Design of Intelligent Self-Tuning Temperature Controller - Itfrindia.org

INTERNATIONAL JOURNAL OF IMAGING SCIENCE AND ENGINEERING (IJISE) 121
Design of Intelligent Self-Tuning Temperature
Controller for Water Bath Process
1 Melba Mary.P, 2 Marimuthu N.S 3 Albert Singh. N.
1 NCE, Anna University, TamilNadu
2 GCE, 3 College of Engineering, University of Kerala.
1 melbance_2k4@yahoo.co.in , 2 drnsmphd@yahoo.co.in, 3 mailalbertsingh@yahoo.co.in
Abstract - This paper proposes a novel approach based on selftuning
fuzzy logic control and genetic algorithm optimized fuzzy
logic controller, for the design of a temperature control process,
capable of providing optimal performance over the entire operating
range of the process. The proposed control system combines the
advantages of Genetic Algorithm and Fuzzy Logic Control schemes.
In order to evaluate the performance of the proposed control system
methods, results from simulation of the process are presented.
Key Words: Genetic Algorithm (GA), Fuzzy Logic Control
(FLC)
I. INTRODUCTION
FUZZY logic control systems, which have the capability
of transforming linguistic information and expert knowledge
into control signals [1], [2], are currently being used in a wide
variety of engineering applications. The simplicity of
designing these fuzzy logic systems has been the main
advantage of their successful implementation over traditional
approaches such as optimal and adaptive control techniques.
Despite the advantages of the conventional Fuzzy Logic
Controller (FLC) over traditional approaches, there remain a
number of drawbacks in the design stages. Even though rules
can be developed for many control applications, they need to
be set up through expert observation of the process. The
complexity in developing these rules increases with the
complexity of the process. FLC’s also consist of a number of
parameters that are needed to be selected and configured in
prior, such as selection of scaling factors, configuration of the
center and width of the membership functions, and selection
of the appropriate fuzzy control rules.
Due to their learning capability, artificial neural networks
are being sought in the development of neuro-fuzzy
controllers or adaptive FLC’s. Berenji [3] developed a FLC
that is capable of learning as well as tuning of its parameters
by using neural length strings. In another development,
Shimojima et al. [4] used GA to tune a type of Radial Basis
Function (RBF) based fuzzy model, with only three fuzzy
memberships for each fuzzy variable. Jang [9] developed a
self-learning FLC based on a neural network trained by
temporal back-propagation. Lee et al. [5] proposed a selforganizing
fuzzified basis function based on the competitive
learning scheme. Recently, Ling [6] proposes a model-based
fuzzy gain scheduling technique and applies it to the real-time
control of laboratory-scale water–gas shift reactor. However,
GA’s are currently being investigated for the development of
adaptive or self-tuning fuzzy logic control systems. This paper
IJISE,GA,USA,ISSN:1934-9955,VOL.1,NO.4, OCTOBER 2007
presents a self-tuning fuzzy and also a fuzzy logic controller
where its gain parameters can be tuned simultaneously by GA.
II. PROBLEM FORMULATION
The continuous-time temperature control system [7] is
described as
dy( t)
f ( t)
Yo − y(
t)
= +
…..(1)
dt C RC
where t denotes time, y(t) is the output temperature in °C, f
(t) is the heat flowing inward the system, Y o , is the room
temperature (constant, for simplicity), C denotes the system
thermal capacity, and R is the thermal resistance between the
system borders and surroundings. Assuming that R and C are
essentially constant, obtaining the pulse transfer function for
the system in (1) by the step response criterion results in the
discrete-time system
y( k + 1) = a(
Ts ) y(
k)
+ b(
Ts)
u(
k)
……(2)
where k is the discrete-time index, u(k) and y( k) denote the
system input and output, respectively, and T s is the sampling
period. Denoting by α and β some constant values depending
on R and C, the remaining parameters can be expressed by
−α ( Ts)
a(
Ts)
= e and
β
− α ( Ts )
b ( T s ) = (1 − e ) ……(3)
α
The system described in (1)-(3) was modified to include a
saturating non-linearity so that the output temperature cannot
exceed some limitation.
The simulated control plant is described by
….(4)
where a(T s ) and b(T s ) are given by (3). The parameters for
simulation are α = 1.00151E-4, β = 8.67973E-3, γ =40.0, and
Yo = 25.0 °C, which were obtained from a real water bath
plant. The plant input u(k) was limited between 0 and 5, and it
is also assumed that the sampling period is limited by
T s
≥ 10s
…….(5)
With the chosen parameters, the simulated system is
equivalent to a SISO temperature control system of a water

P.MELBA MARY, N.S.MARIMUTHU et al.,: DESIGN OF INTELLIGENT SELF-TUNING TEMPERATURE CONTROLLER FOR WATER BATH PROCESS 122
bath that exhibits linear behavior up to about 70°C and then
becomes nonlinear and saturates at about 80°C. The Schematic
Diagram of the water bath process is shown in Fig.1.
with neighboring MF’s as shown in Fig. 3. This is the most
natural and unbiased choice for MF’s.
Computer
1
NB NM NS ZE PS PM PB
D/A
A/D
PWM
SM
-1 -0.5 0 0.5 1
~
Fig.1 Water bath control system
III. DESIGN PROCEDURE
A. MAIN IDEA OF THE FLC
In this section, we present the main ideas underlying
the FLC. To highlight the issues involved, Fig. 2 shows the
basic configuration of an FLC, which comprises four principal
components: a fuzzification interface, a knowledge base,
decision making logic, and a defuzzification interface.
Fuzzification
Interface
Fuzzy
Process output
& state
Knowledge Base
Decision
Making
Logic
Controlled
System [Process]
Heater
Water bath
Defuzzification
Interface
Fuzzy
Fig.2 Fuzzy Logic Controller
Stirrer
Sensor
Actual control
Non fuzzy
NB: Negative Big
NM: Negative Medium
NS: Negative Small
ZE: Zero
PS: Positive Small
PM: Positive Medium
PB: Positive Big
Fig.3 Triangular Membership function
The fuzzy control rules have the form:
R 1 : if x is A 1 and y is BB1 then z is C 1
R 2 : if x is A 2 and y is BB2 then z is C 2
…………………………………….
R n : if x is A n and y is BBn then z is C n
where x, y and z are linguistic variables representing
two process state variables and one control variable; A i , B i
and C i are linguistic values of the linguistic variables x , y and
z in the universes of discourse U , V, and W , respectively,
with i = 1,2; . , n; and an implicit sentence connective also
links the rules into a rule set or, equivalently a rule base. For
converting the inferred fuzzy control action to real value,
centroid method is used.
B. Self-Tuning Fuzzy For Input And Output Gain Tuning
To make the system adaptive the input and output gain of
these controllers are adjusted on-line according to the current
states of the controlled processes, i.e gain scheduling using
fuzzy logic thereby making them self-tuning FLC’s [8]. This
logic is depicted as shown in Fig.4. in which G e and G ce are
proportional and derivative gains respectively in the input side
of the FLC and G u is the output scaling gain. The adaptation
rules for the input gain G e is shown in Table I, whereas for G ce
the rules are opposite to that of G e .
A1. Membership Functions
All Membership Functions (MF’s) for 1) controller
inputs, i.e., error and change of error and 2) incremental
change in controller output for PI-type FLC or controller
output for PD-type FLC, are defined on the common interval
[1, 1]; whereas the MF’s for the gain updating factor is
defined on [0, 1]. We use symmetric triangles (except the two
MF’s at the extreme ends) with equal base and 50% overlap
e
d/dt
Fuzzy Gain Scheduler
G e
G ce
Fuzzy
Logic
Controller
Fig.4 Structure of the self tuning FLC
G u
IJISE,GA,USA,ISSN:1934-9955,VOL.1,NO.4, OCTOBER 2007

INTERNATIONAL JOURNAL OF IMAGING SCIENCE AND ENGINEERING (IJISE) 123
ΔE G e
TABLE I
Inference Rules of the input gain G e
E NB NM NS Z PS PM PB
NB PB PB PB PB PM Z Z
NM PB PB PB PB PM Z Z
NS PM PM PM PS Z NS NS
Z PM PM PS Z NS NM NM
PS PS PS Z NS NM NM NM
PM Z Z NM NB NB NB NB
PB Z Z NM NB NB NB NB
C. Genetic Algorithm for Input And Output Gain Tuning
Though GA can be used as a flexible method for input
space partitioning, it has the major disadvantage of consuming
much time, we have proposed here to use GA to tuning of
input output gains [9] so that the convergence will be quicker
and better result compared the plant without GA. Gain
scheduling using genetic algorithms is shown in Fig.5,wherein
G e and G d represents proportional and derivative gains
respectively in the input side of FLC and G u is the output
scaling gain.
e
G e
GA Gain Scheduler
Fuzzy Logic
Controller
G u
probabilistic decision to guide the search, where the
population improves toward near optimal points from
generation to generation. GA’s consist of three basic
operations: reproduction, crossover, and mutation.
Reproduction is the process where members of the population
reproduced according to the relative fitness of the individuals,
where the chromosomes with higher fitness have higher
probabilities of having more copies in the coming generation.
There are a number of selection schemes available for
reproduction, such as “roulette wheel,” “tournament scheme,”
“ranking scheme,” etc. [10]. Crossover in GA occurs when the
selected chromosomes exchange partially their information of
the genes, i.e., part of the string is interchanged within two
selected candidates. Mutation is the occasionally alteration of
states at a particular string position. Mutation is essentially
needed in some cases where reproduction and crossover alone
are unable to offer the global optimal solution. It serves as an
insurance policy, which would recover the loss of a particular
piece of information.
IV. SIMULATION STUDY
Using the mathematical model of the real water bath plant
our proposed approaches has been tested. From the initial
condition y(0) = Yo = 25°C, the target is to follow a control
reference set to 35.0°C for 0

P.MELBA MARY, N.S.MARIMUTHU et al.,: DESIGN OF INTELLIGENT SELF-TUNING TEMPERATURE CONTROLLER FOR WATER BATH PROCESS 124
Temp in deg.
90
80
70
60
50
40
30
20
10
actual
reference
control signal
0
0 20 40 60 80 100 120 140 160 180
k
Fig.7 Performance of the simulated system
using self-tuning fuzzy logic controller
Temp in deg.
90
80
70
60
50
40
30
20
10
actual
reference
control signal
0
0 20 40 60 80 100 120 140 160 180
k
Fig8 Performance of the simulated system using
Genetic Algorithm tuned fuzzy logic controller
The comparison of the proposed approaches is made by
calculating the performance index absolute error over the
entire simulation period and is shown in Table II.
Table .II
Methodology Absolute error
Conventional Fuzzy 306.22
Self-Tuning Fuzzy 303.5
GA-tuned Fuzzy 302.1
V. CONCLUSION
This paper has presented a comparison performance of a
conventional fuzzy, a self tuned fuzzy and a GA tuned fuzzy
controller where all of its gain parameters can be
simultaneously tuned for a water bath temperature process. By
appropriate coding of the FLC parameters, it can achieve selftuning
properties from an initial random state. By employing
dynamic crossover and mutation probability rates, the tuning
process by GA was further improved. In the simulation study,
the control performance has been compared to a GA tuned
FLC controller, a self tuned FLC and also the conventional
FLC. It was observed that the applied GA tuned FLC
performed relatively better than the other two controllers.
Compared to the conventional FLC, the self tuning FLC can
somewhat eliminate laborious design steps such as manual
tuning of the scaling factors and membership functions, and
also selection of the fuzzy rules. Though it can be argued that
in the proposed FLC, before GA can be used to optimize its
parameters, initial encoding and settings are required, such
procedures are somewhat relatively simpler and more
systematic than heuristic. In addition, this paper also shows
the flexibility of the proposed methodology in applying the
different types of performance indices (i.e. absolute error) for
various types of control systems. The performance indices
used was rather straightforward and simple, yet resulted in
satisfactory system response.
VI. ACKNOWLEDGEMENT
The authors would like to thank the Management and
Principal of NATIONAL COLLEGE OF ENGINEERING for
their constant encouragement and give permission to make use
of the facilities provided in the Electrical and Electronics
Engineering laboratory which is well established with the
installation of MATLAB-7 software with necessary tool boxes
for doing simulation of our water bath process.
VII. REFERENCES
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reinforcements,” IEEE Trans. Neural Networks, vol. 3, pp.724–740, Sept.
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IJISE,GA,USA,ISSN:1934-9955,VOL.1,NO.4, OCTOBER 2007