of the nonlinear ANN with M outputs and N inputs, we can introduce the
learning algorithm by results generalization of the previous paragraph. For the output
layer this generalization is very simple:
( j+
1)( L)
( j)(
L)
( j)
( j)
dF(
e)
( j)(
L)
wim
= wim
+ η ( zm
− ym
) xi
(3.44)
de
30

3. Basics of Artificial Neural Network (ANN)
where L is the output layer number,
the desired and actual output, respectively.
For the hidden layer l we use the chain rule to write:
( j)
( j)
z m , y m are m-th components in the j-th step of
( j)
∂Q
( j)(
l)
∂ym
( j)
( j)(
l)
∂Q
∂e
=
k
∑
=
( j)(
l)
( j)(
l)
k ∂e
∂y
k m
( j)
∂Q
∂ ( j)(
l + 1) ( j)(
l + 1)
∑ ( )( ) ( )( ) ∑wik
y =
j l j l
i
k ∂ek
∂ym
i
( j)
∂Q
( j)(
l + 1) ( j)(
l + 1) ( j)(
l + 1)
∑ w = −
( j)(
l)
mk ∑δ
k wmk
k ∂ek
k
(3.45)
In this case, substituting for the two parts in Eq. 3.37 yields:
( j)(
l)
dF( e)
( j)(
l + 1) ( j)(
l + 1)
δ m = ∑δ
k w
de
mk
(3.46)
k
Using Eq. 3.46, one can obtain the algorithm to adapt weights in the hidden layer l in
the j-th step:
w
( j+
1)( l)
( j)(
l)
( j)(
l)
( j)(
l)
im
= wim
+ ηδ m xim
(3.47)
( j)(
l)
where δ m one can calculate from Eq. 3.46.
Equations Eq. 3.44 and Eq. 3.46, Eq. 3.47 give an recursive algorithm for computing
the weights of the MNN. This algorithm is known as generalized delta rule [149].
Note, that in this case we can use the same improvements like in linear ANN (for
instance learning with momentum).
31

3. Basics of Artificial Neural Network (ANN)
3.4.2.3. The back-propagation training algorithm
The application of the generalized delta rule involves four phases:
(1) - presentation phase: present an input training vector and calculate
each layer's output until the last layer's output is found.
(2) - check phase: calculate the network error vector and the sum squared
error Q (j) for the input vector. Stop if the sum of squared error for all P
training vectors (Eq. 3.12, Eq. 3.13, Eq. 3.14) is less than the specified
value or your specified maximum number of epoch has been reached.
Otherwise continue calculations.
(3) - backpropagation phase: calculate delta vectors for the output layer
using the target vector, then backpropagate the delta vector to
proceeding layers Eq. 3.46.
(4) - learning phase: calculate each layer's new weight matrix, then return
to first phase.
The above given training algorithm is commonly known as error backpropagation
[143, 149].
3.5. Structures of Neuromorphic Controllers
3.5.1. Introduction
The recent efforts in applying neural networks to control of dynamics processes
resulted in the new field of neurocontrol, which can be considered as a nonconventional
branch of adaptive control theory. The attractively of neurocontrol for engineers
can be explained by three following reasons:
32

3. Basics of Artificial Neural Network (ANN)
(1) biological nervous systems are living examples of intelligent adaptive
controllers,
(2) ANN are essentially adaptive systems able to learn how to perform
complex tasks,
(3) neurocontrol techniques are believed to be able to overcome many
difficulties that conventional adaptive techniques suffer when dealing
with nonlinear plants or plants with unknown structure.
Although several ANN architectures have been applied to process control, most of the
actual neurocontrol literature concentrates on multi layer neural networks (MNN).
This is because of the following basic reasons:
• MNN's are essentially feedforward structures in which the information
flows forward, from the inputs to the outputs, through hidden layers. This
characteristic is very convenient for control engineers, used to work with
systems represented by blocks with inputs and outputs clearly defined and
separated,
• MNN's with a minimum of one hidden layer using arbitrary sigmoidal
activation functions are able to perform any nonlinear mapping between
two finite - dimensional spaces to any desired degree of accuracy,
provided there are enough number of hidden neurons. In other words,
MNN's are versatile mappings of arbitrary precision. In control, usually
many of the blocks involved in the control system can be viewed as
mappings and, therefore, can be emulated by MNN's with inputs and
outputs properly defined.
• The basic algorithm for learning in MNN's, the back propagation
algorithm, belongs to the class of gradient methods largely applied in
optimal control, and is, therefore, familiar to control engineers.
33

3. Basics of Artificial Neural Network (ANN)
In this Chapter the main structures of neural controllers (also called neuromorphic
controllers) (NC), i.e., controllers based on an ANN structure, will be described.
3.5.2. Inverse control
The principle of the inverse neurocontroller is shown in Fig. 3.6. The neural network
MNN learn the inverse dynamic of the plant f -1 (u) by using an appropriate training
signal (Fig. 3.6a). When training is performed the ANN's weight are fixed and the
network is used as a feedforward neural controller before the plant (Fig. 3.6b) to
compensate for the plant nonlinearity f(u).
a)
y r
MNN
u
Plant
f(u)
y
TRAINING SIGNAL
b)
y r
NC
f -1 (u)
u
Plant
f(u)
y
Fig. 3.6. Principle of inverse control: a) training phase;
b) feedforward neural controller
The controller's training signal in Fig. 3.6a provides information needed for the NC to
learn the inverse dynamics of the plant in such a way that an error function J of the
plant output error e = y r - y is minimized. Bellow, three controller's training
configurations are briefly presented.
34

3. Basics of Artificial Neural Network (ANN)
3.5.2.1. Direct inverse control (off-line)
The inverse model is built up as shown in Fig. 3.7. and the plant output y for the
known input u is used for input to the MNN to obtain network output u c . The learning
process of MNN is carried out to minimize the overall error e 2 between u and u c .
Therefore, this method is also called general learning architecture [143].
a)
u
Plant
f(u)
y
NC
u c
-
+
e
b)
y r
P
CONTROLLER
u
Plant
f(u)
y
NC
u c
-
+
Fig. 3.7. Direct inverse control architectures:
a) open loop training; b) closed loop training
e
The success of this method depends largely on the ability of the ANN to generalize or
learn to respond correctly to inputs that were not specifically used in the training
phase. In this architecture is not possible to train the system to respond correctly in
regions of interest because it is normally not known which plant inputs correspond to
35

3. Basics of Artificial Neural Network (ANN)
the desired outputs. Some improvement can be achieved by using closed loop training
architecture (Fig. 3.7b) [146].
3.5.2.2. Direct adaptive control (on-line)
To overcome the general training problems, the ANN learns during on-line
feedforward control (Fig. 3.8) [143]. In this method, the NC can be trained in regions
of interest only since the reference value is the input signal for the ANN. The ANN is
trained to find out the plant output that derives the system output y to the reference
value y r . The weights of the ANN are adjusted so that the error between the actual
system output and the reference value is maximal decreased in every iteration step.
y r
NC
u
Plant
f(u)
y
e
+
-
Fig. 3.8. Direct adaptive control
In this method, the dynamic model of the plant can be regarded as an additional layer.
Consequently, it is necessary to use some prior information such as the sensitive
derivatives or the Jacobian of the system in order to apply the back propagation
algorithm. The problem of direct inverse control is that since the ANN controls the
system directly by itself, the controlled system may be unstable at the first stage on
learning. Therefore, it is necessary to prepare the initial value of the weights for the
ANN in the controller, which may be acquired by prior off-line learning as supervized
control, in order to avoid instability.
36

3. Basics of Artificial Neural Network (ANN)
3.5.2.3. Feedback error training
In this method (Fig. 3.9.), the ANN is used as a feedforward controller NC and trained
by using the output of a feedback controller P as error signal.
NC
+
y r
-
e
P
CONTROLLER
+
+
u
Plant
f(u)
y
Fig. 3.9. Feedback error learning configuration.
The problem of their feedback error learning as indirect inverse control is that they
used a priori knowledge as input to the ANN to handle dynamics. There are problems
with such knowledge in that the assumption is that plant dynamics are unknown.
3.5.2.4. Indirect adaptive control
Although in many practical cases the sensitive derivatives or the Jacobian of the
system can be easly estimated or replaced +1 or -1, that is the signum of the
derivative, this is not the general case. In the indirect adaptive control scheme shown
in Fig. 3.10., a ANN based plant emulator NE is used to compute the sensivity of the
error function J with respect to the controller's output. Since NE is a MNN, the
desired sensivity can be easly calculated by using back propagation algorithm.
Furthermore, the configuration in Fig. 3.10. useful when the inverse of the plant is ill
defined, i.e., the function f does not admit a true inverse.
37

3. Basics of Artificial Neural Network (ANN)
+
e c
-
NE
-
e e
y r
NC
u
Plant
f(u)
+
y
Fig. 3.10. Indirect adaptive control
The NE should be off-line trained with a data set sufficiently rich to allow plant
identification, and then both the NC and NE are on-line trained. In a sense, the NE
performs system identification and, therefore, for rapidly changing systems, it is
preferred to update the NE more often than the NC.
3.5.3. Adaptive neurocontrol
In this subsection two configurations of adaptive controllers based on ANN's will be
presented. In Fig. 3.11. the structure of a neural self tuning regulator (STR) is shown.
NI
IDENTIFIER
-
e e
y r
ADAPTIVE
CONTROLLER
u
Plant
f(u)
+
y
Fig. 3.11. Neuro self tuning regulator (STR)
38

3. Basics of Artificial Neural Network (ANN)
The ANN is used to identify system parameters (NI) and tune the conventional
controller. In Fig. 3.12., in turn, a neural model reference adaptive control (MRAC)
system is presented.
NC
+
e c
-
NE
e e
-
y r
NC
u
Plant
f(u)
+
y
Fig. 3.12. Example of neural MRAC system
In this structure both the controller NC and identifier NI use neural networks. The
overall system error e c between model reference y m and system outputs y is applied for
NC tuning, while error e i adjusts the neural network identifier NI.
39

4. ANN based Current Controllers (CC)
4 ANN BASED CURRENT CONTROLLERS (CC)
4.1 Introduction
Current Control (CC) technique of the Voltage Source (VS) Pulse Width Modulated
(PWM) inverters is the key problem in such high performance applications as: AC motor
drives and motion controllers, AC power supplies and active power filters. A review of
current control methods for VS-PWM inverters is presented by Kazmierkowski and
Dzieniakowski [129]. Recently, for current control the neural network (NN) approach has
been applied [111, 110, 115, 117]. Among the main advantages of the NN controllers are
fast signal processing, learning and generalisation abilities, robustness and insensitivity to
the load parameter changes.
The first NN current controller, based on off line trained (by back propagation
algorithm) three layer NN, has been proposed by Harashima et. al. [115] and it has
performance similar to delta modulators[117].
In this chapter the improvements of Harashima NN controller by application of a new
sampling technique and other learning technique is presented. This work shows as
well how the same properties can be achieved using instead of three layer a single
layer perceptron NN with precalculated weights. As results the time consuming
training procedure is eliminated.
In the second part the multilayer NN controller trained off-line by a model PWM pattern
generated using Optimal Current Controller (OC) is investigated. To overcome noise
problem in signal processing instead of EMF voltage, the flux and synchronous frequency
signals are applied as the NN inputs. It is shown that three layers (5-10-10-3 architecture)
feedforward NN controller has the best performance in this class of controllers.
The basic block scheme of the three phase VSI with PWM current control is shown in
Fig. 4.1.
By comparing the command i Ac
(i Bc
, i Cc
) and measured i A
(i B
, i C
) values of the phase
currents, the Current Controller generates the command states S A
, S B
, S C
. for inverter
switching devices.
40

4. ANN based Current Controllers (CC)
U d
i A c
i B c
i C c
ε A
ε B
ε C
PWM
Current
Regulator
S A
S B
S C
Voltage
Sourced
Inverter
3 ph.
Load
i A
i B
i C
Fig. 4.1. Basic block scheme of the VSI PWM current control
4.2 Basics of Current Control (CC) in Three-Phase PWM Voltage
Source (VS) Converters
4.2.1 General Requirements and Performance Criteria
The accuracy of CC can be evaluated with reference to basic requirements, valid in
general, and to specific requirements, typical of some group of application.
General requirements of a CC are:
- no phase and amplitude errors (ideal tracking) in wide output frequency range,
- fast response to provide high dynamic of the system,
- limited or constant switching frequency to guarantee safe operation of converter
semi-conductor power devices,
- good DC-link voltage utilization.
The specific requirements for the most important applications can be summarized as
follows.
- VS PWM inverters:
AC motor control:
wide range of output frequency, variable AC side voltage (motor EMF), high
dynamic, decoupled x-y field oriented control structure, operation in PWM/square
wave transient region
41

4. ANN based Current Controllers (CC)
AC power supply/UPS:
narrow range of output frequency (UPS), reduced harmonic content (output filter),
fault protection.
- VS PWM line rectifiers and active filters:
constant AC side (line power) frequency 50/60Hz nearly constant amplitude and
waveform of AC side voltage, poorly damped AC side network, variable DC link
voltage (power filter).
The evaluation of CC may be done according to performance criteria which
include static and dynamic performance. Table 4.1 presents the static criteria in two
groups:
- those valid also for open loop voltage PWM (see e.g. [1,8,9,16])
- those specific for CC-PWM converters based on current error definition (denoted •).
The following parameters of the CC system dynamic response can be considered:
dead time, settling time, rise time, time of the first maximum and overshoot factor.
The foregoing features result both from the PWM process and from the response of
the control loop. For example, for dead time the major contributions arise from signal
processing (conversion and calculation times), and may be appreciable especially if
the control is of the digital type.
Table 4.1
Performance Criteria
CRITERIA DEFINITION
RMS = [1/T∫(ε α
2 + εβ 2 )dt] 1/2
J = 1/T∫[(ε α
2 + εβ 2 )] 1/2 dt
N = Σ imp⎪t ∈ 〈0,T〉
I hrms = [1/T∫(i (t) - i 1(t) ) 2 dt] 1/2
COMMENTS
the r.m.s. vector error
the vector error integral
number of switchings
(also for nonperiodical)
the r.m.s harmonic current
d = I hrms / I hrms six-step the distortion factor
d = [Σ h 2 i (k⋅f1 )] 1/2 k≠1 synchronised PWM case
d = [∫ h d
2 (f) df] 1/2 f≠f 1
nonsynchronised PWM case
h i (k⋅f 1 )- discrete current spectra
h d (f) - density current spectra
42

4. ANN based Current Controllers (CC)
On the other hand, rise time is mainly affected by the AC side inductances of the
converter. The optimization of the dynamic response usually requires a compromise,
which depends on the specific needs. This may also influence the choice of the CC
technique according to the application considered.
In general, the compromise is easier as the switching frequency increases. Thus,
with the speed improvement of today's switching components (e.g. IGBT's), the
peculiar advantages of different methods lose importance and even the simplest one
may be adequate. Nevertheless, for some applications with specific needs, like active
filters, which require very fast response, or high power inverters where the
commutations must be minimized, the most suitable CC technique must be selected.
4.2.2 Nonlinear Current Controllers
A. Hard Switched Converters
1) Hysteresis Current Controllers
Hysteresis control schemes are based on a nonlinear feedback loop with two-level
hysteresis comparators (Fig. 4.2a) [61]. The switching signals S A ,S B ,S C are produced
directly when the error exceeds an assigned tolerance band h (Fig. 4.2b).
U DC
i Ac
i Bc +
i Cc
+ -
+ -
-
S A
S B
S C
i A
i B
i C
Three-phase
Load
β
B
state 1
Hysteresis
band
state 0
A
500
N
250
(a)
a
b
c
i S
C
-h
+h
α
0 0 ms
40
(b)
(c)
Fig. 4.2. Two-level hysteresis controller: block scheme (a), switching trajectory (b) Number of inverter
switchings N (c) for: a) three two-level hysteresis comparators, b) three-level comparatos and lookup table
working in stationary and c) rotating coordinates
43

4. ANN based Current Controllers (CC)
Variable switching frequency controllers
Among the main advantages of hysteresis CC are: simplicity, outstanding
robustness, lack of tracking errors, independence of load parameter changes, and
extremely good dynamics limited only by switching speed and load time constant.
However, this class of schemes, also known as free-running hysteresis controllers
[16], has the following disadvantages:
- the converter switching frequency depends largely on the load parameters and varies
with the AC voltage,
- the operation is somewhat rough due to the inherent randomness caused by the
limit cycle; therefore, protection of the converter is difficult [56].
It is characteristic of the hysteresis CC that the instantaneous current is kept exact in a
tolerance band except for systems without neutral leaders where the instantaneous
error can reach double the value of the hysteresis band [3,54]. This is due to the
interaction in the system with three independent controllers. The change of
comparator state in one-phase influences the voltage applied to the load in two other
phases (coupling). However, if all three current errors are considered as space vectors
[60], the interaction effect can be compensated, and many variants of controllers
known as space vector based, can be created [41,48,50,58, 63,68]. Moreover, if threelevel
comparators with a look-up table are used, a considerable decrease in the
inverter switching frequency can be achieved [37,48,50,58,63]. This is possible
thanks to appropriate selection of zero voltage vectors [48] (Fig.4.2c).
In the synchronous rotating d-q coordinates, the error field is rectangular and the controller
offers the opportunity of independent harmonic selection by choosing different
hysteresis values for the d and q components [49,62]. This can be used for torque
ripple minimisation in vector controlled AC motor drives (the hysteresis band for the
torque current component is set narrower than that for flux current component).
Constant average switching frequency controllers
A number of proposals have been put forward to overcome variable switching
frequency. The tolerance band amplitude can be varied, according to the AC side
voltage [39,43,47,53-55,57,59,69,103], or by means of a PLL control (Fig.8).
An approach which eliminates the interference, and its consequences, is that of
decoupling error signals by subtracting an interference signal derived from the mean
inverter voltage u N (Fig.4.3) [54]. Similar results are obtained in the case of
44

4. ANN based Current Controllers (CC)
"discontinuous switching" operation, where decoupling is more easily obtained
without estimating load impedance [55]. Once decoupled, regular operation is
obtained and phase commutations may (but need not) be easily synchronized to a
clock.
to other
phases
i c
i
δ′′
δ′ ′
+ δ -
δ′
-
+
Load
Impedance
Simulator
-1
R + pL
Hysteresis
control
β
LP
Filter
S
S
+
+
+
+
+
Upper
PD
Lower
PD
from other
phases
r
r
Driver
Switching
frequency
refrence
Fig. 4.3. Decoupled, constant average switching frequency hysteresis controller [54]
Although the constant switching frequency scheme is more complex and the main
advantage of the basic hysteresis control - namely the simplicity - is lost, these
solutions guarantee very fast response together with limited tracking error. Thus,
constant frequency hysteresis controls are well suited for high-performance, high
speed applications.
2) Controllers with On Line Optimization
This class of controllers performs a real time optimization algorithm and requires
complex on-line calculations, which usually can be implemented only on
microprocessors.
Minimum switching frequency predictive algorithm
The concept of this algorithm [92] is based on space vector analysis of hysteresis
controllers. The boundary delimiting the current error area in the case of independent
controllers with equal tolerance band +h in each of three phases makes a regular
symmetrical hexagon (Fig. 4.2b).
Suppose only one hysteresis controller is used - the one acting on the current error
vector. In such a case, the boundary of the error area (also called the switching or
error curve) might have any form (Fig. 4.4b). The location of the error curve is
determined by the current command vector i sc . When the current vector i s reaches a
45

4. ANN based Current Controllers (CC)
point on the error curve, seven different trajectories of the current are predicted, one
for each of seven possible (six active and zero) inverter output voltage vectors.
Finally, based on the optimisation procedure, the voltage vector which minimises the
mean inverter switching frequency is selected (Fig. 4.4c). For fast transient states the
strategy which minimises the response time is applied.
U DC
i sc
T
+
- -
i s
e
Calculation of
voltage
command
vector
u sc
PWM
modulator
Load
model
(a)
Three-phase
Load
q
ω s
i s
(t,u k
)
Error
area
Actual
trajectory
i s
(t 0
,t k
)
i sc
i s
(t 0
)
Ψ r
d
(b)
i sc
+
Sampling Error
time area
T
Prediction of
the current
- vector
i s trajectory
e
PWM
modulator
Load
model
U DC
Three-phase
Load
(c)
Fig 4.4. Predictive current controllers: Linear constant switching frequency controller (a),
an example of error area (b), Minimum switching frequency controller (c)
46

4. ANN based Current Controllers (CC)
Control with field orientation
The minimum frequency predictive CC can be implemented in any rotating or stationary
coordinates. Like the three level hysteresis controller working in d-q field oriented
coordinates [49], a further switching frequency reduction can be achieved by the
selection of a rectangular error curve with higher length along rotor flux direction [96].
In practice, the time needed for the prediction and optimisation procedures limits the
achieved switching frequency. Therefore, in more recently developed algorithms, a reduced
set of voltage vectors consisting of the two active vectors adjacent to the EMF
vector and the zero voltage vector are considered for optimisation without loss of
quality [8].
Trajectory tracking control
This approach, proposed in [89,90], combines an off-line optimized PWM pattern for
steady state operation with an on-line optimization to compensate for the dynamic
tracking errors of converter currents. Such a strategy achieves very good stationary
and dynamic behaviour even for low switching frequencies.
B) Soft Switched Resonant DC Link (RDCL) Converters
In soft switched RDCL three-phase converters with Zero Voltage Switching (ZVS),
the commutation process is restricted to the discrete time instants T when the DC link
voltage pulses are zero (Fig.2b). Therefore, special techniques called Delta
Modulation (DM) or Pulse Density Modulation (PDM) are used [70-82].
1) Delta Modulation (DM)
The basic scheme, the Delta Modulation-Current Controller (DM-CC) [74,82], is
shown in Fig. 4.5a. It looks quite similar to that of a hysteresis CC (Fig. 4.2a), but the
operating principle is quite different. In fact, only the error sign is detected by the comparators,
whose outputs are sampled at a fixed rate so that the inverter status is kept
constant during each sampling interval. Thus, no PWM is performed; only basic voltage
vectors can be generated by the converter for a fixed time. This mode of operation gives
a discretization of the inverter output voltage, unlike the continuous variation of output
voltages which is a particular feature of PWM. One effect of the discretization is that,
when synthesizing periodic waveforms, a non-negligible amount of sub-harmonics is
generated [74,76,77]. Thus, to obtain comparable results, a DM should switch at a
frequency about seven times higher than a PWM modulator [76]. However, DM is very
simple and insensitive to the load parameters. When applied to three-phase inverters
with an insulated-neutral load, the mutual phase interference and the increased degree
47

4. ANN based Current Controllers (CC)
of freedom in the choice of voltage vector must be taken into account. Therefore,
instead of performing independent DM in each phase control, output vectors are chosen
depending not only on the error vector, but also on the previous status, so that the zero
vector states become possible [73]. Due to the S&H block applied after the ideal
comparator, the switching frequency is limited to the sampling frequency f s . The
amplitude of the current harmonics is not constant but is determined by the load
parameters, DC-link voltage, AC side voltage and sampling frequency.
S H A
S H B
S H C
U D C
i A c
+ -
i B c
i C c
+
+ -
-
S & H
i A
S A
S B
S C
i B
i C
(a)
T h ree-p h ase
L o ad
SH A
Conventional
sampling
SH A
Shifted
sampling
SH B
SH B
SH C
SH C
(b)
(c)
Fig. 4.5. Delta modulation current controller: basic scheme (a), sampling techniques (b)
quality factors (c)
48

4. ANN based Current Controllers (CC)
If the sampling signal in the three-phase system is shifted 120° in each S&H block
(Fig.4.5b), only one of the inverter legs will change its state during the sample period
1/f s . This guarantees only adjacent and zero voltage vector selection, and
consequently a better quality of current waveform (lower RMS, J) at this same
sampling frequency f s (Fig.4.5c) [71]. It is noted that the DM-CC can also be applied
in the space vector based controllers working in either stationary or rotating
coordinates [75,79,81]. The main advantages of DM-CC are extremely simple and
tuning-free hardware implementation, and good dynamics.
2) Optimal discrete modulation algorithm
For the RDCL converters an optimal algorithm selects the voltage vector which
minimizes the RMS current error for each resonant pulse [80,93,106].
U s
Synch.
RDCL
i sc
+
- -
i s
T
e
Calculation
of voltage
referen
vector
Voltage
vector
Load
model
Three-phase
Load
Fig. 4.6. Optimal (mode) discrete modulation controller for RDCL
As shown in [106] this is equivalent to selecting the nearest available voltage vector
commands u sc (T). So, instead of the PWM algorithm (Fig.4.4a) only the voltage
vector selector is required (Fig.4.6). However, errors and subharmonics typical of the
discrete modulation are obtained.
4.2.3 Linear Current Controllers
The linear controllers operate with conventional voltage type PWM modulators [21-
36]. In contrast to the nonlinear controllers (see Section 4.2.2), linear controller
schemes have clearly separated current error compensation and voltage modulation
parts. This concept allows us to exploit the advantages of open loop modulators
(sinusoidal PWM, space vector modulator, optimal PWM) which are: constant
49

4. ANN based Current Controllers (CC)
switching frequency, well-defined harmonic spectrum, optimum switch pattern and
DC link utilisation. Also, full independent design of the overall control structure as
well as open loop testing of the inverter and load can be easily performed. In the
linear group, the following controllers are described: PI stationary and synchronous,
state feedback, predictive with constant switching frequency.
A. Stationary controller PI
The Stationary Controller, also called the Ramp Comparison Current Controller,
uses three PI error compensators to produce the voltage commands u Ac ,u Bc , u Cc for a
three-phase sinusoidal PWM (Fig.4.7) [5].
i Ac +
i Bc + -
i Cc + -
-
Carrier
u Ac
u Bc
u Cc
S A
S B
S C
U DC
i A
i B
i C
Three-phase
Load
Fig. 4.7. Linear current controller: stationary PI
In keeping with the principle of sinusoidal PWM, comparison with the triangular
carrier signal generates control signals S A
,S B
, S C
for the inverter switches. Although
this controller is directly derived from the original triangular suboscillation PWM
[19], the behaviour is quite different, because the output current ripple is fed back and
influences the switching times. The integral part of the PI compensator minimizes
errors at low frequency, while proportional gain and zero placement are related to the
amount of ripple. The maximum slope of the command voltage u Ac (u Bc , u Cc ) should
never exceed the triangle slope. Additional problems may arise from multiple crossing
of triangular boundaries. As a consequence, the controller performance is satisfactory
only if the significant harmonics of current commands and the load EMF are limited
at a frequency well below the carrier (less than 1/9 [4]). The main disadvantage of this
technique is an inherent tracking (amplitude and phase) error. To achieve
50

4. ANN based Current Controllers (CC)
compensation, use of additional PLL circuits [24] or feedforward correction [29, 38]
is also made.
B. Synchronous Vector Controller (PI)
In many industrial applications an ideally impressed current is required, because
even small phase or amplitude errors causes incorrect system operation (e.g. vector
controlled AC motors). In such cases the control schemes based on space vector
approach are applied. Fig. 4.8a illustrates the Synchronous Controller, which uses two
PI compensators of current vector components defined in rotating synchronous
coordinates d-q [5,12,14,31,32,35]. Thanks to the coordinate transformations, i sd and
i sq are dc-components, and PI compensators reduce the errors of the fundamental
component to zero.
i sdc +
+
-
Current
regulator
PI
-
PI
Coordinate
transformation
dq
αβ
αβ
ABC
sin γ s
i sqc
i sq
(a)
PWM
modulator
U DC
i sd
dq
αβ
cos γ s
αβ
ABC
i A
iB
i C
Three-phase
Load
i α
i αc + -
ω c
K1
K2
i βc
+ + u βc
+ K2
- + + i α
i K1 β
i β
+
+
+
+ u αc
αβ
(b)
ABC
αβ
PWM
modulator
ABC
i A
iB
i C
U DC
Three-phase
Load
Fig. 4.8. Synchronous PI current controllers: (a) working in rotating coordinates with
DC components, (b) working in stationary coordinates with AC components
51

4. ANN based Current Controllers (CC)
Based on work [34] (where it has been demonstrated that is possible to perform
current vector control in an arbitrary coordinates), a synchronous controller working
in the stationary coordinates α-β with ac components has been presented [33]. As
shown in Fig.4.8b by the dashed line, the inner loop of the control system (consisting
of two integrators and multipliers) is a variable frequency generator, which always
produces reference voltages uαc , u βc for the PWM modulator, even when in the
steady state the current error signals are zero.
In general, thanks to the use of PWM modulators, the linear controllers make a well
defined harmonic spectrum available, but their dynamic properties are inferior to
those of bang-bang controllers.
C. State Feedback Controller
The conventional PI compensators in the current error compensation part can be
replaced by a state feedback controller working in stationary [29] or synchronous
rotating coordinates [13,25,27,28,30].
Feedforward
K f
K d
Disturbance
U DC
i sc
+
-
K 2
u sc
PWM
modulator
Integral part
K 1
State
feedback
i s
Three-phase
Load
Fig. 4.9. State feedback Current controller
The controller of Fig. 4.9 works in synchronous rotating coordinates d-q and is synthesised
on the basis of linear multivariable state feedback theory. A feedback gain
matrix K=[K 1 ,K 2 ] is derived by utilising the pole assignment technique to guarantee
sufficient damping. While with integral part (K 2 ) the static error can be reduced to
zero, the transient error may be unacceptably large. Therefore, feedforward signals for
the reference (K f ) and disturbance (K d ) inputs are added to the feedback control law.
52

4. ANN based Current Controllers (CC)
Because the control algorithm guarantees the dynamically correct compensation for
the EMF voltage, the performances of the state feedback controller are superior to
conventional PI controllers [27,28].
D. Predictive and Dead Beat Controllers
This technique predicts at the beginning of each sampling (modulation) period the
current error vector on the basis of the actual error and of the AC side (load)
parameters R,L,E. The voltage vector to be generated by PWM during the next
modulation period is thus determinated so as to minimize the forecast error
[60,102,105,107-109].
Hybrid CC combining predictive and hystersis techniques have also been proposed
[99].
1) Constant switching frequency predictive algorithm
In this case the predictive algorithm calculates the voltage vector commands u sc (T)
once every sample period T. This will force the current vector according to its
command i sc (Fig. 4.4c). The inverter voltage u s (T) and EMF voltage e(T) of the load
is assumed to be constant over the sample period T. The calculated voltage vector
u sc (T) is then implemented in the PWM modulator algorithm, e.g. space vector
[60,86,100,102] or sinusoidal modulator [107,108]. Note that while the current ripple
is variable, the inverter switching frequency is fixed (1/T). The disadvantage of this
algorithm is that it does not guarantee the inverter peak current limit.
2) Dead Beat Controllers
When the choice of the voltage vector is made in order to null the error at the end of
the sample period, the predictive controller is often called a dead beat controller
[85,94,95,97]. Among the additional information given to the controller, nonavailable
state variables (e.g. flux, speed) can be included. Their determination can require the
use of observers or other control blocks, which often may be shared with the control
of the entire scheme, as in case of AC drives [83,97].
53

4. ANN based Current Controllers
4.3. Off-line trained neural comparator
4.3.1. Introduction
In this section the application of off-line trained ANN working as a comparator in
current control loop of the PWM inverter will be presented. This idea has been
published by Harashima et al [115]. In this section this idea will be developed and
extended. In the first part, the configuration presented is the same as in [115] and a
block scheme of this system is shown. In the second part, in contrast to the previous
approach, we will introduce controller working in α-β coordinates. Finally simulation
results will be presented, and comparative study with delta modulator and hysteresis
comparators will be carried out. The new solutions based on the perceptron will be
presented as well, and will be shown, that such a simple NN is enough to implement
the Delta Regulator.
4.3.2. NN controller in three phase ABC coordinates
4.3.2.1. Current control scheme
Harashima et. al. [115] have proposed NN regulator (Fig. 4.10b) which should have
similar input-output relation to that of the hysteresis comparator (Fig. 4.10a).
The three layer (3-5-3 architecture) feedforward NN has been trained according to the
rules given in the Table 4.2 using back propagation algorithm [149].
After learning process, when the errors between the desired output and the actual NN
output were less than 1%, the NN has been applied as current regulator. However, for
the three phase symmetrical load (without zero leader) the sum of the instantaneous
current errors is always zero:
ε A
+ ε B
+ ε C
= 0
54

4. ANN based Current Controllers
a)
ε A
K
S A
ε B
K
S B
ε C
K
S C
SH
b)
ε A
K
S A
ε B
K
S B
ε C
K
S C
SH
c)
ε A
K
S&H
S A
ε B
K
S&H
S B
ε C
K
S&H
S C
SH
Fig. 4.10. Current regulators for three phase PWM inverters:
(a) three hysteresis comparators, (b) three layer feedforward NN regulator [6],
(c) Delta modulation Regulator (DR)
55

4. ANN based Current Controllers
Table 4.2
Learning table for three input ANN
INPUT OUTPUT VECTOR
ε A
ε B
ε C
V(S A
,S B
,S C
)
1 δ δ δ V 7
(1,1,1) *
2 -δ δ δ V 4
(0,1,1)
3 δ -δ δ V 6
(1,0,1)
4 δ δ -δ V 2
(1,1,0)
5 δ -δ -δ V 1
(1,0,0)
6 -δ δ -δ V 3
(0,1,0)
7 -δ -δ δ V 5
(0,0,1)
8 -δ -δ -δ V 0
(0,0,0) *
Therefore, the current errors have never the same signs and NN regulator trained
according to the rules given in Table 4.2 cannot select inverter zero vectors V 0
(000)
and V 7
(111).
As a result, the NN regulator operates rather more similar to Delta Regulator (DR)
than to hysteresis comparator (see oscilogram presented in Fig. 4.11)
4.3.2.2. Learning rules
The performance of the NN regulator depends strong on the applied learning method.
In the previous Sections we discussed the NN regulator trained according to the rules
given in Table 4.2. This rules guarantee that NN learn "static" type of the input-output
relation and parameter δ determinate the accuracy around error zero crossing point.
However, other method can be applied in which a "PWM time pattern" generated by
model system (i.e. hysteresis or Delta Regulator) is used for NN learning . In this case
NN can be trained with different Number of Data Points (NDP). In Table II the result
of the comparison of two learning rules for the same Number of learning steps (NLS)
is presented.
56

4. ANN based Current Controllers
Hysteresis Regulator (a)
NN Regulator (b)
Fig. 4.11 Simulated waveforms for current regulators (δ= 0.05)
I - i α
, i β
, II - u β
, III - u α
= f(u β
) , IV -voltage vectors
57

4. ANN based Current Controllers
Table 4.3
Comparison of the learning rules
learning rules
Table 4.2
learning rules
PWM pattern
δ 0.001 0.01 0.1 ⎯ ⎯
NDP ⎯ ⎯ ⎯ 150 450
PSE 87% 87% 72% 94% 92%
NDP - number of data points; NLS - number of learning steps (NLS = 100000); PSE
- pattern selection efficiency factor.
The Number of Learning Steps (NLS) is assumed constant = hundred thousand. It can
be seen that Pattern Selection Efficiency factor
Number of correct pattern selection
PSE =
,
Total number of pattern selection
which shows how often the NN generates the "correct voltage vector", is better for
NN trained according to the rules given by "PWM time pattern" than by the rules
given in Table 4.2. However, the learning method according to rules given in
Table 4.2 is independent of system parameters and, therefore, is much simpler for
implementation.
4.3.2.3. Improved Neural Network Current Regulator
The discussion and results presented in the previous Section show that the NN
regulator proposed by Harashima has performance similar to that of Delta Regulator
(Fig. 4.10b). From the other side it is known that Delta Regulator never selects the
zero voltage vectors. This leads to poor quality of the output current generation and
creates ±1 transition of the DC voltage. These transitions (corresponds to the
switching between not adjacent vectors i.e. V 1
→V 3
, etc.) cause voltage stress on the
inverter devices, and, instantaneous reversal in DC link current. Also, as a result of
58

4. ANN based Current Controllers
not going to zero vector the Pulse Polarity Consistency Rules (PPCR) is violated. To
eliminate these disadvantages and force the NN regulator to select zero vectors and
only adjacent active vectors a modified sampling technique is proposed (Fig. 4.12.).
a)
ε A
K
S&H
S A
ε B
K
S&H
S B
ε C
K
S&H
S C
b)
SH A SH B
SH
C
Fig. 4.12. Improved NN regulator : a) block scheme, b) modified sampling technique
When the sign of the NN outputs signals are sampled not at the same instant but with
a phase shift (Fig. 4.12b) i.e.2π/3, the regulator output signals S A
,S B
,S C
can have the
same values. The inverter under such control operates as shown in Table 4.4. and
illustrates in Fig. 4.14.
59

4. ANN based Current Controllers
Table 4.4
Voltage Vector Selection
For Improved NN Regulator
, , ,
, ,
,
,
,
,
Fig. 4.13. Operation of the improved NN regulator from
Note that in contrast to conventional sampling case (Fig. 4.11b), the improved NN
regulator selects systematically the zero voltage vectors and always chooses adjacent
active vectors (see voltage vector time sequence and switching trajectory in α-β
coordinates Fig. 4.14b).
60

4. ANN based Current Controllers
(a) Delta Regulator
(b) Improved NN Regulator
Fig. 4.14. Simulated waveforms for current regulators
I - i α
, i β
, II - u β
, III - u α
= f(u β
), IV - voltage vectors
61

4. ANN based Current Controllers
The voltage vector state can be changed in the proposed method three times during
the sampling period, whereas in conventional approach only once. It means
increasing of the internal switching frequency, but the total number of switching in
period (and the mean switching frequency) does not change. Therefore, the harmonic
performance of this regulator is superior to the conventional NN since the zero vector
is being used to avoid ±1 transitions.
This regulator, however, cannot guarantee conformance to the PPCR because the
precise point in time where the line to line voltage fundamental crosses zero cannot
be estimated without the knowledge of the counter EMF.
4.3.2.4. Comparison with three hysteresis controllers
As has been suggested in [115] the input-output relation of three teaching signal is
similar to that of the hysteresis comparator with hysteresis width of δ. Note, that
introduction of such a similarity is false. The reasons of this conclusion is as follows:
• The feedforward ANN presented in this Section cannot implements
characteristic with hysteresis, because the system presented is without
memory;
• If the system is with symmetrical load, it does not choose zero vectors (i.e.
vector number 0 and 7), in spite of this, that we teach system such states.
The reason is, that it is not possible to obtain all values of error positive or
negative, because the sum of these errors has to be zero. So, this situation
is different as compared to hysteresis comparators;
• δ in Table 4.2 has no correlation with width of the hysteresis;
• The system presented is similar to delta modulator
In the next subsection ANN controller in α-β coordinates is introduced. The
considerations described in this subsection are explained and developed.
62

4. ANN based Current Controllers
4.3.3. NN controller in α−β coordinates
4.3.3.1. Current control scheme
The block diagram of an off-line trained ANN based current control has two inputs
and three outputs. This scheme is similar to the scheme presented in Fig. 4.10b
The differences between reference and actual currents for α (i αref -i α ) and β (i βref -i β )
components are delivered to the blocks with gain factor K. The output signals of the
K-blocks are inputs to the ANN. So, the inputs to the ANN are amplified current
errors in α−β coordinates. The ANN output signals, in turn, after digitization in
comparator blocks generates the inverter control signals S A , S B , S C .
4.3.3.2. Off-line training
The three-layer feedforward ANN with sigmoidal nonlinearities is trained by using
back propagation algorithm according to the rules given in Table 4.5.
Table 4.5
Learning table for two inputs ANN
INPUT OUTPUT VECTOR
ε α ε β V(S A
,S B
,S C
)
1 1
− δ 3 V 5
(0,0,1) *
− δ
2 2
2 -δ 0 V 4
(0,1,1)
3
4
1
− δ 3 V 3
(0,1,0)
δ
2 2
1
δ
2
−
3
δ
2
V 6
(1,0,1)
5 δ 0 V 1
(1,0,0)
6
1
δ
2
3 δ
V (1,1,0)
2
2
63

4. ANN based Current Controllers
As training signals for the ANN the random generated inputs chosen from the Table
4.6 were applied.
Note that the same results can be obtained in a system described in previous
subsection after recalculating in α-β coordinates. Therefore, in fact, in this both cases,
the systems are approximations of delta modulator scheme.
4.3.4. Results
4.3.4.1. Comparison ANN with classical delta modulator and three hysteresis
controllers
The trained ANN is used in the PWM inverter current control loop. Furthermore, the
systems presented in Fig 4.10a and Fig 4.10c are used for comparison with ANN
controllers. The simulated oscillograms of actual currents, phase voltages errors and
quality indexes in two neural network systems and two delta modulators and with
hysteresis controller are presented in Fig. 4.15-Fig. 4.27 respectively
4.3.4.2. Quality indexes in ANN, classical delta modulator and three hysteresis
controllers
To compare two ANN controllers and delta modulator and hysteresis systems a
different quality factors are considered (see Table 4.1):
• Nrs − the number of switching in a period;
• the integral vector error J.
•
In Table 4.6. quality factors in two ANN, delta modulation and hysteresis controllers
systems are presented. It can be seen, that there are no significant differences between
results obtained using ANN algorithms and Delta Regulator. Otherwise the hysteresis
system is different compared to three remaining ones.
64

4. ANN based Current Controllers
Table 4.6
Frequency
Regulator 5 Hz 25 Hz 50 Hz
J NRS J NRS J NRS
ANN regulator 0.0737 4522 0.0753 886 0.0739 425
ANN modified 0.0579 4472 0.0582 883 0.0593 424
Delta Regulator 0.0652 4518 0.0658 890 0.0667 431
DR modified. 0.0538 4513 0.0550 889 0.0554 427
Hysteresis Regulator 0.0667 2125 0.0660 430 0.0646 197
65

4. ANN based Current Controllers
Fig. 4.15. Behaviour of Neural Network current regulator for f = 50 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
66

4. ANN based Current Controllers
Fig. 4.16. Behaviour of Delta current regulator for f = 50 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
67

4. ANN based Current Controllers
Fig. 4.17. Behaviour of hysteresis current regulator for f = 50 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
68

4. ANN based Current Controllers
Fig. 4.18. Behaviour of modified Neural Network current regulator for f = 50 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
69

4. ANN based Current Controllers
Fig. 4.19. Behaviour of modified Delta current regulator for f = 50 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
70

4. ANN based Current Controllers
Fig. 4.20. Behaviour of Neural Network current regulator f = 25 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
71

4. ANN based Current Controllers
Fig. 4.21. Behaviour of Delta current regulator for f = 25 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
72

4. ANN based Current Controllers
Fig. 4.22. Behaviour of hysteresis current regulator for f = 25 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
73

4. ANN based Current Controllers
Fig. 4.23. Behaviour of modified Neural Network current regulator for f = 25 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
74

4. ANN based Current Controllers
Fig. 4.24. Behaviour of modified Delta current regulator for f = 25 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
75

4. ANN based Current Controllers
Fig. 4.25. Behaviour of Neural Network current regulator f = 5 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
76

4. ANN based Current Controllers
Fig. 4.26. Behaviour of Delta current regulator for f = 5 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
77

4. ANN based Current Controllers
Fig. 4.27. Behaviour of hysteresis current regulator for f = 5 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) number of voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
78

4. ANN based Current Controllers
4.3.5. Current Controller based on single layer perceptron model
4.3.5.1. Block scheme
The configuration of the proposed NN discrete current controller is shown in
Fig. 4.28a. In this very simple case the three inputs-three outputs, single layer NN
with hard nonlinearity activation functions (ideal comparators) corresponds to the
architecture known as perceptron [145].
When compare with Delta modulation discrete controller (Fig. 4.28b), the proposed
NN controller include additionally to w A , w B , w C weighted phase error connections,
only w AB , w AC ,..., w CB weighted interphase connections. These typical for NN
interphase connections, however, have decided influence on the controller operation
and robustness.
4.3.5.2. Selection of NN weights
On the basis of the Fig. 4.28a the following equation describing NN inputs - outputs
relations can be obtain:
e A = w A ⋅ε A + w BA ⋅ε B + w CA ⋅ε C ,
e B = w AB ⋅ε A + w B ⋅ε B + w CB ⋅ε C ,
e C = w AC ⋅ε A + w BC ⋅ε B + w C ⋅ε C ,
(4.1a)
(4.1b)
(4.1c)
where:
ε A , ε B , ε C
- instantaneous line current errors in phases A, B, C, respectively
w A , w B , w C
- weight factors in phases A, B, C respectively
w AB , w AC ,..., w BC - weight factors in interphase connections.
79

4. ANN based Current Controllers
a)
ε
w
w
e
A A A
AB
S&H
S
A
ε
B
e
B
S&H
S B
ε
C
w
C
e
C
S&H
S
C
SH SH SH
A B C
b)
ε A
S&H
S
A
ε
B
S&H
S
B
ε
C
S&H
S
C
SH SH SH
A B C
c)
Conventional
Modified
Fig. 4.28. Current controllers for three phase PWM inverters: (a) proposed NN
controller, (b) Delta modulation controller, (c) modified sampling technique
80

4. ANN based Current Controllers
Assuming equal values of weights:
w A = w B = w C = 1,
w AB = w AC = ... = w BC = -1,
(4.2a)
(4.2b)
the equations Eq.4.1a, Eq.1b, Eq.1c can be rewritten as follows:
e A = ε A - ε B - ε C ,
e B = - ε A + ε B - ε C ,
e C = - ε A - ε B + ε C .
(4.3a)
(4.3b)
(4.3c)
However, for the three phase symmetrical load (without zero leader) the sum of the
instantaneous current errors is always zero:
ε A + ε B + ε C = 0. (4.4)
Therefore, the equations Eq.4.3a, Eq.3b, Eq.3c can be represented as:
e A = 2ε A ,
e B = 2ε B ,
e C = 2ε C .
(4.5a)
(4.5b)
(4.5c)
The last equations show clearly, that when the values of the phase and interphase
weights are equal (equations. Eq.4.2a, Eq.4.2b), the NN operates as conventional
Delta modulation controller without any interphase connections (Fig. 4.28b).
Assuming, however, that:
w A = w B = w C = k,
w AB = w AC = ... = w BC = -1,
(4.6a)
(4.6b)
81

4. ANN based Current Controllers
the equations Eq.4.3a, Eq.4.3b, Eq.4.3c can be written as:
e A = k⋅ε A - ε B - ε C ,
e B = - ε A + k⋅ε B - ε C ,
e C = - ε A - ε B + k⋅ε C .
(4.7a)
(4.7b)
(4.7c)
In this case, for k >> 1, when one error signal is lacking (for example ε A = 0) from
equations. Eq.4.7a, Eq.4.7b, Eq.4.7c and Eq.4.4 the following formulas can be obtain:
e A = - ε B - ε C ,
e B = k⋅ε B ,
e C = k⋅ε C .
(4.8a)
(4.8b)
(4.8c)
Hence, the lacking error signal of phase A is reconstructed from the errors of other
two phases B and C. Therefore, NN controller has robust behaviour and is able to
operate correctly even when one of the error input signals is lacking.
Note, that here the robust behaviour of the controller is achieved using only the simple
one layer NN with precalculated weight factors, whereas in controller proposed by
Harashima et al. [115] the three layer feedforward NN (with 3-5-3 architecture)
trained by back propagation algorithm has been applied.
4.3.5.3. Results
The proposed NN current controller has been investigated by simulation and
implemented in hardware. The simulated and experimental waveforms for
investigated Delta and NN current controllers are shown in Fig. 4.29 and Fig. 4.30,
respectively. In both controllers a modified (shifted) sampling technique is applied.
This modified sampling technique force controller to select zero voltage vectors (not
possible in conventional Delta controller) and always chooses only adjacent active
vectors (see voltage vectors switching path u α
= f(u β
) in Figs. 4.29 and 4.30).
Note, that in contrast to the Delta controller, the proposed NN controller operate
correctly without phase A error signal ε A = 0.
82

4. ANN based Current Controllers
I - NN controller
II - Modified delta controller
Fig. 4.29. Simulated waveforms for current controllers, when error signal in phase A
is lacking (ε A =0):
a) phase voltage u sα , b) phase current i sα , c) voltage vector path u sβ = f(u sα ),
d) current vector path i sβ = f(i sα ).
83

4. ANN based Current Controllers
a) I - NN controller a) II - Modified delta controller
b) b)
c) c)
Fig.4.30. Experimental waveforms for current controllers, for ε A =0:
a) phase voltage u sα and phase current i sα , b) voltage vector path u sβ = f(u sα ),
b) current vector path i sβ = f(i sα ).
84

4. ANN based Current Controllers
4.4. Optimal mode ANN CC
4.4.1. Optimal mode CC
In the case of such a type of controller an optimal algorithm in every sampling
interval T s selects voltage vector that minimise RMS current error (see the section 4.2.
as well). This is equivalent to selection the available inverter voltage vector that lies
nearest to command vector u Sc (t). The command vector is calculated by assumption
that the inverter voltage u Sc (t) and EMF voltage e r (T) of the load is constant over the
sampling interval T s . Based on the calculated u Sc (t) value the voltage vector selector
chooses the nearest available inverter voltage vector (Fig. 4.31.)
u s
synch.
RDCL
i sc
i s
+
-
e r
T
Calculation
of voltage
command
vector
u sc
Voltage
vector
selector
VSI
load
model
3 ph.
load
Fig. 4.31. Optimal discrete modulation controller
Desired voltage vector can be calculated using motor parameters r s , l σ and
electromotive force EMF according to the following equations:
l
u σ
s αc
= ( isαc
− isα
) + rs
isαc
+ eα
(4.9a)
∆t
85

4. ANN based Current Controllers
and
l
u σ
s βc
= ( isβc
− isβ
) + rs
isβc
+ eβ
(4.9b)
∆t
2 2
usc( n) = usαc + usβc
(4.10a)
s c
γ
u
= arctg u α
usβc
(4.10b)
Using these formulas it is possible to calculate for each inverter vector (seven
possibilities) the quality factor J:
J( n) = ( usαc( n) − usα( n)) + ( usβc( n) −usβ ( n))
(4.11)
2 2
and chose the vector, which minimise this index.
Note that:
n – voltage vector number, u sαc – command voltage, u sα - actual voltage.
If we assume that:
ε uα( n) uSαC( n) usα( n)
= − (5.12a)
ε uβ( n) usβc( n) usβ( n)
= − (5.12b)
the equation Eq.4.11 has the following form:
2 2
J = εuα( n) + εuβ( n) (5.13)
The above described procedure is repeated in each sampling time, and it implies, that
implementation of such a system requires very fast microprocessors.
The performance of optimal regulator is much better than in the case of Delta
Regulator. To illustrate this feature the simulation results obtained in both systems are
shown in Fig. 4.32 and Fig. 4.33 respectively.
86

4. ANN based Current Controllers
Fig. 4.32. Behaviour of current Delta Regulator for f = 25 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
87

4. ANN based Current Controllers
Fig. 4.33. Behaviour of current Optimal Regulator for f = 25 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
The presented oscillograms show that the behaviour of optimal regulator is much
better compare to Delta Modulator.
88

4. ANN based Current Controllers
4.4.2. Three layers NN controller trained by optimal PWM pattern
4.4.2.1. Description of the system
The optimal discrete current controller from Fig. 4.31 can be replaced by an off line
trained NN as shown in Fig. 4.34.
u s
synch.
RDCL
+
i sc
-
i s
(ψ
NN
regulator
VSI
(ψ r
T, , ω
)
s
load
model
3 ph.
load
Fig. 4.34. Neural Network discrete modulation controller.
As controller two (5-10-3) and three (5-10-10-3) layers feedforward NN with
sigmoidal nonlinearity are investigated. Before using as controller, the NN was
trained (by back propagation algorithm [149]) with random selected data from the
optimal PWM pattern generated by simulated controller.
In the system with PWM supply there is a practical problem with noise. Therefore, in
signal processing instead of EMF voltage, the rotor flux ψ r components and
synchronous frequency ω s signals are applied to the NN inputs. These signals are
used in conventional vector control schemes of AC motors [12].
89

4. ANN based Current Controllers
The multilayer feedforward NN has been trained using the back propagation
algorithm. The learning samples have been calculated before the learning process and
were created in the system with optimal discrete current regulator.
4.4.2.2. Results
The simulation results have been obtained in NN systems with one and two hidden
layers. In each of these cases ten neurons in these layers have been used. In the
figures Fig. 4.35-Fig. 4.40. the behaviour of the system for three frequencies and two
kinds of neural network are presented respectively. In these oscillograms the voltages,
currents and quality indexes are shown. Some of quality indexes are presented in the
Table 4.7 as well.
Table 4.7.
f
Parameters
[Hz] PSE RMS J
50 - 0.05160 0.04685
Optimal Regulator 25 - 0.05038 0.04679
5 - 0.06056 0.05660
50 0.68 0.07675 0.06804
NN with one hidden layer 25 0.71 0.06851 0.06042
5 0.70 0.07811 0.07075
50 0.92 0.05433 0.04894
NN with two hidden layers 25 0.94 0.05224 0.04814
5 0.96 0.06084 0.05675
It can be seen that Pattern Selection Efficiency factor which shows how often the NN
generates the "correct voltage vector", is about 0.94 for three layers, and about 0.7 for
two layers NN. So, the performance of the NN controller only slightly differs from
Optimal Controller and is much better than for Delta Controller.
90

4. ANN based Current Controllers
Fig. 4.35. Behaviour of NN with two hidden layers for f = 50 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
91

4. ANN based Current Controllers
Fig. 4.36. Behaviour of NN with two hidden layers f = 25 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
92

4. ANN based Current Controllers
Fig. 4.37. Behaviour of NN with two hidden layers for f = 5 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
93

4. ANN based Current Controllers
Fig. 4.38. Behaviour of NN with one hidden layer for f = 50 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
94

4. ANN based Current Controllers
Fig. 4.39. Behaviour of NN with one hidden layer for f = 25 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
95

4. ANN based Current Controllers
Fig. 4.40. Behaviour of NN with one hidden layer for f = 5 Hz
a) i α , i β = f(t) , b) i β = f(i α ) , c) u β = f(t) , d) u β = f(u α ) ,
e) voltage vector = f(t) , f) RMS, J = f(t) , g) ε 2 α = f( t) , h) NRS = f(t)
96

5. Speed estimation of induction motor
5. SPEED ESTIMATION OF INDUCTION MOTOR
5.1. Introduction
A variety of different method for sensorless IM drives has been developed in the past
few years [12, 14, 134, 135]. This Chapter gives a general review of different
techniques with special attention to ANN based speed estimators, and presents an
improved on line trained ANN estimator proposed and implemented by the author.
5.2. Basic Techniques of Speed Estimation
The operation of speed controlled IM drives without mechanical speed sensor
requires the estimation of state variables of the drive. This estimation is based
exclusively on measured motor voltages and currents, which are available in every
PWM inverter-fed drive system. Low performance, low cost sensorless drives can be
designed using simple algebraic estimators. However, high performance systems are
based on dynamic models for the estimation of the magnitude and special position of
magnetic flux in the stator or in the rotor as well as rotor counter EMF vector.
Development of speed sensorless IM control methods has been based on
different approaches and techniques. A historical review is presented in Tab. 5.1. The
development has been started with algebraic slip frequency estimation proposed by
Abbondanti and Brenner in 1975. The newest proposal by Ben-Brahim and
Kurosawa, based on ANN approach, is dated 1993 [130].
The most successful method (which is an extension of torque current estimation
proposed by Kazmierkowski and Koepcke for CSI [132]) is proposed by Othani et. al
and is used in Yasakawa standard inverter-fed drive systems.
The general classification of speed sensorless control techniques is shown in
Fig. 5.1. In this thesis only high performance methods based on open and closed loop
estimators are the subjects of consideration.
97

5. Speed estimation of induction motor
Table 5.1.
Review of Speed Sensorless Induction Motor Control
1975 A. Abbondanti
Slip calculation - stationary
M. B. Brenner
1982 R. Jötten, G. Mäder Slip estimation - dynamic
(EMF - oriented control)
1983 M.P. Kazmierkowski
H.J. Köpcke
Torque current estimation
(EMF - oriented control)
1990 D. S. Zinger, F. Profumo
Speed estimation based on Space Harmonics
T. A. Lipo,D. W. Novotny
1991 W. Lotzkat V/Hz with active stator current control
1991 X. Xu + D.W. Novotny Direct Stator Flux Oriented-slip estimation
1992 L. Kreindler,
Stator Phase Voltage Third Harmonics
J. C. Moreira
A. Testa, T. A. Lipo
1992 B. Ohtani
C. Takada
Torque current and rotor flux estimation
Field oriented control
K. Tanaka
1995 H. Tajima, Y. Matsumoto
Speed estimation from induced speed voltage e T
H. Umida , M. Kawano
1992 U. Baader
M. Depenbrock, G. Girse
DSC scheme with speed estimation from hysteresis torque
controller
1992 C. Schander MRAS - flux criterion
1994 F.Z. Peng
MRAS - Reactive Power Criterion (no R s influence)
T. Fukao
1991 G. Hanneberger
Kalman Filter
B.-J. Brunsbach
Th. Klepsch
1994 Y.R. Kim, S.K. Sul
Extended Kalman Filter
M.H. Park
1993 H. Kubata, K. Matsuse
Full order adaptive speed obserwer with R r compensation
T. Nakano
1993 T. Kanmachi
Estimation ω m = (i r × pψ r )/(i r ψ r )
I. Takahashi
1990 S. Doki, S.I. Yong,
Adaptive Sliding Mode Observers
S. Sangwongwani et. al,
1994 J.W. Chooi
Estimation based on High Frequency Current Injection
S.K. Sul
1993 L. Ben-Brahim
R. Kurosawa
Neural Network Based Estimation
98

5. Speed estimation of induction motor
Sensorless Speed Control Techniques
Low performance
dynamic requirements
High performance
dynamic requirements
Constant V/Hz
control
Slip frequency
compensation
Estimators using
machine
imperfections
Open and closed
loop estimators
Estimators using
saliency effects
Estimators based on
space harmonics
Estimator based
on Artificial
Inteligence
Open loop
estimators
MRAS
Observers
(Luenberger ,
Kalman)
ANN based
estimator
Neuro-fuzzy
based estimator
Fuzzy logic
based estimator
Fig. 5.1. General classification of speed sensorless control techniques
5.2.1. Open loop estimators
In the books [12, 14] many open loop estimation methods based on IM model
is discussed. Below seven basic estimator equations are presented:
99

5. Speed estimation of induction motor
ω
m
= ω −ω
=
T
N
s
d
dt
r
⎛ψ
rβ
⎞ T
arctan⎜
⎟ −
ψ
⎝ rα
⎠ T
N
r
x
M
( ψ
rα
sβ
2
rα
+
ψ
i
−ψ
ψ
i
rβ
sα
2
rβ
)
(5.1)
ω
m
= ω −ω
=
T
N
s
d
dt
r
⎛ψ
sβ
⎞ T
arctan
⎜ −
ψ
⎟
⎝ sα
⎠ T
N
r
xs
( ψ sαisβ
−ψ
sβ
isα
)
ψ s ( ψ s − xσ
isx
)
(5.2)
ωm
= ωs
−ωr
=
d ⎛ erβ
⎞ T
T arctan
N
N ⎜ ⎟ − ωs
dt
e
⎝ rα
⎠ Tr
xM
xr
xs
( e
i
rα
sα
2
erα
+
+ e
e
i
rβ
sβ
2
rβ
)
(5.3)
ω
m
= ω −ω
=
T
N
s
d
dt
r
⎛ esβ
⎞ T
arctan
⎜ −
e
⎟
⎝ sα
⎠ T
N
r
ω
s
xs
( esαisα
+ esβ
isβ
)
es
( es
−ωs
xσ
isx
)
(5.4)
ω
m
ψ
⎡
d
r
⎤
d
r
⎢(
ψ − xM
i s ) × T
r
N ⎥ ( ψ − x
r M is
) × TN
= sgn ⎢
dt ⎥ ⋅
dt
(5.5)
⎢ ( ψ − x
r M is
) ⋅ψ
ψ − x
r ⎥ (
r M is
) ⋅ψ
r
⎢
⎣
⎥
⎦
ψ
i
i
sy
sy
ψ
i
−ψ
i
rα
sβ
rβ
sα
= (5.6)
2 2
ψ rα
+ ψ rβ
e
i
+ e
i
rα
sα
rβ
sβ
= (5.7)
2 2
erα
+ erβ
The accuracy of speed estimators using Eq.5.1-5.7 depends greatly on the motor
parameters used, and also on the scheme used for the estimation of the flux/EMF
components. The basic properties of open loop speed estimators are summarized in
the Tab. 5.2.
100

Table 5.2.
Basic open loop speed estimators
5. Speed estimation of induction motor
Method
1 Based on rotor flux vector
estimation (Eq. 5.1)
2 Based on stator flux vector
estimation (Eq. 5.2)
3 Based on voltage induced by rotor
flux –rotor EMF (Eq. 5.3)
4 Based on voltage induced by stator
flux –stator EMF (Eq. 5.4)
5 Based on vector and scalar product
(Eq. 5.5)
6 Based on torque current estimation
(Eqs. 5.6, 5.7)
Parameter
sensitivity
r s , σx s , T r ,
x M
r s , σx s , T r ,
x s
r s , σx s , T r ,
xM
xr
r s , σx s , T r ,
x s
r s , σx s , T r ,
x M
r s , σx s ,
xM
xr
Remarques
Higher accuracy when
flux is calculated in polar
coordinates
Higher accuracy when
flux is calculated in polar
coordinates
Two integrations are
eliminated
Two integrations are
eliminated
Valid only for waveform
with harmonics
Only for Field oriented
Control Schemes
Note that four important parameters influence the accuracy of open loop estimators:
stator resistance r s , stator transient reactance σx s , stator reactance x s and rotor time
constant T r . These parameters convary due to temperature (r s , r r ), saturation (x M , x s ,
x r ) and skin effect (r r ).
In low speed region, the accuracy of the open loop estimation is reduced, and in
particular, parameter deviations from their actual values have great influence on the
steady state and transient performance of the drive system, which uses an open loop
estimator. Higher accuracy is achieved if the stator flux is calculated by a scheme,
which avoids using of pure integrators (Fig. 5.2.). This leads to improved schemes
working with polar coordinates ψ = ψ , γ ] (Fig. 5.3.). It is important, that in the
s
[ s s
case of rotor field-oriented system stator flux must be recalculated to the rotor flux.
Finally, it should be noted that the robustness against parameter mismatch and noise
(in the measured signals) can be considerably improved by using closed loop
observers.
101

5. Speed estimation of induction motor
a)
isα
usα
rs
_
1
∫
Ψsα
isβ
usβ
rs
_
T N
1
T N
∫
Ψsβ
b)
isα
usα
usβ
isβ
αβ isx
rs
_
usx
esx 1
Ψsx
= Ψs
T N
∫
usy
esy
_
isy
xy rs
÷
esy
ω
s
=
sin γ s
Ψsx
cos ∫
γ s
Fig. 5.2. Stator flux vector estimators: a) Stator flux estimator in cartesian coordinates
b) Stator flux estimator in polar coordinates
5.2.2. Closed loop estimators – observers
Having an open loop estimator of a dynamic system state variables, by introducing a
correction term involving the estimation error, one obtains a closed loop estimator
which is referred to as an observer.
If the plant is considered to be deterministic, then the observer is deterministic
observer, otherwise it is a stochastic observer. The most popular observers are
Luenberger and Kalman types.
102

5. Speed estimation of induction motor
a)
isα
usα
usβ
isβ
αβ isx
rs
_
usx
esx 1
Amplitude Ψsx
= Ψs
T Limiter
N
usy
esy
_
isy
xy rs
÷
esy
ω
s
=
sin γ s
Ψsx
cos ∫
γ s
b)
+
T dΨ sx
= 1
N
esx
Ψsx
= Ψ
dt
s + ω
s
c y LPF
+
ωc
s + ω
c
Limiter
Fig. 5.3. Improved stator flux estimator in polar coordinates:
a) stator flux estimator with amplitude limiter, b) amplitude limiter
5.2.2.1. Luenberger Observer
Luenberger observer (LO) is of the deterministic type and basically is applicable to
linear time-invariant deterministic systems. The extended Luenberger observer (ELO)
is applicable to nonlinear time-varying deterministic system.
x&
= Ax
+ Bu
i
s
= Cx
s
(5.8)
where
103

5. Speed estimation of induction motor
x = [ i
u
s
s
= [ u
ψ ]
sα
r
= [ i
⎡A11
A12
⎤
A = ⎢ ⎥
⎣A21
A22
⎦
⎡1
0⎤
C = [ I 0],
I = ⎢ ⎥
⎣0
1⎦
T
,
i
s
T
usβ
]
sα
T
isβ
]
, ψ
r
= [ ψ
rα
ψ ]
rβ
T
(5.9)
u s
B
Induction
Motor
i s
^
i s
+ -
I/s
+
C
+ +
^
ω m
A
^
ψ r
∧ ∧ ∧
ω m
(r s
,T r
)
Adaptive scheme
Fig.5.4. Block diagram of adaptive flux and speed observer
K
Based on a Lyapunov function
V
T
= e e + ( ˆ ωm
−ωm
) / c
(5.10)
where c is positive factor, and applying the conventional procedure of pole placement
technique, the gain matrix K can be calculated as follows:
⎡k
K = −⎢
⎣k
1
3
I + k
I + k
2
4
J⎤
⎥,
J⎦
⎡0
J = ⎢
⎣1
−1⎤
0
⎥
⎦
(5.11)
104

5. Speed estimation of induction motor
with
k
k
k
k
1
2
3
4
η ≥ 1
⎛ 1
= −(
η −1)
⎜
⎝τ
s′
= ( η −1)
ˆ ω
m
1 ⎞
+
⎟
τ r′
⎠
2 ⎡⎛
1 1−σ
⎞ x′
= ( η −1)
⎢
⎜ +
⎟
s x
⎣⎝τ
s′
τ r′
⎠ xr
x
+
τ
xs′
xM
⎛ 1 1 ⎞
( η −1)
⎜ +
⎟
xr
⎝τ
s′
τ r′
⎠
2 x
= −(
η −1)
ˆ ω
s xM
m
x
r
M
M
r
⎤
⎥ +
⎦
(5.12)
where
x′
s = σxs
,
x′
′ = s
s ,
rs
τ
τ
xr′
= σxr
,
xr′
r′
= ,
rr
τ
r
=
xr
rr
(5.13)
In a discrete implementation, however, for small sampling time and low speed,
accurate computation is required. This is because of stability problems which can
occur (roots are close to stability limit). Therefore, another pole-placement procedure
has to be used, which ensures that the low speed roots are select away from the
stability limit.
5.2.2.2. Extended Kalman Filter (EKF)
The EKF is a recursive optimum stochastic state estimator, which can be applied for
common state and parameter estimation of nonlinear dynamic systems in real time by
using measured signals with random distributed noise. Of course, it assumes that the
measurement noise w and disturbance noise v (Fig. 5.5) are uncorrelated.
105

5. Speed estimation of induction motor
u s
Induction Motor
v
.
+ x
B
I/s
x
C
+ +
+
i s
+
w
B
A(x)
^
+ x ^.
x^ i s -
+
C
I/s
+ +
A(x)
^
K
Fig. 5.5. Block diagram of EKF
In fact the EKF is a variant of the Kalman Filter, but the extended KF can be used for
a nonlinear systems. In the speed adaptive flux observers, the speed is considered as a
state variable. The design procedure is complicated and includes the following steps
for the discrete EKF algorithm
• Selection of discretized IM model,
• Determination of the noise and state covariance matrices,
• Implementation of the EKF algorithm
• Tuning
The most important features of the ELO and EKF can be summarized as below
106

5. Speed estimation of induction motor
ELO
• Can be used in a majority of industrial
systems since they can be considered
as deterministic
• Its performance can be chosen by
selection the gain matrix; fast
convergence and robust design can be
obtained
• Lower computational requirements
(no matrix inversion as in the EKF)
• It is large flexibility in design of the
ELO, because of existed redundancy
in the gain matrix specification
EKF
• It is effective for an industrial systems
which can be considered as stochastic
• Its performance is adjusted by tuning
the covariance matrices
• Because of fact that a limitation
implying optimality condition has to
be satisfied, it is no design flexibility
• The nonlinear nature of the IM and an
“ad hoc” tuning of covariance matrix
may result in non-optimal estimator
and a bias problem
5.2.3. Model Reference Adaptive Systems (MRAS)
Another method to increase the accuracy of the open loop estimators discussed in
section 5.2.1, is application of an closed loop approach. The Model Reference
Adaptive System (MRAS) constitutes a wide class of the closed loop flux and speed
observers.
As can be seen in Fig.5.6. in a MRAS system, some state variables x (e.g. rotor flux
vector components x = [ ψ rα
ψ rβ
] or back EMF components x = [ e r α erβ
]) of
IM (calculated from the monitored voltage vector u s and current vector i s ) are
estimated in a Reference Model (RM) and then compared to state variable xˆ
estimated in an Adaptive Model (AM). The error between these state variables is then
in an Adaptation Algorithm to obtain estimated speed ω m which adjusts the AM.
Adaptive algorithm is derived by using Popov’s hyperstability criterion.
107

5. Speed estimation of induction motor
u s
Reference
Model
x
i s
i s
Adaptation
ε
Adaptive
Model
∧
x
ω^m
Algorithm
Fig.5.6. Block scheme of MRAS based speed estimator
Depending of the definition of the error signal for speed tuning, several types of the
MRAS can be defined
⎧ = ˆ
*
ε1
Im( ψ ψ ) with ψ = ψ +
⎪
r r
r rα
jψ
rβ
⎪
*
ε 2 = Im( er
eˆ
r ) with er
= erα
+ jerβ
ε = ⎨
⎪
*
ε3
= Im( ∆er
i s ) with ∆er
= er
− eˆ
r
⎪
⎪
*
⎩ε
4 = Im( ∆erdi
s / dt)
with ∆er
= er
− eˆ
r
(5.14)
where •ˆ denotes the quantities estimated by the AM
*
• denotes conjugate complex quantities.
Basic features of MRAS speed estimation algorithms given by Eq.5.x are
summarized in Tab. 5.3. The ε 3 algorithm is insensitive to stator resistance changes
and, therefore, seems to be most attractive. Also, it has been shown that when for
rotor FOC schemes the same value of T r as in the MRAS speed observer is used, then
108

5. Speed estimation of induction motor
the drive system will be robust to the T r changes as well. Another ε 4 algorithm is
insensitive to leakage reactance x σ changes. However, it requires calculation of stator
current i s derivative, which in PWM inverter fed IM is strong noisy signal.
Finally, it should be pointed out that MRAS based structures also create basics
for Artificial Intelligence estimators, which are discussed in the next section 5.2.4.
Table 5.3.
MRAS speed estimation algorithms
1
2
3
4
Adaptation criterion
Parameter
sensitivity
ε Im( ˆ
*
1 = ψ )
r ψ
r s , x σ , T r ,
r
xM
x
ε Im( ˆ
*
2 = e r e r ) r s , x σ , T r ,
xM
x
ε *
3 = Im( ∆e r i s ) x σ , T r ,
xM
x
ε 4 = Im( ∆erdis
/ dt)
*
r
r
r
r s , T r ,
xM
x
r
Computational
requirements
High
Medium
Low
Medium
Remarques
Initial
condition and
drift problem
(pure
integration)
No pure
integration
problem
r s effect is
eliminated
x σ effect is
eliminated
5.2.4. Estimators based on Artificial Intelligence (AI)
There are many possibilities of using AI based speed estimators. One can use ANN
approach or neuro-fuzzy or fuzzy logic schemes. In this thesis only the ANN based
estimators are described.
ANN speed estimators have the following advantages compare to the classical
solutions:
• The calculation time can be shorter, because of the parallel processing,
• The system can calculate almost correctly, even if the information is not complete
(redundancy of the system)
109

5. Speed estimation of induction motor
• The ANN can work as low pass filter, so one do not need the additional filters,
• The development time of such an estimator is rather short comparing to classical
solutions,
• The systems based on ANN are robust to parameter variations and noise.
The block diagram of sensorless control of induction motor based on ANN
speed estimation is shown in Fig.5.7. The speed command signal ω mc is compared
with estimated value ω m and the error is delivered to the speed controller. As input
signals to the ANN speed estimator are stator voltage and current vectors. The actual
speed ω m is measured by tachogenerator for testing only.
u d
ω mc
+
-
Speed &
Vector
Controller
VSI
∧
ω m
NN Based
Speed
Estimator
u s
i s
ω m
IM
Fig.5.7. Sensorless control of PWM inverter-fed IM based on ANN speed estimator
One can use the ANN estimator in on-line and off-line fashion. In the system,
which works on-line the ANN is used as MRAS, and mechanical speed is
proportional to weights of this neural network. The block diagram is very similar to
Fig.5.6 and it is shown in Fig.5.8.
110

5. Speed estimation of induction motor
u s
Reference
Model
x
i s
i s
Learning
ε
ANN
∧
x
ω^m
Algorithm
Fig.5.8. Block scheme of an on-line ANN based speed estimator
As Adaptive Model the one layer linear ANN is used. More detailed description of
this approach is shown in the next section.
In the off-line approach a three-layer feedforward ANN is used, and the
mechanical speed is the output of the neural network. The input vector to the ANN
could be as follows:
xin
= [ u
sα
(
i
k)
sα
(
k)
u
sβ
(
i
k)
sβ
(
k)
u
sα
(
i
sα
(
k −1)
k −1)
u
i
sβ
(
sβ
(
k −1)
k −
T
1)]
(5.15)
The block diagram of this approach is presented in Fig. 5.9.
Because of the its simplicity, and the advantages of an ANN in the further part
of this thesis only approaches based on ANN are detailed described and used in real
system.
111

5. Speed estimation of induction motor
ψ rc
-
ω mc
+
Control
Inverter
IM
i s (k)
i s (k)
u s (k)
^
ω m
ANN based
speed
estimator
i s
(k-1)
u s
(k)
u s
(k-1)
Z −1
Z −1
Fig.5.9. Block scheme of an off-line ANN based speed estimator
112

5. Speed estimation of induction motor
5.3. ANN based speed estimators
5.3.1. Speed estimators with on-line ANN
In this part of the thesis three methods based on an on-line ANN is presented. The
first approach has been originally published by Ben-Brahim and Kurosawa [130] and
is based on two flux models. The second method is a small modification of the first
one, but with big improvement in the length of the learning time.
The third method is the new method originally invented by the author, and is
based on stator current calculations.
5.3.1.1. Method based on two flux models
The concept proposed in [130] is based on two independent rotor flux simulators
[12]:
- voltage model
TN(dΨru/dt) = (xr/xM)[us - rs is - σxs TN(dis/dt)] (5.16)
- current model
TN(dΨri/dt) = [-(TN/Tr) + jωm]Ψri + (TN xM/Tr) is (5.17)
where:
Tr = (TN xr/rr) — rotor time constant,
TN = (1/2πFSN) = (1/ 2π50 Hz) — nominal time constant,
σ = 1- (xMxM/xrxs) — leakage factor.
The block diagram of the NN speed estimator is shown in Fig.5.10.
113

5. Speed estimation of induction motor
u s
i s
Flux Model
z -1
ψ ru
-
ε
Neural Netwok
with
Weight ^ ω m
+
ψ ri
Fig.5.10 . Block diagram of the NN based speed estimator
The discrete current model of rotor flux one can calculate from Eq.5.17.
Ψri(k) = [(1-Ts/Tr)+jωmTs/T N ]Ψ ri(k-1)+(TsxM/Tr) is(k-1) (5.18)
where Ts is the sampling time.
The model based on Eq.5.18 is similar to neural network. One weight is proportional
to mechanical speed, and the output is Ψri [130].
Ψri(k) = w 1 Ψ ri(k-1) + w 2 jΨ ri(k-1) + w 3 is(k-1) (5.19)
The error output is given by
e(k) = Ψri(k) - Ψru(k) (5.20)
Therefore, to calculate estimated mechanical speed ωm one can use back propagation
training algorithm [144].
The ANN in this case has very simple form and is presented in Fig.5.11.
114

5. Speed estimation of induction motor
W1
ψ_
u
x 1
x 2
x 3
W3
Σ
ψ_
i
ε
W2
ω^
m
LA
x 1
x 2
= ψ_
(k-1)
R
= jψ
_
(k-1)
R
x 3 = _ i s
(k-1)
Fig.5.11. Structure of linear ANN used in on-line speed estimation method
Using back propagation learning method one can get following formula:
w2
= w2
−η(
−eα
Ψriβ
+ eβΨriα
) + α∆w
2
T
ˆ N
m = w2
Ts
ω
(5.21)
where η is called learning rate and α - momentum factor.
Note, that one can use the same NN to estimate T r instead of mechanical speed.
115

5.3.1.2. Improved method based on two flux models
5. Speed estimation of induction motor
In this method in contrast to the method presented in 5.3.1.1, the block diagram of NN
based speed estimator is a little bit different. The improvement is presented in
Fig.5.12, and it implies much better behavior of this estimator.
u s
i s
Flux Model
Z −1
ε
+
ψ ri
Weight ω m
Neural Network
with
ψ ru
-
Fig.5.12 . Block diagram of the modified NN based speed estimator
5.3.1.3. Method based on current estimation error
The new method presented in this paper is based on stator current calculation:
di s xM
T
⎛ 2
⎛ N ⎞ xM
T ⎞
σ x N
s =
j ⎜
m r
r ⎟
s i s + us
dt x
⎜ − ω − +
r T
⎟ Ψ
(5.22)
⎝
⎜
r ⎠ xrT
⎟
⎝ r ⎠
This equation one can use to calculate the estimate value of stator current, using
Eq.5.16 to obtain rotor flux value.
116

5. Speed estimation of induction motor
i s
z -1
^+
i
i s
Neural Network
s
Ψr
u with weight ω ^
m
s z -1
Flux estimation
i s
-
Fig. 5.13. Block diagram of the new NN based speed estimation method
x 1
W1
x 3
W3
Σ
^
i s
_
i s
ε
x 4
W4
x 2
W2
^
ω m
LA
x 1
x 2
= ψ_
(k-1)
R
= j ψ_
(k-1)
R
x 3 = _ i s
(k-1)
x 4
= u s
(k-1)
Fig.5.14. Structure of linear ANN used in new on-line speed estimation method
117

Therefore, the discrete model of stator current is as follows:
5. Speed estimation of induction motor
ˆ
x ⎛ T
i ( k)
=
M
s
⎜
xrσxs
⎝ T
⎡ 1
⎢ 1−
⎢ σx
⎣
s
2
M
⎛
⎜
x T
⎜
⎝
xrTr
s
s
r
− jω
+ r
s
T
T
m
s
N
T
T
s
N
⎞
⎟ Ψ r ( k −1)
+
⎠
⎞⎤
⎟ ˆ
T
⎥i
( k −1)
+
s
u
⎟ s
⎠⎥
T x
⎦
Nσ
s
s
( k −1)
(5.23)
This equation can be rewrite in NN form, with one weight proportional to mechanical
speed ω m .
iˆ
s ( k)
= w1ψ ( k −1)
+ w2
jψ
( k −1)
+ w3i
s ( k −1)
+ w4us
( k −1)
(5.24)
r
r
The block scheme of new calculation method of speed estimation based on Eq.5.23 is
presented in Fig. 5.13. The linear ANN is shown in Fig. 5.14.
Note that current estimation error
e( k)
= iˆ
( k)
− i ( k)
(5.25)
s
s
is used to NN tuning.
Therefore, one can calculate estimated speed using the following formula:
w2
= w2
−η(
−eα
Ψriβ
+ eβΨriα
) + α∆w
2
T x
ˆ ω
N r
m = − σx
sw2
Ts
xM
(5.26)
Instead of estimate mechanical speed, using this NN one can estimate motor
parameters.
118

5.3.1.4. Comparison of two presented methods
5. Speed estimation of induction motor
The structure of the new method described in 5.3.1.3. is similar to the method
presented in 5.3.1.1 [130]. The differences are as follows:
a) different error signals for NN tuning,
b) more NN weights in new method,
c) NN depends on more number of motor parameters in new method.
d) using above approaches to estimate motor parameters, more information we can
get from the new method (especially information about stator resistance, which
can be used to parameter adaptation, as is shown in next chapter).
119

6. ANN sensorless Field Oriented Conrol of IM
6 ANN SENSORLESS FIELD ORIENTED CONTROL OF IM
6.1 Principles of field oriented control (FOC)
6.1.1 Introduction
In this chapter the short description of vector control will be presented. The field
orientation concept (vector control) [126, 122] is widely used for high-performance
control of ac motors. The main feature of field oriented approach is to enable
decoupling control of torque and flux similar to the control of a separately excited dc
motor.
In the further part the block diagrams of direct and indirect FOC will be described,
and the design of current and speed controllers will be shown.
6.1.2 FOC description
The principle of vector control method is based on a mathematical model of induction
motor in the rotating reference coordinate frame. It is very convenient to select the
angular speed of the coordinate system ω K = ω sψ . In this case the coordinate system is
oriented along the space vector of the rotor flux linkages ψ r (see fig. 6.1).
We can assume that:
and
= ψ
r r ψ rx
(6.1)
ψ =
ψ = 0
(6.2)
ry
Let us assume, moreover, that it is a cage motor, i.e.
u u = 0
(6.3)
rx = ry
120

6. ANN sensorless Field Oriented Conrol of IM
β
Y
isβ
is
ψ R
X
δ
isx
i sy
γ s
α
isα
Fig. 6.1. Vector diagram of induction motor
If we for the sake of simplicity omit the equation of stator voltage (current control),
than the rest of equation we can write as:
d r r
T
r
N = −
dt xr
dωm
x
T
M
M =
dt xr
r
ψ
ω = ω
sψ
−
ω
ψ
ψ
rr
r + xM
isα
xr
risy
− mL
rr
xM
m =
xr
isy
ψ
r
(6.4)
From these equations, it can be noted, that i sx is control signal of rotor flux dynamic
and i sy is control signal of electromagnetic torque m, where
x
m = M
ψ risy
(6.5)
xr
and ω r is a slip frequency.
121

6. ANN sensorless Field Oriented Conrol of IM
The whole description of the motor (with stator voltage equations) can be calculated
as follows:
TN
TN
TN
TN
ψ
d r rr
r
= − ψ
r
r + xM
isx
dt xr
xr
2 2
disx
xM
rr
xr
rs
+ xM
r
= ψ
r
r −
isx
+ ωmisy
+
dt 2
2
σxs
xr
οxs
xr
2
r i
r sy 1
xM
+ usx
xr
ψ r σxs
di
2 2
sy xM
xr
rs
+ xM
r
= − ω
r
mψ
r −ωmisx
−
isy
−
dt σxs
x
2
r
οxs
xr
r i
r sxisy
1
xM
+ usy
xr
ψ r σxs
dθ
r i
r sy
= ωm
+ xM
dt xr
ψ r
(6.6)
Where
⎛ψ
rβ
⎞
θ = arctan ⎜
⎟
(6.7)
⎝ψ
rα
⎠
is the phase position of the ψ r space vector in α-β coordinates.
The block scheme, which represents equations Eq. 6.4, is shown in Fig. 6.2.
If we compare this system and the separately excited dc we can note some similarities.
In x-y frame the rotor flux ψ r is at rest and is directed along x-axis. If the stator
current rotate with the synchronous angular speed (steady state), then we obtain
motionless vectorial graph in the field coordinates x-y
122

6. ANN sensorless Field Oriented Conrol of IM
Fig. 6.2. Block diagram of induction motor in x--y field coordinates
These considerations give us the following analogies:
• i sx component of the stator current vector in induction motor corresponds
to the exciting current in the separately excited dc motor,
• i sy component of the rotor current vector in induction motor corresponds
to the armature current in the separately excited dc motor.
123

6. ANN sensorless Field Oriented Conrol of IM
The basic control properties of induction motor can be presented as:
• The relationship between i sx component and rotor flux ψ r is not static. The
dynamic is represented by the first order system with the rotor time
constant T r , where:
x
T r
r = TN
(6.8)
rr
therefore, i sx component is equal to the magnetizing current
iMr
ψ
= r
(6.9)
xM
only in steady state,
• The torque m and flux ψ r are dependent on the stator current vector i s and
cannot be controlled independent,
• It is good idea to make decoupling, in such a way, that the change of i sx
component does not influence on i sy component and vice versa. In this case
we can control rotor flux using i sx control signal, and torque using i sy . If we
additionally keep the value of i sx as constant, the situation is analogous to
the separately excited dc motor.
124

6. ANN sensorless Field Oriented Conrol of IM
6.2 Block scheme description
6.2.1 General description
The basics of the field-oriented control have been presented in the previous section.
The main feature of this approach is the coordinate transformation, which allows to
calculate the decoupled field oriented coordinates i sx , i sy of the vector stator current to
the fixed stator frame i sα ,i sβ :
i sα = i sx cosγ s - i sy sinγ s
i sβ = i sx sinγ s + i sy cosγ s
(6.10a)
(6.10b)
Depending to the way of rotor flux angle calculations one can distinguish two kinds of
field oriented control:
• Direct field oriented control (DFOC) (Fig. 6.3)
• Indirect field oriented control (IFOC) (Fig. 6.4)
DIRECT FIELD ORIENTED CONTROL
REFERENCE
FLUX
REFERENCE
TORQUE
FIELD
ORIENTED
CONTROLLER
INVERTER
IM
γ s
VOLTAGE
ROTOR FLUX
MEASURMENT OR
ESTIMATION
CURRENT
ωm
TACHO
Fig. 6.3. Structure of direct field oriented control (DFOC)
125

6. ANN sensorless Field Oriented Conrol of IM
INDIRECT FIELD ORIENTED CONTROL
REFERENCE
FLUX
REFERENCE
TORQUE
FIELD
ORIENTED
CONTROLLER
INVERTER
VOLTAGE
CURRENT
IM
γ s
∫
ω S
SLIP
FREQUENCY
CALCULATION
ω r
+
+
ω m
TACHO
Fig. 6.4. Structure of indirect field oriented control (IFOC)
In DFOC system (Fig. 6.3.) the rotor flux vector is directly measured or estimated
from stator voltages and currents. The rotor flux vector angle is then calculated from
the rotor flux coordinates.
In IFOC system (Fig. 6.4.) the rotor flux angle γ S is estimated using the reference
values of flux and torque (the slip frequency model) and the value of mechanical
speed ω m .
γ S = ∫ (ω m + ω r ) dt ; (6.11)
and
r i
r syc
ω r =
(6.12)
xr
isxc
126

ω
r
6. ANN sensorless Field Oriented Conrol of IM
6.2.2 Description of block schemes implemented in practice
In previous subsection the general schemes of the direct and indirect field oriented
control have been presented. Now the more detailed description of the control
structure will be discussed.
In the Fig. 6.5 block diagram of DFOC is shown. Note that as speed controller the PI
regulator is used. The current regulators control currents in field oriented frame.
These regulators are decoupled. The structure and the way of tuning these regulators
will be presented in the next section.
ω re
f
Ψref Ψrc 1
x M
ω re
f
-
ω m
Ψr
PI
me c
u sxc
αβ
u sαc
i sxc
xy
αβ
-
PI
1 i syc
u syc
αβ
u sβc γ
Ψ u u,
s
rc
- sinγ cos γ
γ S
sinγ
u
cosγ
sαc
u sβc
sinγ cosγ
i sx
xy
αβ
i sy
DECOUPLED PI
CURRENT CONTROL
ABC
γ u
u s
VECTOR
MODULATOR
U , I
2/3
S A
S B
S C
u dc
VSI
IM
~
u sαc
i sα
u sβc
FLUX
ESTIMATOR
i sβ
Ψr
ω m
Fig. 6.5. Block scheme of the direct field oriented (DFOC)
In the Fig. 6.6. the block scheme of the indirect field oriented control is presented.
The control blocks are similar to these presented in Fig. 6.5. Only difference is the
way of coordinates transformation calculation as it was mentioned in previous
subsection.
127

6. ANN sensorless Field Oriented Conrol of IM
Ψref
ω s
ω ref
-
PI
me c
Ψrc
1
Ψ rc
1
1
i sxc
XM
i syc
-
-
DECOUPLED PI
CURRENT CONTROL
u sxc
u syc
sinγ
xy
αβ
u sαc
u sβc
cosγ
γ u
u
γ s
u , u s
αβ
VECTOR
MODULATOR
S A
S B
S C
u dc
VSI
i sy
i sx
sinγ
sinγ
cosγ
xy
αβ
cosγ
γ S
1/s
ω s
U , I
IM
~
i sα
i sβ
1
T i
r sxc
u sαc
u sβc
ω m
ω m
ω m
αβ
ABC
2/3
ω r
Fig. 6.6. Block scheme of the Indirect Field Oriented Control (IFOC)
ω ref
Ψref Ψrc 1
ω s
XM
me c 1 i syc
PI
Ψ rc
-
^ ω m
1/s
1
T r
i sxc
ω s
i sxc
-
-
DECOUPLED PI
CURRENT CONTROLLERS
u sxc
u syc
xy
αβ⎺
αβ
u sαc
u sβc
si n γs
cosγ s
γ S sin γs
cos γs
si n γ cosγ
s
s
i i
sx
sα
xy
i sy
i sβ
αβ
u s
γ u
u sαc
u sβc
αβ
ABC
γ u
u s
VECTOR
MODULATOR
U , I
2/3
S A
S B
S C
u dc
VSI
IM
~
ω r
^ ω m
u sαc
u sβc
ANN BASED
SPEED
ESTIMATOR
i sα
i sβ
Fig. 6.7. Block scheme of the speed sensorless Indirect Field Oriented Control (IFOC)
with ANN based speed estimator
128

6. ANN sensorless Field Oriented Conrol of IM
In the Fig. 6.7. the block scheme of sensorless indirect field oriented control is shown.
As the speed estimator is used neural network based system described in chapter 5.
This system has been implemented in laboratory. The results obtained in experiments
will be described in the next chapter.
6.3 Design of current controller
6.3.1 Introduction
In this section the design methodology for the current regulators will be presented.
The current regulators are very important part of the field oriented based control
systems (see Fig. 6.5—Fig. 6.7). The good dynamic behavior and proper results in
steady state operation are desired to good operation of the whole system.
The review of current regulators has been presented in chapter four. In this section our
interest is limited to the linear PI controllers, and we assume that in the system exists
vector modulator which controls PWM voltage source inverter.
6.3.2 Decoupled current regulators
For decoupled torque and flux control the rotor flux and torque current have to
be properly controlled. The basic requirements for current controllers can be specified
as follows:
• Fast response which assure the high dynamics of the system,
• Overload protection,
• The instantaneous changes of the currents should be controlled,
• Load parameter compensation,
• Sinusoidal waveform.
In practical implementation the PI regulators are used very often because of their
simple structure, simplicity of tuning process and robustness.
129

6. ANN sensorless Field Oriented Conrol of IM
Unfortunately the x and y stator voltage components are coupled to each other. It
means, that any changes of the voltage component in x (y) axes results in changes of
the both current components (x and y). This implies that the classical design methods
of linear and decoupled systems are not valid.
In Fig 6.8 the decoupling system is presented. The more detailed description of this
system will be presented in the further part of this section.
Due to limited dc voltage of the voltage source inverter the PI controllers have to
include anti windup protections. This kind of protection is achieved by updating only
the integral terms as long as saturation in the voltage is not detected.
i syc
i sy
xσ
PI
anti windup
-
u syc
ω s
i sx
xσ
PI
anti windup
+
u sxc
i sxc
Fig. 6.8. The current controllers with decoupling
6.3.3 Controller design for field oriented IM
In the sake of the current regulators synthesis, it is necessary to make analysis of the
voltage equation of field oriented induction motor.
130

6. ANN sensorless Field Oriented Conrol of IM
2 2
disx
xM
rr
xr
rs
+ xM
r
T
r
N = ψ r −
isx
+ ωmisy
+
dt 2
2
σxs
xr
οxs
xr
2
r i
r sy 1
xM
+ usx
xr
ψ r σxs
di
2 2
sy xM
xr
rs
+ xM
r
T
r
N = − ωmψ
r −ωmisx
−
isy
−
dt σxs
x
2
r
οxs
xr
r i
r sxisy
1
xM
+ usy
xr
ψ r σxs
dθ
r i
r sy
ωsψ = TN
= ωm
+ xM
dt xr
ψ r
(6.13)
The first two equations we can rewrite in complex form:
σ x
s
T
N
r
j
x
r
di
r
dt
x
s
M
x
+
2
r
r
r
s
2
xM
rr
2
r
+
x
isy
σxs
i
ψ
s
i
x
=
x
M
r
s
+ jω
σx
i
⎛ r
⎜
⎝ x
r
r
m
s
− jω
m
s
+
⎞
⎟ψ
r
⎠
+ u
s
(6.14)
and because the last equation in Eq. 6.13 is fulfilled, the equation Eq. 6.14 has the
following form
σ x
s
T
N
x
=
x
di
dt
M
r
s
x
+
⎛ r
⎜
⎝ x
r
r
2
r
r
s
− jω
2
xM
rr
2
r
+
x
m
⎞
⎟ψ
r
⎠
i
s
+ u
+
s
jω
σx
s
s
i
s
(6.15a)
If we introduce notation
131

6. ANN sensorless Field Oriented Conrol of IM
r
im
=
x
xσ = σx
2
r rs
s
+ x
x
2
r
2
M rr
(6.15b)
finally we obtain
x
di
x ⎛ r ⎞
+
⎝ ⎠
s
M r
σ TN
+ rimis
+ jωs
x σ is
= j m u
r s
dt
x
⎜ − ω
r x
⎟ψ
(6.16)
r
Eq. 6.16. can be rewritten in the matrix form:
⎡usx
⎤ ⎡sx
+ rim
⎢ ⎥ = ⎢
⎣
usy
⎦ ⎣ ωsxσ
⎡ xM
rr
⎤
− ω
−
⎤⎡
⎤ ⎢ r
s x i
ψ
σ sx x ⎥
⎥⎢
⎥ + r
sx + ⎢ x ⎥
σ rim
⎦⎣
isy
⎦
M
⎢−
ωmψ
r ⎥
⎣ xr
⎦
σ
2
(6.17)
Note that this system is coupled because the matrix is not diagonal. Therefore it is
impossible to control both current components separately. In this section the part of
the Eq. 6.17. with the rotor flux will be treated as the constant distortion and will be
not taken into account in the dynamic behaviour investigation. Let us call the output
signals of the v x and v y respectively. If we omit the part with rotor flux the equation
Eq. 6.17 obtains the following form
⎡usx
⎤ ⎡vx
⎤ ⎡−ωs
xσ
isy
⎤
⎢ ⎥ = ⎢ ⎥ + ⎢ ⎥
⎣
usy
⎦ ⎣
v y ⎦ ⎣ ωs
xσ
isx
⎦
(6.18)
and
⎡vx
⎤ ⎡sxσ
+ rim
⎢ ⎥ = ⎢
⎣
v y ⎦ ⎣ 0
0 ⎤⎡isx
⎤
⎥⎢
⎥
sxσ
+ rim
⎦⎣
isy
⎦
(6.19)
The whole current controller with decoupling in Fig. 6.8 is presented. The matrix
transfer function of the decoupled current controlled induction motor is equal
132

6. ANN sensorless Field Oriented Conrol of IM
⎡ 1
⎤
⎢
0
sx + r
⎥
G s
im
o = ⎢ σ 1
( )
⎥ = I
(6.20)
⎢
1
0
⎥ sxσ
+ rim
⎢⎣
sxσ
+ rim
⎥⎦
where I is identity matrix.
6.3.4 Internal model control
6.3.4.1 General description of Internal Model Control
The structure of internal model control is presented in Fig. 6.9. In this approach the
internal model G i (s) is used in parallel; with controlled object G o (s). Additional the
IMC controller C(s) is used in outer loop. Note that G o (s), G i (s) and C(s) are transfer
function matrices.
r(t)
+
-
C(s)
u(t)
G(s)
y(t)
G i
(s)
-
+
Fig. 6.9. The basic scheme of IMC regulator
133

6. ANN sensorless Field Oriented Conrol of IM
G r
(s)
r(t)
+
+
+
C(s)
u(t)
G(s)
y(t)
G i
(s)
Fig. 6.10. Equivalent scheme in classic control structure
There is interesting that this scheme is the special case of the classical control
structure (see Fig. 6.10), where the regulator has the following transfer function.
G r (s)=[I-C(s) G i (s)] -1 C(s) (6.21)
Additional we assume that internal model is exactly the same like the controlled
object i.e.
G i (s)=G o (s) (6.22)
In this case closed-loop system has the following transfer function
G c (s)=G o (s)C(s) (6.23)
Note, that if we assume the closed loop transfer function as multivariable first orders
system i.e.
1
G c ( s)
= LP(
s)
= I
(6.24)
1 + τs
then the behavior of the system is dependent only on one time constant, and the tuning
is very simple.
134

6. ANN sensorless Field Oriented Conrol of IM
6.3.4.2 Design of current loop with internal model approach
In the case of induction motor, after decoupling the open loop transfer function is
defined by equation Eq. 6.20. If we substitute this formula to equation Eq. 6.21 and
assume the closed loop system defined by equation Eq. 6.24, we can obtain
⎡ 1 ⎤
Gr
( s)
=
⎢
I − I
⎣ 1+
τs
⎥
⎦
−1
G
−1
o
1 sx r
s
σ +
( ) =
1+
τs
τs
im
I
(6.25)
or in different form
⎡ ⎤
x ⎢ ⎥
Gr
s =
σ 1
( )
⎢
1+
I
x ⎥
(6.26)
τ σ
⎢ s
⎣ r im
⎥
⎦
It means that to control i sx and i sy currents we should use the PI controllers with the
same parameters
K pc
=
xσ
x
, Tic
= σ TN
(6.27)
τ
rim
where the K pc is the gain factor of the PI controller, and T ic is the time constants of this
controller.
Note that in this case we have the desired transfer function of the closed loop system
(Eq. 6.24) which is useful in tuning of the speed control part. Furthermore because of
this that decoupled system is the first order system, we do not need to use more
complicated regulators. As result the design of PI controller is unique.
135

6. ANN sensorless Field Oriented Conrol of IM
6.4 Design of speed controller
6.4.1 Introduction
In Fig. 6.11 the simplified scheme of the speed controller is shown. The error between
speed reference and measured speed (or estimated speed in the case of speed
sensorless control) is feed to PI regulator which output is torque command. Using the
current controller described in previous section the whole electrical part of induction
motor is reduced to the first order system with time constant τ.
K p
T i ττ T M
K o
m e
ω mref
ω m
Fig. 6.11. The simplified diagram of speed controller
The mechanical part is represented by the integrator with mechanical time constant,
which is created due the inertia of the rotor. The transfer function of the open loop
system is given by the following formula
K
G s o
o( ) =
(6.28)
sTM
( 1 + sτ )
The continues PI regulator has the transfer function which is shown in equation
⎛ 1 ⎞
Gc( s)
= K p
⎜1
+
⎟
(6.29)
⎝ Ti
s ⎠
In the case of such system very often the symmetry or modulus criterion are used.
136

6. ANN sensorless Field Oriented Conrol of IM
Other method is very good known in classical control theory Ziegler-Nichols method
(in continues case) or similar to this method Takahashi algorithm (in discrete case).
6.4.2 Design methods
6.4.2.1 Symmetry and modulus criterion
The most popular criterions in tuning PI regulators in drive system are symmetry and
modulus criterion. In speed control the symmetry criterion is used more often then
modulus criterion. The parameters of PI controllers tuned using these criterions are
collected in the Table 6.1
K p /K o
Modulus
Criterion
T M
2τ
Table 6.1. Modulus and symmetry criterions
Discrete
Modulus
Criterion
0.5
TM
− Ts
2τ + Ts
Symmetry
Criterion
T M
2τ
Discrete
Symmetry
Criterion
2τ
TM
+ Ts
T i T M T M -0.5T s 4τ 4τ+2T s
Where T s is the sampling time in discrete regulator.
Note, that in the case of symmetry criterion the additional first order filter of the
reference value is used. Time constant of this filter should be equal T i .
For T M < 4τ the modulus criterion is more useful,
For τ

6. ANN sensorless Field Oriented Conrol of IM
Table 6.2. Ziegler-Nichols algorithm
K p /K o T i T D
P
PI
PID
T M
τ
0 .9 T M
τ
1 .2 T M
τ
3.3 τ
2 τ 0.5 τ
Table 6.3. Takahashi algorithm
K p /K o T p /T i T D /T p
P
τ
TM
+ Ts
0.9TM
0. 135TM
Ts
0. 27T
PI −
M TsKo
τ + 0.5T
( 0.5 )
2
2
τ + T K ( τ + 0.5 T )
s
s
p
s
1.2TM
0. TM
Ts
6T
PID −
M TsKo
τ + 0.5T
( )
2
2
τ +
30.5 T K
0.( τ + 0.5 T )
s
s
p
s
0 .5
TM
Ko
K pTs
6.4.2.3 PI and IP controllers
Instead of the PI controller sometimes is better use the IP controller, which is similar
to PI. In this controller only the error signal is integrated and the proportional part is
applied to the output signal (see Fig. 6.12).
r
K p
T i
s
PLANT
y
K p
Fig. 6.12. The block diagram of IP controller
138

6. ANN sensorless Field Oriented Conrol of IM
It is easy to show, that IP controller is equivalent to PI regulator with the first order
filter in the input. The equivalent circuit is shown in Fig. 6.13.
r
T i
K p
T i
PLANT
y
Fig. 6.13. The equivalent of IP controller
Note that:
1. The controller tuned by the symmetry could be build using the IP structure
2. Where we add to the remain groups of PI controllers first order filter in the input
we can obtain lower overshooting. This give us the possibility to use IP regulator
with the same tuning criterions like in PI case.
6.5 Rotor and stator resistance adaptation
6.5.1 Introduction
The speed estimator, which is used in the system presented in Fig. 6.7. was
presented in section 5.3. It is easy to see that the following motor parameters have the
influence on this estimator:
• Rotor resistance r r ,
• Stator resistance r s ,
• Main inductance x M ,
• Leakage inductance σx s .
Two of these parameters x M and σx s do not vary with temperature, and can be
measured precisely. Therefore, the main problem is to make speed identification
robust to stator and rotor resistance variations. The solution of this task is to apply the
139

6. ANN sensorless Field Oriented Conrol of IM
same neural network (Eq. 5.23), which was used for speed estimation. Unfortunately,
it is impossible to calculate at the same time instant the value of motor speed and the
rotor resistance (or rotor time constant). The reason of this phenomenon can be
explained based on Fig. 5.13 and Fig. 6.7. It is obvious, that the neural network must
set the value of mechanical speed in the way, which assure correct field-oriented
current transformation. Therefore, the estimated synchronous speed and the load angel
δ should have the correct value. These conditions we can write in the following form:
ω
s
isy
= ˆ ωs
and tg(
δ ) = = Trωr
= Tˆ
r ˆ ωr
(6.30)
isx
From these equations we can conclude that:
• It is impossible to separate the rotor time constant and slip frequency.
• Even, if the rotor time constant is not correct, the current transformation work still
good and there is no influence on the torque production.
• The error of the speed in closed loop caused by the rotor time constant mismatch
is as follows:
⎛ T −
m
1
r
( ˆ )
e
ω = ⎜ ⎟
ω
ˆ r = rr
− rr
T
(6.31)
2
⎝ r ⎠
ψ r
e
⎞
Note, that this error is small, in high speed region with the small value of the load
torque. The influence of the speed and load torque on the speed estimation error is
presented in Fig. 6.14 and Fig.6.15.
6.5.2 Stator resistance adaptation
Stator resistance can be obtained using the same ANN scheme (Fig. 5.13.), which
was constructed to the speed estimation. In this case the Eq. 5.23. can be written as:
140

6. ANN sensorless Field Oriented Conrol of IM
rˆ
Fig. 6.14. The relative speed estimation error for r = 0.7, 0.85,1.15, 1.3
rr
Motor load torque m L =0.2
respectively
rˆ
Fig. 6.14. The relative speed estimation error for r = 0.7, 0.85,1.15, 1.3
rr
Motor load torque m L =0.5.
respectively
141

6. ANN sensorless Field Oriented Conrol of IM
ˆ
x T
i ( k)
=
M
s
x σx
T
⎡ 1
⎢ 1−
⎣ σx
s
r
s
⎛ T
⎜rs
⎝ T
s
N
s
r
( Ψ
⎞⎤
⎟⎥i
⎠⎦
s
r
( k −1)
− x
T
( k −1)
+
s
T σx
N
M
T
i ( k −1))
− j
s
s ωm
T
s
u ( k −1)
s
N
Ψ ( k −1)
+
r
(6.32)
This equation can be rewrite in NN form, with one weight w 3 including r s and one
weight proportional to mechanical speed ω m (w 2 ).
iˆ
s ( k)
= w1
( ψ ( k −1)
− xM
is
( k −1))
+ w2
jψ
( k −1)
+
r
r
w3i
s ( k −1)
+ w4us
( k −1)
(6.33)
It is possible to estimate the mechanical speed and stator resistance in one time, using
back-propagation learning algorithm for the ANN defined by Eq. 6.33, and setting
only weights w 2 and w 3 . This approach gives us the adaptation of the stator resistance
in the following form:
rˆ
= rˆ
+ η
α
s
s
1 ( eα isα
+ eβisβ
) − 1∆w
2
(6.34)
where e is defined by Eq. 5.25 and η 1 is the learning rate for stator resistance. This
adaptation should be performed only in low speed region, where the influence of the
stator resistance on the system behaviour is significant. In other situation the
adaptation mechanism should be turn off, because using of this estimator for high
speeds can give not correct value of estimation.
6.5.3 Rotor resistance adaptation
As it was mentioned, it is impossible to estimate rotor resistance and
mechanical speed simultaneously. There are two ways, to omit this problem [135]:
• By adding additional ac signal to flux command component
• By tracking the changes of stator resistor estimated value.
142

6. ANN sensorless Field Oriented Conrol of IM
The first method is more complicated, and it is not very easy for implementation. The
second approach is very simple, but it has the disadvantage that we must know the
ratio of the values of stator and rotor resistance. The changes of these resistances are
caused by the temperature variations. For this reason, there is the good approximation
to assume that this ratio is constant and equal r sr .
The algorithm is as follows:
1) Calculate the estimation of r s according to Eq. 6.34.
2) Calculate the estimation of rotor resistance according to
rˆ = rsrrˆ
s
(6.35)
These calculations are performed only in low speed region, where the influence of
stator resistance is more significant. The adaptation process for speed ω m =0.05 and
load torque m L =0.2 is presented in Fig. 6.36. and Fig. 6.37.
Note that the above procedure is possible only in the proposed ANN presented in
Fig. 5.14. and not possible in structure proposed in [130] (Fig. 5.11).
Fig. 6.36. The r r adaptation process in IFOC system with ANN speed estimator.
Mechanical speed ω m =0.05 and load torque m L =0.2
143

6. ANN sensorless Field Oriented Conrol of IM
Fig. 6.37. The r r adaptation process in IFOC system with ANN speed estimator.
Mechanical speed ω m =0.05 and load torque m L =0.2
144

7. Simulation and experimental results
7. SIMULATION AND EXPERIMENTAL RESULTS
7.1. Introduction
In this chapter the simulation and experimental results obtained in the system
described in Chapter 6 will be shown. The parameters of this system are presented in
Appendix A3. The experimental set-up is described in Appendix A2. The steady state
behaviour as well as the dynamic waveforms will be presented and discussed. The
influence of the learning rate on the speed estimator is shown, and the short
discussion, how to choose this coefficient is made.
7.2. The choice of the learning rate
The influence of learning rate on the NN estimator behaviour in steady state
operation is shown in Fig. 7.1. It can be observed that the higher learning rate causes
bigger ripples in estimated speed. However, the dynamic behaviour of the estimator
with the smaller learning rate could be not correct and the estimated speed could not
follow the real mechanical speed of the induction motor. This situation is presented in
Fig. 7.2., where the dynamic results of the NN speed estimator are shown.
It is possible to conclude that the learning rate should be big enough to achieve fast
response of speed estimator and small enough to avoid big ripples in steady state
operation. In the system, which is presented in this thesis, the value of the learning
rate is assumed η=0.1.
145

7. Simulation and experimental results
Fig. 7.1. Influence of learning rate on the NN estimator behaviour in steady state
(η=0.02, η=0.2, η=2.0 from upper to lower figure respectively).
On the left – experimental results. On the right – simulation results
Fig. 7.2. Influence of learning rate on the NN estimator behaviour in dynamic state
Speed step response: lower fig.-speed from encoder, upper fig.-speed from estimator.
left fig. present results for η=0.01, rigth fig. present results for η=0.001
146

7. Simulation and experimental results
7.3. Steady state behaviour
The simulation and experimental results obtained in steady state for the system
described in the previous chapter are presented in Fig. 7.3-Fig. 7.20.
The first part of these graphs (Fig. 7.3.-Fig. 7.11) corresponds to the system
with measured speed taken to the feedback and coordinate transformation. These
investigations have been performed to show the behaviour of the FOC system,
without influence of the speed estimation. In these graphs estimated speed, stator
phase current, rotor flux component and electromagnetic torque are shown, for
different values of the mechanical speed and load torque. Note that the bahaviour of
the system in steady state is correct and the simulation results are similar to the
experimental ones.
The second part of graphs (Fig. 7.12-Fig. 7.20) corresponds to the system with
estimated speed taken to the feedback and coordinate transformation. These results
confirm the good behaviour of neural network speed estimator.
Figure 7.3 Steady state for the induction motor controlled via FOC with the encoder
speed signal taken to feedback and transformation ( ω m = 0.1p.
u ; m L = 0 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
147

7. Simulation and experimental results
Figure 7.4 Steady state for the induction motor controlled via FOC with the encoder
speed signal taken to feedback and transformation ( ω m = 0.5p.
u ; m L = 0 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
Figure 7.5 Steady state for the induction motor controlled via FOC with the encoder
speed signal taken to feedback and transformation ( ω m = 1.0p.
u ; m L = 0 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
148

7. Simulation and experimental results
Figure 7.6. Steady state for the induction motor controlled via FOC with the encoder
speed signal taken to feedback and transformation ( ω m = 0.1p.
u ; m L = 0.2 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
Figure 7.7. Steady state for the induction motor controlled via FOC with the encoder
speed signal taken to feedback and transformation ( ω m = 0.5p.
u ; m L = 0.2 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
149

7. Simulation and experimental results
Figure 7.8. Steady state for the induction motor controlled via FOC with the encoder
speed signal taken to feedback and transformation ( ω m = 1.0p.
u ; m L = 0.2 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
Figure 7.9. Steady state for the induction motor controlled via FOC with the encoder
speed signal taken to feedback and transformation ( ω m = 0.1p.
u ; m L = 0.5p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
150

7. Simulation and experimental results
Figure 7.10. Steady state for the induction motor controlled via FOC with the encoder
speed signal taken to feedback and transformation ( ω m = 0.5p.
u ; m L = 0.5p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
Figure 7.11. Steady state for the induction motor controlled via FOC with the encoder
speed signal taken to feedback and transformation ( ω m = 1.0p.
u ; m L = 0.5p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
151

7. Simulation and experimental results
Figure 7.12. Steady state for the induction motor controlled via FOC with estimated
speed signal taken to feedback and transformation ( ω m = 0.1p.
u ; m L = 0 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
Figure 7.13. Steady state for the induction motor controlled via FOC with estimated
speed signal taken to feedback and transformation ( ω m = 0.5p.
u ; m L = 0 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux,
4) electromagnetic torque.
152

7. Simulation and experimental results
Figure 7.14. Steady state for the induction motor controlled via FOC with estimated
speed signal taken to feedback and transformation ( ω m = 1.0p.
u ; m L = 0 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
Figure 7.15. Steady state for the induction motor controlled via FOC with estimated
speed signal taken to feedback and transformation ( ω m = 0.1p.
u ; m L = 0.2 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
153

7. Simulation and experimental results
Figure 7.16. Steady state for the induction motor controlled via FOC with estimated
speed signal taken to feedback and transformation ( ω
m
= 0.5p.
u ; m L = 0.2 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
Figure 7.17. Steady state for the induction motor controlled via FOC with estimated
speed signal taken to feedback and transformation ( ω
m
= 1.0 p.
u ; m L = 0.2 p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
154

7. Simulation and experimental results
Figure 7.18. Steady state for the induction motor controlled via FOC with estimated
speed signal taken to feedback and transformation ( ω
m
= 0.1p.
u ; m L = 0.5p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
Figure 7.19. Steady state for the induction motor controlled via FOC with estimated
speed signal taken to feedback and transformation ( ω
m
= 0.5p.
u ; m L = 0.5p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
155

7. Simulation and experimental results
Figure 7.20. Steady state for the induction motor controlled via FOC with estimated
speed signal taken to feedback and transformation ( ω
m
= 1.0 p.
u ; m L = 0.5p.
u ).
Experimental and simulation results:
1) estimated speed, 2) stator phase current, 3) rotor flux component,
4) electromagnetic torque.
In the end of this subsection the rms of speed estimation error divided by the
measured speed in percent (rms%), and the mean value of error modulus divided by
measured speed in percent (jeps%) as the function of mechanical speed in steady state
is presented. Note, from these graphs (Fig. 7.21, Fig. 7.22.), that in the wide range of
the speed region the estimation error is below 1%. Only for the small values of the
speed and the values lying in neighborhood of the ω m =1 p.u., the error is bigger.
In the small speed region the bigger error is caused by the influence of the rotor flux,
which in this region is calculated not precisely.
The other reason of the bigger estimation error is in high-speed region. In this case the
influence of the sampling time caused, that the calculations for faster signals are
performed with the raised error.
156

7. Simulation and experimental results
Fig. 7.21. The rms%=(e est,rms /ω m )*100% as the function of the mechanical speed in
steady state.
Fig. 7.22. The jeps%=(e est,jeps /ω m )*100% as the function of the mechanical speed in
steady state.
157

7. Simulation and experimental results
7.4. Dynamic behaviour
The simulation and experimental results obtained in dynamic state for the induction
motor controlled via FOC are presented in Fig. 7.23-Fig. 7.40.
The presented graphs, as in previous subsection, are divided into two parts. The first
part of graphs (Fig. 7.23.-Fig. 7.31) corresponds to the system with measured speed,
and the second part (Fig. 7.32-7.40) with the estimated speed, taken to the feedback
and coordinate transformation. The speed step responses and speed reversals are
presented in Fig. 7.23.-Fig. 7.26 and Fig. 7.32.-7.35. respectively. The response time
of the system with estimator is only about 10% longer compare to this one with speed
sensor. Besides, in Fig. 7.27. and Fig.7.36. the load torque step response is drawn. In
these graphs reference and mechanical speed, rotor flux magnitude and
electromagnetic torque are shown. In this case the speed error area is a little bit bigger
in system with estimator. Note, that the bahaviour of the system in dynamic state and
the results confirm the good behaviour of neural network speed estimator.
The rest of graphs (Fig. 7.28-Fig. 7.31 and Fig. 7.37-Fig. 7.40) show the decoupling
of the current controllers in x and y-axes
Figure 7.23. Speed step response for the induction motor controlled via FOC with the
encoder speed signal taken to feedback and transformation ( ω m = 0.0
→ 0. 1).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) rotor flux amplitude,
4) electromagnetic torque.
158

7. Simulation and experimental results
Figure 7.24 Speed step response for the induction motor controlled via FOC with the
encoder speed signal taken to feedback and transformation ( ω m = 0.0
→ 0. 6 ).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) amplitude of rotor flux,
4) electromagnetic torque.
Figure 7.25. Speed reversal for the induction motor controlled via FOC with the
encoder speed signal taken to feedback and transformation ( ω m = −0.1→
0. 1 ).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) amplitude of rotor flux,
4) electromagnetic torque.
159

7. Simulation and experimental results
Figure 7.26. Speed reversal for the induction motor controlled via FOC with the
encoder speed signal taken to feedback and transformation ( ω m = −0.5
→ 0. 5).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) amplitude of rotor flux,
4) electromagnetic torque.
Figure 7.27. Load torque step response for the induction motor controlled via FOC
with the encoder speed signal taken to feedback and transformation ( m L = 0.0
→ 0. 4 ).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) amplitude of rotor flux,
4) electromagnetic torque.
160

7. Simulation and experimental results
Figure 7.28. Decoupling in y-axis with the encoder speed signal taken to feedback and
transformation. Experimental results ( i sxc = 0.1→
0. 5, time=1s):
1) x-axis reference current, 2) x-axis current, 3) y-axis reference current,
4) y-axis current.
Figure 7.29. Decoupling in y-axis with the encoder speed signal taken to feedback and
transformation. Experimental results ( i sxc = 0.1→
0. 5, time=5ms):
1) x-axis reference current, 2) x-axis current , 3) y-axis reference current ,
4) y-axis current
161

7. Simulation and experimental results
Figure 7.30. Decoupling in x-axis with the encoder speed signal taken to feedback and
transformation. Experimental results ( i = −0.3
→ 0. 3, time=1s):
1) x-axis reference current, 2) x-axis current, 3) y-axis reference current,
4) y-axis current.
syc
Figure 7.31. Decoupling in x-axis with the encoder speed signal taken to feedback and
transformation. Experimental results ( i = −0.3
→ 0. 3, time=5ms):
1) x-axis reference current, 2) x-axis current, 3) y-axis reference current,
4) y-axis current.
syc
162

7. Simulation and experimental results
Figure 7.32. Speed step response for the induction motor controlled via FOC with the
estimated speed signal taken to feedback and transformation ( ω m = 0.0
→ 0. 1 ).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) rotor flux amplitude,
4) electromagnetic torque.
Figure 7.33. Speed step response for the induction motor controlled via FOC with the
estimated speed signal taken to feedback and transformation ( ω m = 0.0
→ 0. 6 ).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) rotor flux amplitude,
4) electromagnetic torque.
163

7. Simulation and experimental results
Figure 7.34. Speed reversal for the induction motor controlled via FOC with the
estimated speed signal taken to feedback and transformation ( ω m = −0.1→
0. 1 ).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) amplitude of rotor flux,
4) electromagnetic torque.
Figure 7.35. Speed reversal for the induction motor controlled via FOC with the
estimated speed signal taken to feedback and transformation ( ω m = −0.5
→ 0. 5).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) amplitude of rotor flux,
4) electromagnetic torque.
164

7. Simulation and experimental results
Figure 7.36. Load torque step response for induction motor controlled via FOC with
the estimated speed signal taken to feedback and transformation ( m L = 0.0
→ 0. 4 ).
Experimental and simulation results:
1) reference speed, 2) mechanical speed, 3) amplitude of rotor flux,
4) electromagnetic torque.
Figure 7.37. Decoupling in y-axis with estimated speed signal taken to feedback and
transformation. Experimental results ( i sxc = 0.1→
0. 5, time=1s):
1) x-axis reference current, 2) x-axis current, 3) y-axis reference current,
4) y-axis current.
165

7. Simulation and experimental results
Figure 7.38. Decoupling in y-axis with estimated speed signal taken to feedback and
transformation. Experimental results ( i sxc = 0.1→
0. 5, time=5ms):
1) x-axis reference current, 2) x-axis current, 3) y-axis reference current,
4) y-axis current.
Figure 7.39. Decoupling in x-axis with estimated speed signal taken to feedback and
transformation. Experimental results ( i = −0.5
→ 0. 5 , time=1s):
1) x-axis reference current, 2) x-axis current, 3) y-axis reference current,
4) y-axis current.
syc
166

7. Simulation and experimental results
Figure 7.40. Decoupling in x-axis with estimated speed signal taken to feedback and
transformation. Experimental results ( i = −0.5
→ 0. 5 , time=5ms):
1) x-axis reference current, 2) x-axis current, 3) y-axis reference current,
4) y-axis current.
syc
167

8. Conclusions
8. CONCLUSIONS
The research results presented in this thesis based on the simulation and experimental
investigations can be summarized as follows:
In case of the ANN based PWM current controllers:
ANN COMPARATOR
• The neural network (ANN) based controllers are an interesting alternative to
the conventional regulators;
• The main advantages of the ANN controllers include robustness, learning
ability and insensitiveness to the parameter changes;
• The off-line trained multi-layers nonlinear ANN comparator has operation
characteristics similar to the delta modulators. This is because the feedforward
ANN cannot implement characteristic with hysteresis. Therefore, to obtain
comparable accuracy of the current generation as in controller with three
hysteresis comparators much higher switching frequency has to be applied.
• The simple perceptron based ANN can be applied instead of the multilayer
ANN. The results obtained in these two models are almost the same.
OPTIMAL MODE ANN
• The NN optimal regulator switches only between adjacent active vectors and
zero voltage vectors. There are no ±1 transitions in the line to line voltage
which reduces the stress on the inverter switching devices,
• The RMS current error of the proposed optimal NN regulator is superior to the
conventional Delta Regulator and the NN regulator presented in Section 4.3.
• Three layers feedforward NN is able to regulate PWM inverter output current
very well without on-line calculations needed in the case of the Optimal
Regulator and have almost the same control quality as this optimal regulator.
• The off-line NN can work faster, in the hardware implementation based on
microprocessor or DSP system, compare to the Optimal Regulator. From this
reason one can expect possibility of increasing the PWM frequency.
168

8. Conclusions
In case of the ANN based speed estimator
• Application of artificial NN speed estimators for PWM inverter-fed
induction motors creates many new schemes.
• One of the simplest NN estimator schemes is based on combination of
the voltage and current rotor flux estimation proposed in [115].
• This thesis shows the possibility of improvement of the classical
scheme, using new structure (Section 5.3). The implementation of the
improved system and new NN method based on digital signal processor
TMS320C31 is presented and experimental results are shown.
• The speed tracking by the ANN based estimator is good in steady state
and in dynamical state.
In the case of the sensorless Field Oriented Control (FOC)
• The steady state operation and dynamical behaviour is correct.
• There is a very fast torque response,
• The system allows the independent control of rotor flux and motor
torque,
• There is no problem with start and stop of the system,
• Even without speed sensor the system behaviour is correct in low speed
region,
• Sensorless FOC of induction motor, described in this thesis, could be
used in the high performance motor drives of the electrical vehicles (for
example hybrid cars) and in the factories, in which the measurement of
the mechanical speed is expensive or even impossible
169

References
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discrete-time systems", IEEE-IECON Conference Record, pp. 1454-1458, 1991
[151] J. Tanomaru and S. Omatu, "Process control by on-line trained neural
controllers", IEEE Transaction on Industrial Electronics, vol. 39, no. 6, pp.
511-521, 1992
[152] P. J. Werbos, "Artificial neural networks: General Capabilities and Control
Applications - Tutorial", IEEE-IECON Conference Record, pp. 5-66, 1991
[153] B. Widrow and M. A. Lehr, "30 Years of adaptive neural networks: perceptron,
madaline, and backpropagation", Proceedings of IEEE, vol. 78, no. 9, pp. 1415-
1442, 1990.
179

A1. Description of the simulation program
A1. Description of the simulation program
A1.1.
Structure of the Program
Program consist of the following files:
• Main file (include parts described in Sections A1.1 - A1.3.) file rootmain.c
• Control part (section A1.4) file rootster.c
• Configuration and data files files readpar.c, simfile.c
• Graphics file simgraph.c
• Menu file simmenu.c
• Procedure for differential equations solution (RKF45) file rkf45.c
Declaration of variables and procedures are located in following overhead files:
rootdef.h, rootdefe.h, rootmain.h, sim.h, simfile.h, simgraph.h, simmenu.h.
It should be noted that user could modify all source and header files with the first part
of the name root-
A1.2.
Configuration and Data Files
A1.2.1.
Introduction
The program allows you to read the configuration parameters and data from
one file and write it to other file(s). After the program is run such a parameters and
data as configuration, graphics, load, control, numerical, are read from the following
files:
• root.cfg
• graph.dat
• mot.dat
• rootctrl.dat
• rootnum.dat
• rootint.dat
180

A1. Description of the simulation program
A1.2.2.
Configuration File
A1.2.2.1.
Listing configuration file root.cfg
# Config file created by C:\USR\ROOT.EXE
graph.dat
mot.dat
rootctrl.dat
rootnum.dat
rootint.dat
root
names
PAGE 1 WINDOW 1
PAGE 1 WINDOW 2
PAGE 1 WINDOW 3
PAGE 1 WINDOW 4
PAGE 2 WINDOW 1
PAGE 2 WINDOW 2
PAGE 2 WINDOW 3
PAGE 2 WINDOW 4
file
time isalf isbet ubet ualf vec nrs
screen 2 2 2 2
time omega_m 1 1 red
time isalf 1 2 red
time me 1 3 red
time psira 1 4 red
psira psirb 2 1 red
isalf isbet 2 2 red
ualfc ubetc 2 3 red
ualf ubet 2 4 red
scale
1 1 0 1.2
1 2 -8 8
1 3 -5 5
1 4 -1.2 1.2
2 1 -1.5 1.5 -1.5 1.5
2 2 -10 10 -10 10
2 3 -3 3 -2 2
2 4 -3 3 -2 2
181

A1. Description of the simulation program
A1.2.2.2.
Description of the configuration file root.cfg.
File root.cfg (see Section A1.2.1) includes:
h # comments line;
h names of data files, as: graphic file (graph.dat), induction motor parameters
file (mot.dat), numerical file (rootnum.dat), control file (rootctrl.dat), integer file
(rootint.dat);
h initial name of the file (here for example root) in which (if required by user)
simulation results are stored (program automatically extents the name with three
digits of simulation number: 001, 002, etc.);
h names of graphics windows;
h variables which should by stored in file during simulation;
h number of windows for graphic pages.
For example command: screen 2 2 1 2,
means that there are 2x2 diagrams versus time in graphic window
No 1 (time), and 1x2 function diagram in graphic window No 2;
h axes definitions for diagrams. On the one diagram several function can be
shown, but in the same scale.
For example line: time me 1 3 red,
means that diagram 3 in graphic window No 1 present the torque me versus time,
with red colour.
h scales definition for each axes. For the first graphic page, which present
diagrams versus time, only Y scale is required. For the second page scaling for X
and Y axes should be defined.
A1.2.3.
Data files
A1.2.3.1.
Listing data files
h File graph.dat with graphic parameters :
182

A1. Description of the simulation program
# parameter file created by C:\USR\ROOT.EXE
graphdrv 1
graphmode 1
npage 1
page_op 1
bkc1 7
bkc2 3
blc -1
ac 1
bc 3
ec 1
hc 9
gc 8
tc 9
pc 1
stc 8
gls 1
gul 17500
flag_hw 4
mlbc 1
mlfc 7
mwidth 15
iwidth 15
dwidth 25
doslines 10
doswidth 50
mboption 1
mbfc 14
mbtc 1
fsg 4
fsm 4
fc 1
mc 14
gridx 1
gridy 1
nxt 5
nyt 10
xnmb 3
ynmb 3
vnmb 3
dstep 10
h File mot.dat with induction motor parameters:
# parameter file created by C:\USR\ROOT.EXE
183

A1. Description of the simulation program
rs 0.0314
xs 2.184
rr 0.0464
xr 2.237
xM 2.133
Tm 0.2
omega_n 314.159
n_s 1
mL 0
h File rootctrl.dat with control parameters:
# parameter file created by C:\USR\ROOT.EXE
ud 2.5
tgen 0.0002
amps 1
ampsin 0.85
h File rootint.dat with integer parameters:
# parameter file created by C:\USR\ROOT.EXE
flag_f 0
npl 0
flag_ctrl 0
flag_dscrt 0
max_nsub 50
File rootnum.dat with numerical data:
# parameter file created by C:\USR\ROOT.EXE
tb 0
te 0.17
tsamp 1e-05
tprint 1e-05
tstop 1e4
relerr 1e-06
abserr 1e-06
omega_m 0.0
psira 0.0
psirb 0.0
isalf 0.0
isbet 0.0
theta 0.0
184

A1. Description of the simulation program
A1.2.3.2.
Short description of selected parameters
Most important graphic parameters are:
• graphics driver selection:
graphdrv 0 - Hercules
1 - VGA
2 - SVGA16
3 - SVGA256
4 - VESA16
For:
- graphdrv 0 ( Hercules graphics),
following parametr should be set:
- graphmode 0 dla HERCMONOHI 720*348, mono, 2 graphic pages;
- graphdrv 1 (VGA graphics),
following parametr should be set:
- graphmode 0 dla VGALO 640*200, 16 colours, 4 graphic pages;
- graphmode 1 dla VGAMED 640*350, 16 colours, 2 graphic pages;
- graphmode 2 dla VGAHI 640*480, 16 colours, 1 graphic page;
- graphdrv 2 (tzn. SVGA16),
following parametr should be set::
- graphmode 0 dla SVGA 320*200, 16 colours;
- graphmode 1 dla SVGA 640*200, 16 colours;
- graphmode 2 dla SVGA 640*350, 16 colours;
- graphmode 3 dla SVGA 640*480, 256 colours;
- graphmode 4 dla SVGA 800*600, 16 colours;
- graphmode 5 dla SVGA 1024*768, 16 colours;
- graphdrv 3 (tzn. SVGA256),
following parametr should be set:
- graphmode 0 dla SVGA 320*200, 256 colours,
- graphmode 1 dla SVGA 640*400, 256 colours;
- graphmode 2 dla SVGA 640*480, 256 colours;
- graphmode 3 dla SVGA 800*600, 256 colours;
185

A1. Description of the simulation program
- graphmode 4 dla SVGA 1024*768, 256 colours;
• Selection of graphic pages number:
- npage = number of pages - 1;
• if npage is 0 then we have options:
- page_op 0 without second graphic page;
- page_op 1 second page below the first ones;
- page_op 2 second graphic page on the right relative to the first;
- page_op 3 without first graphic page;
• header mode - flag_hw;
• grid on/off - gridx, gridy;
• number of ticks on axes - nxt, nyt;
• number of significant digits on axes and overheads (window title) - xnmb, ynmb,
vnmb;
• windows width - ...width (i.e. all variables with this ending);
• colours - ...c (i.e. all variables with this ending);
• how often the results are displayed - dstep;
Induction motor parameters:
• resistances and reactances - rs, xs, rr, xr, xM;
• mechanical (acceleration) time constant - Tm;
• nominal speed - omega_n;
• reference synchronous speed - n_s;
• load torque - mL;
Control parameters:
• DC link voltage - ud;
• triangular carrier period - tgen;
• sinus wave amplitude - ampsin;
• triangular carrier amplitude - amps;
Integer parameters:
• writing to file - flag_f;
• number of output file - npl;
186

A1. Description of the simulation program
• control selection - flag_ctrl;
• discrete or continuous system - flag_dscrt;
• maximum steps number in RKF45 numerical procedure - max_nsub;
Numerical parameters:
• starting and final simulation time - tb, te;
• sampling time - tsamp;
• how often results will be written to file - tprint;
• simulation stops - tstop;
• relative and absolute accuracy of RKF45 numerical procedure - relerr, abserr;
• initial values of state variables:
- mechanical angular speed of IM - omega_m;
- rotor flux in alpha-beta coordinates - psira, psirb;
- stator current in alpha-beta coordinates - isalf, isbet;
- position of IM shaft - theta;
A1.3.
Description of selected variables
Variable, which we can read from file and change during program execution,
are calculated in each step and can be presented as diagrams (oscillograms) or written
to output file in text format. In the program are integer and real variables.
As example of real variables used in the program are:
• Stator flux components in alpha-beta coordinates - psisa, psisb;
• electromagnetic torque - me;
• inverter output voltages in alpha-beta coordinates - ualf, ubet;
• inverter output voltages (3-phase) - uA, uB, uC;
• inverter voltage commands in alpha-beta coordinates - ualfc, ubetc;
• voltages commands (3-phase)- uAc, uBc, uCc;
• stator current amplitude (modulus) - is;
• stator currents (3-phase) - iA, iB, iC;
• time - time.
187

A1. Description of the simulation program
As example of integer variables used in the program are:
• switch states of inverter - d1, d2, d3;
• number of applied inverter voltage vector - vec;
• number of inverter switchings - nrs;
A1.4.
Menu options
The program can change and store selected parameters. In each moment of
execution the program can be stopped (by appropriate button) and arbitrary graphics
and/or simulation parameters can be changed. Also, the results can be observed.
Additionally, each variable or parameter can be seen in edition window. It is possible
to write and read new and old configuration files as well as data files with name given
by user.
Examples of Menu options:
• P (or M-P) - activation of parameter window. To change arbitrary parameter,
write the name of the parameter, push Enter and write the new
value.
• F (or M-F) - activation of parameter and configuration window sub-menu:
G - write current graphics parameters to file with user defined name;
M - write current induction motor parameters to file with user defined
name;
N - write current numerical parameters to file with user defined
name;
T - write current control parameters to file with user defined name;
I - write current integer parameters to file with user defined name;
C - write all current parameters to files with user defined names. This
option is equivalent to all above and S option;
D - write all current parameters to files with extension dft.
Configuration data are written to the file default.cfg;
S - actualization of configuration parameters in configuration file to
current values;
188

A1. Description of the simulation program
• L (or M-L) - activation of reading parameters and configuration file window
submenu:
G - read new graphics parameters from file with user defined name;
M - read new induction motor parameters from file with user defined
name;
N - read new numerical parameters from file with user defined name;
T - read new control parameters from file with user defined name;
I - read new integer parameters from file with user defined name;
C - read new configuration parameters from configuration file with
user defined name;
D - read all parameters from configuration file default.cfg;
S - change configuration parameters to current values existing in
configuration file;
• O (or M-O) - activation of changes and view window submenu:
1) name of output file in which variable will be stored during simulation;
2) list of variables which values will be stored during simulation;
3) window variables and coulors of diagrams in selected windows;
4) axes scaling in selected windows;
5) windows names;
Modification of variables according to 2) and 3) can be done using commands as
add, new, del. To remove all window variables, a command clear can be used.
N - change name of output file;
F-W - view of variables, which values will be stored during simulation;
V-W - view of window variables and diagram colours in selected
window;
A-W - view of axes scaling in selected windows;
D-W - view of selected windows names;
O-M - selection (modification) of variables, which values will be stored
during simulation.
For example, to introduce a new variable isalf, write: add isalf
To create a new set of variables, write for example:
new isalf isbet
189

A1. Description of the simulation program
To delete a variable write for example: del isalf
S-M - selection (modification) of window variables and coulors of
diagrams in selected window.
For example to select in window 1 on the 1st graphic page
electro-magnetic torque waveform drawn with red line: select
submenu: Page 1 Window 1,
and than write in edit window: add time me RED
C-M - selection of axes scaling in selected window. For the first graphic
page only Y scale is required (time diagrams) whereas for second
graphic page both X and Y scaling is necessary.
For example to change scale in the 2 nd window on the 1 st graphic
page, write: 1 2 -0.5 0.5
And for the 1 st window of the 2 nd graphic page, write:
2 1 0 0.15 -0.01 0.01
W-M - change name of selected window.
• V(or M-V)- - activation of view window submenu:
1) name of configuration file;
2) names data files;
3) first part of name of output file;
4) all parameters and variables;
5) location of root.exe file in catalog
C -name of current configuration file;
G - name of current graphic parameters file;
R - name of current induction motor parameters file;
N - name of current numerical data file;
T - name of current control data file;
I - name of current integer parameters file;
O - initial name of output file;
P -activation of edit window to view all parameters and variables;
S - location of the file root.exe in catalog.
190

A1. Description of the simulation program
A1.5.
Design example using ANN-LAB software
As the example, how to use this program to simulate the ANN optimal mode current
controller (see section 4.4), the algorithm divided in few steps is presented as follows.
A1.5.1.
General information about the ANN model:
A1.5.1.1.
Limitations
There are some limitations in the ANN structure:
max number of neurons 40
max number of weights 300
max number of inputs 10
max number of outputs 10
A1.5.1.2.
ANN structure (file: int.DATA)
Weights description is: w xyz,
where x denoted No. of layer, y denoted No. of input connection, z denoted No. of
output connection
x y z are numbers 0 9
A1.5.1.3.
Data scaling:
There are adjustable gain factors on ANN inputs: kr0 - kr9
191

A1. Description of the simulation program
A1.5.2.
Off-line trained ANN design procedure for using as PWM Current
Controller
The simulation algorithm consists of the following steps:
A1.5.2.1.
Creating a training file: nnf000.asc
⎝ Run opt.exe with data file opt.cfg for 3 (or more) values of speed (steady state),
⎝ Store the simulation results as files nnf001.asc, nnf002.asc, nnf003.asc (by stetting
flag_f to 1, and variable npl to 1,2,3 respectively)
⎝ Create a sum file under DOS:
nnf001.asc+nnf002.asc+nnf003.asc, and change the name of the resulting file to:
nnf000.asc
A1.5.2.2.
Training ANN
⎝ Execute opt.exe with data file nn3w.cfg for different:
- learning factors eta,
- forgetting factors mu.
Usually training time is about 10 s
⎝ Save data (F) and create numerical data (N) file weights.dat
⎝ Edit file weights.dat and change the regulation time (tb start and te final time) which
is much shorter compare to training time
A1.5.2.3.
Running ANN as PWM Current Controller
⎝ Go to file: om3.cfg (or om3a.cfg) and write in the numerical data (3 row) the name
of the new created in point 2 file weights.dat with ANN weights.
⎝ Run opt.exe with data file om3.cfg
Observe the performance factors: PSE and PR.
If PSE is lower as 0.75 reaped the procedure and go to point 1.
192

A1. Description of the simulation program
A1.6.
Summary
The presented program has following features and advantages:
• is written in C language,
• fast operation,
• high numerical accuracy,
• user friendly graphic interface,
• simply extending and modification of existing controllers,
• easy implementation even complex control structures,
• possibility to read and write parameters to files,
• flexible graphics configuration,
• possibility to change parameters values during simulation.
193

A2. Laboratory setup
A2. Laboratory setup.
A2.1.
System configuration
The practical results have been made on the laboratory setup based on the
dSpace board DS1102 which is controlled by Texas Instrument TMS320C31 3rd
generation floating-point Digital Signal Processor (master processor) and the
TMS320P14 (slave processor).
Inverter
Reversable
converter
Encoder
Tachogenerator
Reference signals
Feedback signals
Induction motor
DC motor
RS232
DSP SYSTEM
dSPACE
TMS 320C31
Measurement system
RS232
Host computer
Local computer
Fig. A2.1 Laboratory setup
194

A2. Laboratory setup
Fig.A2.1 presents the system configuration that consists of the following components:
- Machine kit – induction motor and the DC motor as a load,
- 3 phase inverter with IPM modules,
- Reversable converter for DC motor control,
- dSpace DC1102 board inside PC,
- Isolated system between dSpace board and the inverter,
- Measurement system builds on the LEM converters.
A2.2.
Inverter
The power circuit contains two Mitsubishi Electric modules: one as a rectifier and
the second one as an inverter based on IGBT transistors. The IPM consists seven
transistors, the extra one works as a security in case to high DC voltage.
B W V U
D1 D2 D3
+
D7
T7
T6
T5
RT1
t
R1
C1
IGBT
IGBT
IGBT
RT2
RT3
t
t
C11
1.5u/750V
T1
T2
T3
T4
D4 D5 D6
+
C2
R2
IGBT
IGBT
IGBT
IGBT
RELAY 4PST
Fig. A2.2 High power circuit
The optic fibbers are used as interface between PWM-VSI and the DSP controller
board, which provide good isolation between dSpace board and inverter. The inverter
parameters are as follows:
- Voltage 1200 V,
- Current 50 A,
- Switching frequency 15kHz,
- Dead time 3µs.
195

A2. Laboratory setup
A2.3.
dSpace DS1102 board.
The dSPACE is based on the Texas Instrument TMS320C31 3rd generation
floating-point Digital Signal Processor (master processor) and the TMS320P14 (slave
processor). The master processor builds the main processing unit providing fast
instruction cycle time for numeric intensive algorithms. The slave processor is
responsible for PWM signal generation. A PC is used for software development and
the results visualisation.
The dSpace board consists of the following components:
- A/D converters,
- D/A converters,
- I/O circuits,
- Encoder co-operation circuit.
128kx32
RAM
TMS 320P14
Digital I/O
16-bit ADC 1
Serial
interface
TMS320C31
16-bit ADC 2
12-bit ADC 3
12-bit ADC 4
12-bit DAC 1
Analog/digital I/O connector
JTAG
connection
12-bit DAC 2
12-bit DAC 3
JTAG
Interface
12-bit DAC 4
Encoder 1
Filter
PC/AT Interface
Encoder 2
Filter
PC/AT BUS
Fig. A2.3 DS 1102 board block scheme
196

A2. Laboratory setup
A2.3.1.
The TMS320C31 DSP
The TMS320C31 third generation floating-point DSP is a high performance member
of Texas Instruments’ TMS320 family of VLSI digital signal processor. It performs
parallel multiply and ALU operations on integers or floating-point numbers in a single
cycle. The TMS320C31 supports a large address space with various addressing modes
allowing the use of high-level languages for application development. Some key
features of the TMS320C31 are:
- 50 ns single cycle instruction execution time,
- object code compatible with the TMS320C30,
- Two 1K x 32-bit dual access on-chip data RAM blocks,
- 64 x 32 bit floating-point/integer multiplier and ALU,
- 32-bit barrel shifter,
- Eight 40-bit accumulators,
- Two independent address arithmetic units,
- 2- and 3- operand instructions,
- Serial port,
- DMA controller for concurrent DMA and CPU operation,
- Four external interrupts,
- Two 32-bit timers.
A2.3.2.
A/D Subsystem
The DS1102 contains two types of ACDs:
- Two 16-bit autocalibrating sampling A/D converters with integrated
sample/holds,
- Two 12-bit sampling A/D converters with integrated sample & holds.
All ADCs have single ended bipolar inputs with +-10V input span. All return lines are
connected to system ground.
197

A2. Laboratory setup
Offset
calibration
EEPROM
DAC
IN
+
Sample
&
Hold
12-bit
A/C
EEPROM
DAC
IN
+
Sample
&
Hold
12-bit
A/D
IN
Sample
&
Hold
16
A/D
serial
parallel
calibration
IN
Sample
&
Hold
16 - bit
A/D
serial
parallel
calibration
Offset&Gain
calibration
Fig. A2.4 Block diagram of the AD subsystem
The DS1102 contains two 16-bit charge redistribution ADCs with integrated
sample/holds. Each of the ADCs contains a 16-bit successive approximation (SAR)
type AD converter, a sample/hold circuit and a microcontroller based autocalibraction
circuit. The converter achieves a conversion time of 10 µs. There is also the second
pair 12-bit charge distribution successive approximation ADCs with integrated
sample/hold circuits and a digitally controlled offset calibration units. Each converter
achieves a conversion time of 3 µs.
198

A2. Laboratory setup
A2.3.3.
D/A Subsystem.
The DS1102 contains a quad 12-bit DAC with programmable output voltage ranges.
The DA subsystem consists of four data registers, four output registers, a mode
register and a strobe bit in the IOCTL register.
INPUT
Data
register
Output
register
12-bit
D/A
prog. Output
range
+
Data
register
Output
register
12-bit
D/A
prog. Output
range
+
Data
register
Output
register
12-bit
D/A
prog. Output
range
+
OUTPUT
Data
register
Output
register
12-bit
D/A
prog. Output
range
+
Control
Control logic
EEPROM
&
DAC
Gain
calibration
Reference
offset
calibration
Fig. A2.5 Block diagram of the DA subsystem.
The DACs have single ended voltage outputs with +- 10 V span. The return lines of
the outputs are connected to system ground. Each DACs features a set of two back to
back registers, a data register connected to the data inputs and an output register
connected to the DA converter. This allows to sequentially preload new output values
and then to update the DAC outputs simultaneously by copying the contents of the
data registers to the output registers by a common transfer strobe. The DA subsystem
features a digital controlled offset and gain calibration unit. The circuit is intended to
be used to eliminate the offset and gain errors of the DACs. The calibration unit
199

A2. Laboratory setup
consists of an EEPROM device connected to a DAC. It is adjusted during
manufacturing and doesn’t need to be changed under normal operating conditions.
A2.3.4.
Incremental encoder subsystem.
The DS1102 contains two incremental sensor interfaces to support optical incremental
sensors commonly used in position control. Each interface contains line receivers for
the input signals, a digital noise pulse filter eliminating spikes on the phase lines, a
quadranture decoder which converts the sensor’s phase information to count-up and
count-down pulses, a 24-bit output latch.
25 MHz
RESET
STROBE
Ph 0
Ph 90
Line
receiver
Noise filter
Quadranture
decoder
24-bit position
counter
24-bit output
latch
INDEX
Line
receiver
DSP INT
Fig. A2.6 Block diagram of an incremental encoder interface.
The minimum encoder state width is 120 ns resulting in a maximum count frequency
of 8.3 MHz. Noise pulses shorter than 80 ns are eliminated by the digital noise pulse
filter.
A2.3.5.
Software
The control algorithm is done in high level C language. There are also two others
programs made by dSpace: Cockpit and Trace.
Cockpit is a Windows based graphical application purposive to change program
internal variables. This software provide:
- processor memory cell state tracking,
- processor registers and ports state tracking,
- interactive modification of chosen variables.
200

A2. Laboratory setup
COCKPIT
INACTIVE
COCKPIT
ACTIVE
DSP MEMORY
DSP MEMORY
Cockpit allocated
buffer
data
buffer
serwis code
Data
Data
DSP
application
TRAPU
DSP
application
TRAPU
code
RETS
code
Fig. A2.7 Implementation of COCKPIT on the DSP
A piece of service code is downloaded to the DSP board (see Fig. A2.7 ). The purpose
of this is to copy the contents of all required variables to a small buffer in the DSP
memory. This buffer can be read as one block of data by Cockpit, so that the
communication between the host computer and the signal processor board is
minimized.
Trace is the Windows based application purposive to presentation all DSP programs
signals and variables. This program can be used as an oscilloscope. The basis function
is the same as a Cockpit program.
201

A3. Motor parameters
A3. MOTOR PARAMETERS
A3.1. Parameters used in Chapter 4
DC link voltage = 2.5 pu
Induction motor parameters data (pu):
rr = 0.0464
rs = 0.0314
xr = 2.237
x s = 2.194
x M = 2.133
TM = 0.4 s
A3.2. Parameters used in Chapter 7
DC link voltage = 1.74 pu
Induction motor parameters data (pu):
r r = 0.0543
rs = 0.0543
xr = 1.96
xs = 1.88
x M = 1.96
TM = 0.1 s
T s =350µs
202

A4. Notation
A4. NOTATION
A4.1.
Symbols
• i - current, p.u. value
- i r - rotor current space vector
- i rx , i ry - rotor current vector components of the induction motor in
field-oriented x, y coordinates
- i rα , i rβ - rotor current vector components of the induction motor in
stationary α, β coordinates
- i s - stator current space vector
- i sx , i sy - stator current vector components of the induction motor in
field-oriented x, y coordinates
- i sα , i sβ - stator current vector components of the induction motor in
stationary α, β coordinates
• r - resistance, p.u. value
- r r - rotor resistance
- r s - stator resistance
• T - time constant, absolute value
- T M - inertia time constant of the electric motor
- T N - nominal time constant
- T r - rotor electromagnetic time constant of the induction motor
- T s - sampling time
• u - voltage, p.u. value
- u r - rotor voltage space vector
- u rx , u ry - rotor voltage vector components of the induction motor in
field-oriented x, y coordinates
- u rα , u rβ - rotor voltage vector components of the induction motor in
stationary α, β coordinates
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A4. Notation
- u s - stator voltage space vector
- u sx , u sy - stator voltage vector components of the induction motor in
field-oriented x, y coordinates
- u sα , u sβ - stator voltage vector components of the induction motor in
stationary α, β coordinates
• x - reactance, p.u. value calculated for nominal frequency
- x M - induction motor main reactance
- x r - rotor windings self-reactance
- x s - stator windings self-reactance
- x σ - total leakage reactance of the induction motor
• η- neural network learning rate
• ψ - flux, p.u. value
- ψ r - rotor flux space vector
- ψ rx , ψ ry - rotor flux vector components of the induction motor in fieldoriented
x, y coordinates
- ψ rα , ψ rβ - rotor flux vector components of the induction motor in
stationary α, β coordinates
- ψ s - stator flux space vector
- ψ sx , ψ sy - stator flux vector components of the induction motor in fieldoriented
x, y coordinates
- ψ sα , ψ sβ - stator flux vector components of the induction motor in
stationary α, β coordinates
• σ - total leakage factor
• ω - angular speed, p.u. value
- ω m - angular speed of the motor shaft
- ω r - slip angular speed
- ω s - synchronous angular speed
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A4. Notation
A4.2.
Rectangular coordinate systems
• x, y - field-oriented (rotated) coordinates
• α, β - stator-oriented (stationary) coordinates
A4.3.
Indices
• M - main, magnetizing
• m - mechanical
• N - nominal value
• r - rotor
• s - stator
A4.4.
Abbreviations
• ANN - artificial neural network
• DFOC - direct field-oriented control
• FOC - field-oriented control
• IFOC - indirect field-oriented control
• MNN - multilayer neural network
• PWM - pulse-width modulation
• VSI - voltage-sourced inverter
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