Relay Approach for tuning of PID controller - International Journal of ...
Relay Approach for tuning of PID controller - International Journal of ...
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Amar G Khalore et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 1237-1242<br />
ISSN:2229-6093<br />
<strong>Relay</strong> <strong>Approach</strong> <strong>for</strong> <strong>tuning</strong> <strong>of</strong> <strong>PID</strong> <strong>controller</strong><br />
Amar g khalore<br />
Assistant pr<strong>of</strong>essor<br />
Svkm’s NMIMS,mpstme,shirpur campus<br />
pappukhalore@gmail.com<br />
Abstract<br />
In recent years, relay feedback method has found<br />
a new lease <strong>of</strong> life in the automatic <strong>tuning</strong> <strong>of</strong> <strong>PID</strong><br />
<strong>controller</strong>s and in the initialization <strong>of</strong> other<br />
sophisticated adaptive <strong>controller</strong>s. This tuner is<br />
based on the approximate estimation <strong>of</strong> the critical<br />
point on the process frequency response from relay<br />
oscillations. A continuous cycling <strong>of</strong> the controlled<br />
variable is generated from a relay feedback<br />
experiment and the important process in<strong>for</strong>mation,<br />
ultimate gain and ultimate period can be extracted<br />
directly from the experiment. This is a very efficient<br />
way, i.e., a one shot solution, to generate sustained<br />
oscillations. The success <strong>of</strong> this auto tuner is due to<br />
the fact that the identification and <strong>tuning</strong> mechanism<br />
is simple so that process operators understand how it<br />
works. Moreover, it works well even in slow and nonlinear<br />
processes.<br />
1. “Introduction”<br />
The <strong>PID</strong> control algorithm remains the most<br />
popular approach <strong>for</strong> industrial process control<br />
despite continual advances in control theory. This is<br />
not only due to the simple structure which is<br />
conceptually easy to understand and which makes<br />
manual <strong>tuning</strong> possible but also to the fact that the<br />
algorithm provides adequate per<strong>for</strong>mance in the vast<br />
majority <strong>of</strong> applications. For many industrial<br />
problems, the proportional-integral derivative (<strong>PID</strong>)<br />
control module is a building block which provides<br />
the regulation and disturbance rejection <strong>for</strong> single<br />
loop, cascade multi loop and MIMO control system.<br />
It is widely used in process industries because <strong>of</strong> its<br />
simple structure and robustness to the modeling error.<br />
Sophisticated control algorithms, such as model<br />
predictive control are built on the basis <strong>of</strong> the <strong>PID</strong><br />
algorithm. Even in non-linear control development,<br />
<strong>PID</strong> control has been used as comparison reference.<br />
The <strong>PID</strong> <strong>controller</strong> deals with important practical<br />
issues such as actuator saturation and integral wind<br />
up. According to a survey conducted by Japan<br />
electric Measuring Instruments Manufacturers<br />
Association in 1989, 90% <strong>of</strong> the control loops in<br />
industries are <strong>of</strong> <strong>PID</strong> type and only small portion <strong>of</strong><br />
the control loop works well. Also survey by Ender<br />
indicates 30% <strong>of</strong> the <strong>controller</strong> is operated in manual<br />
mode and 20% <strong>of</strong> the loops use factory <strong>tuning</strong>. It<br />
means that <strong>PID</strong> <strong>controller</strong> is widely used but poorly<br />
tuned.<br />
Poor <strong>tuning</strong> can lead to mechanical wear<br />
associated with excessive control activity, poor<br />
control per<strong>for</strong>mance and even poor quality products.<br />
The present work is aimed to provide <strong>PID</strong> <strong>controller</strong><br />
<strong>tuning</strong> guidelines using relay feedback approach.<br />
Recently much research ef<strong>for</strong>t has been focused on<br />
the automatic <strong>tuning</strong> <strong>of</strong> <strong>PID</strong> <strong>controller</strong>s, which was<br />
first proposed by Astrom and Hagglund (1984). They<br />
have introduced novel relay <strong>tuning</strong> method <strong>for</strong><br />
finding the critical gain and critical frequency <strong>of</strong><br />
closed loop process and proposed several <strong>tuning</strong> rules<br />
<strong>for</strong> <strong>PID</strong> <strong>controller</strong>s based on this in<strong>for</strong>mation. The<br />
relay based <strong>PID</strong> <strong>tuning</strong> concept <strong>of</strong> Astrom and<br />
Hagglund is one <strong>of</strong> the simplest and most robust<br />
<strong>tuning</strong> techniques <strong>for</strong> process <strong>controller</strong>s and has<br />
been successfully applied to industry <strong>for</strong> more than<br />
15 years. Progresses in relay feedback method are<br />
summarized by Yu (1999) and Wang and Lee (2003).<br />
The relay feedback test is carried out under closedloop<br />
control so that with an appropriate choice <strong>of</strong> the<br />
relay parameters, the process can be kept close to the<br />
set point.<br />
2. “System description”<br />
2.1 Tuning techniques:<br />
The <strong>PID</strong> Controller <strong>tuning</strong> is method <strong>of</strong><br />
computing the three control parameters viz.<br />
Proportional gain, Derivative time and Integral time,<br />
such that the <strong>controller</strong> meets desired per<strong>for</strong>mance<br />
specification. Since, the exact dynamics <strong>of</strong> the plant<br />
is generally unknown; the basic function <strong>of</strong> auto<br />
tuners is some experimental procedure through which<br />
plant in<strong>for</strong>mation is obtained in order to compute the<br />
<strong>controller</strong> parameters. Auto <strong>tuning</strong> techniques can<br />
IJCTA | MAY-JUNE 2012<br />
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Amar G Khalore et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 1237-1242<br />
ISSN:2229-6093<br />
there<strong>for</strong>e be classified according to this experimental<br />
procedure. The Tuning methods can be broadly<br />
classified into the following categories where the<br />
classification is based on the availability <strong>of</strong> the<br />
process model and the model type.<br />
2.1.1 Limit cycle method:<br />
This method was proposed by Niederlinski<br />
(1971) which is a more natural extension <strong>of</strong> the ZN<br />
<strong>tuning</strong> procedure <strong>of</strong> the MIMO case. It is based on<br />
replacing the <strong>controller</strong>s by gains and identifying a<br />
critical point consisting <strong>of</strong> n scalar critical gains and<br />
the critical frequency. The main departure from the<br />
SISO case is that MIMO systems have infinitely<br />
many critical points. The collection <strong>of</strong> these points<br />
defines a hyper surface in the gains space called the<br />
stability limit. Consequently, one has to prespecify<br />
the desired critical point, e.g. equal loop gains. The<br />
choice <strong>of</strong> the desired critical point depends on the<br />
relative importance <strong>of</strong> the various loops, which is<br />
commonly expressed through weighting factors.<br />
Once the parameters <strong>of</strong> the critical point have been<br />
determined, the <strong>controller</strong>s are tuned in a fashion<br />
similar to the classical ZN rules, possibly with some<br />
modifications. This method is briefly described<br />
below:<br />
(i) Choose n weighing factors ci (i = 1, 2 . . . n) <strong>for</strong><br />
the relative control quality <strong>of</strong> the n controlled<br />
variables.<br />
(ii) Using the best input output pairing bring the P -<br />
controlled system to the stability limit keeping the<br />
following relations between loop gains as<br />
K . G C<br />
K . G C<br />
ci i, i(0)<br />
i<br />
ci 1 i 1, i 1(0) i 1<br />
--------------------------- (2.1)<br />
Where Kc, i is the gain <strong>of</strong> the P <strong>controller</strong> in the ith<br />
loop and Gi,i are the diagonal process gains.<br />
(iii) Determine the critical frequency wci from the<br />
oscillation period Tu and the critical gain<br />
Kui when the oscillations just commences with Kci at<br />
Kui<br />
(iv) Determine the <strong>controller</strong> parameters using the<br />
Generalised Ziegler Nichols <strong>for</strong>mulae listed in table<br />
2.1 where the choice <strong>of</strong> coefficients αi depends on the<br />
ratio<br />
i<br />
c<br />
ci<br />
.<br />
Such that Ωc is the critical frequency when all the P-<br />
controlled loops are active, whereas wci is the critical<br />
frequency <strong>of</strong> the ith loop.<br />
(v) Check whether the control quality is satisfactory.<br />
If not change αi appropriately and return to step (ii).<br />
“Table 1: Generalised Ziegler Nichols Tuning Rules”<br />
where,<br />
Controller<br />
P<br />
Parameters<br />
K c T i T d<br />
α 1 K u<br />
PI α 2 K u 0.8T u<br />
<strong>PID</strong> α 3 K u 0.5T u 0.12T u<br />
0.5 ≤ α 1 ≤ √0.5, 0.45 ≤ α 2 ≤ √0.45 and 0.6 ≤ α 3 ≤ √0.3<br />
2.1.2 Biggest log modulus method:<br />
The BLT (biggest log modulus <strong>tuning</strong>) method<br />
also aims at <strong>tuning</strong> decentralized <strong>PID</strong> <strong>controller</strong>s.<br />
First, the settings <strong>for</strong> the individual <strong>controller</strong>s are<br />
determined via ZN rules, ignoring interactions, and<br />
then all settings are detuned by a common factor that<br />
is determined via a Nyquist-like plot <strong>of</strong> the closedloop<br />
characteristic polynomial and some distance<br />
criterion. This method is an extension <strong>of</strong> the classical<br />
Nyquist stability criterion method <strong>for</strong> SISO systems.<br />
The farther away the Nyquist plot <strong>of</strong> the loop transfer<br />
function is from the (−1, 0) point the more stable the<br />
system is. One commonly used measure <strong>of</strong> the<br />
distance <strong>of</strong> G(jw)H(jw) contour from the (−1, 0)<br />
point is the maximum log modulus<br />
GH<br />
(L c ) max where Lc<br />
20log 1 GH<br />
For multivariable system this measure becomes the<br />
closed loop log modulus given by<br />
L<br />
cm<br />
W ( jw)<br />
20log 1 W ( jw )<br />
----------------------- (2.2)<br />
The proposed <strong>tuning</strong> method on varying a factor F<br />
until the “Biggest log modulus” (L c ) max is equal to<br />
some reasonable number and hence the name<br />
“Biggest Log Modulus Tuning” (BLT).<br />
IJCTA | MAY-JUNE 2012<br />
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Amar G Khalore et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 1237-1242<br />
ISSN:2229-6093<br />
This method can be outlined as in the following<br />
steps:<br />
(i) Compute the Ziegler Nichols PI <strong>tuning</strong> parameters<br />
<strong>for</strong> each individual loop, based on the ultimate gain<br />
and ultimate period in<strong>for</strong>mation.<br />
(ii) Choose a factor F between 2 to 5 and compute the<br />
proportional gain Kc and the integral time τi <strong>for</strong> each<br />
loop using the relationships<br />
K<br />
c<br />
K<br />
F<br />
ZN<br />
----------------------------------------- (2.3)<br />
(iii) Calculate the function in equation (2.2) over<br />
appropriate frequency range.<br />
(iv) Compute the closed loop log modulus equation<br />
(2.3) and keep adjusting F till the value <strong>of</strong> (L c ) max =<br />
2n, where n is the order <strong>of</strong> the system.<br />
In the improved BLT method, the modeling is<br />
accomplished under certain structural assumptions by<br />
two relay experiments <strong>for</strong> each function <strong>of</strong> the<br />
process transfer matrix. Both the BLT method and<br />
the improved one are thus <strong>of</strong>f-line methods that<br />
require good analytical models.<br />
2.1.3 <strong>Relay</strong> feedback method:<br />
The <strong>PID</strong> relay auto-tuner <strong>of</strong> Astrom and<br />
Hagglund is one <strong>of</strong> the simplest and most robust<br />
auto-<strong>tuning</strong> techniques <strong>for</strong> process <strong>controller</strong>s and<br />
has been successfully applied to industry <strong>for</strong> more<br />
than 15 years. In recent years, relay feedback method<br />
have found a new lease <strong>of</strong> life in the automatic <strong>tuning</strong><br />
<strong>of</strong> <strong>PID</strong> <strong>controller</strong>s and in the initialization <strong>of</strong> other<br />
sophisticated adaptive <strong>controller</strong>s. This tuner is based<br />
on the approximate estimation <strong>of</strong> the critical point on<br />
the process frequency response from relay<br />
oscillations. A continuous cycling <strong>of</strong> the controlled<br />
variable is generated from a relay feedback<br />
experiment and the important process in<strong>for</strong>mation,<br />
ultimate gain and ultimate period can be extracted<br />
directly from the experiment. This is a very efficient<br />
way, i.e., a one shot solution, to generate a sustained<br />
oscillations. The success <strong>of</strong> this auto tuner is due to<br />
the fact that the identification and <strong>tuning</strong> mechanism<br />
is so simple that process operators understand how it<br />
works. Moreover, it works well even in slow and<br />
non-linear processes. To understand the relay<br />
feedback system it is vital to understand the<br />
describing function (DF) analysis.<br />
Describing Function Analysis:<br />
The describing function (DF) <strong>of</strong> a nonlinear<br />
element is defined as the complex ratio <strong>of</strong> the<br />
fundamental component <strong>of</strong> the output to the<br />
sinusoidal input. A more general definition says it is<br />
the covariance <strong>of</strong> the given input signal and the<br />
output divided by the variance <strong>of</strong> the input. The DF is<br />
a quasilinear representation <strong>of</strong> the non-linear element<br />
subjected to usually a sinusoidal input, and its use in<br />
the analysis <strong>of</strong> a non-linear system is thus based on<br />
the assumption that the nonlinear element has a<br />
sinusoidal input. Assume that the non-linear element<br />
has a sinusoidal input.<br />
x( t) a cos 2 t<br />
T<br />
----------------------------- (2.4)<br />
For two periodic signals x(t) and u(t) <strong>of</strong> period T, the<br />
cross correlation function Rxu(ŧ ) is<br />
Defined by,<br />
T<br />
1<br />
Rxu<br />
( ) x( t). u( t ) dt ------------------ (2.5)<br />
T<br />
0<br />
Where is the time delay. Also, the covariance <strong>of</strong><br />
two signals is the value <strong>of</strong> their cross correlation<br />
function, with zero delay. Hence, the definition <strong>of</strong> the<br />
describing function N(a) <strong>of</strong> the non-linear element<br />
becomes,<br />
Na ( )<br />
R<br />
R<br />
xu<br />
xx<br />
(0)<br />
(0)<br />
----------------------------------- (2.6)<br />
Let x(t) be the input to the non-linear element and<br />
u(t) its output. As assumed earlier the input is<br />
sinusoidal and the relay output which would be a<br />
rectangular wave could be written as a Fourier sum as<br />
shown below,<br />
x( t) acos( t )<br />
u( t) a cos( s t )<br />
s 1<br />
s<br />
Thus, the cross- correlation function between the<br />
input x(t) and the output u(t) is computed tobe,<br />
2<br />
1<br />
aa1<br />
xu<br />
( ) cos( ) ( ) cos( )<br />
2 2<br />
0<br />
R t a t u t d t<br />
------------------------------------- (2.7)<br />
IJCTA | MAY-JUNE 2012<br />
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ISSN:2229-6093<br />
Similarly, the autocorrelation functions becomes,<br />
2<br />
a<br />
Rxx( ) cos( t)<br />
---------------------------- (2.8)<br />
2<br />
Na ( )<br />
Rxu<br />
(0) a1<br />
R (0) a<br />
xx<br />
---------------------------- (2.9)<br />
In case <strong>of</strong> the relay non-linearity, the output u(t) <strong>of</strong><br />
the relay using the Fourier series<br />
expansion can be written as,<br />
ut ()<br />
4d cos(2s 1) t<br />
2s<br />
1<br />
s 1<br />
---------------- (2.10)<br />
Where d is the relay amplitude and hence the relay<br />
describing function becomes,<br />
Na ( )<br />
4d<br />
q<br />
------------------------------------- (2.11)<br />
A DF can be used to determine whether a class <strong>of</strong><br />
non-linear systems will generate oscillations. Refer<br />
figure 1 to determine the conditions <strong>for</strong> oscillation,<br />
the non-linear block, N is approximated by the DF<br />
N(a) which depends on the signal amplitude a at the<br />
input <strong>of</strong> the Non-linearity.<br />
oscillation, the position <strong>of</strong> one point <strong>of</strong> the Nyquist<br />
curve can be determined.<br />
2.2 Auto <strong>tuning</strong> by relay feedback method :<br />
The <strong>PID</strong> <strong>controller</strong>s can be tuned in open loop<br />
and closed loop. In open loop various methods like<br />
Process Reaction method, Ziegler Nichol’s method<br />
are used. The <strong>PID</strong> <strong>controller</strong> tuned in open loop does<br />
not guarantee about stability when the loop is closed.<br />
The tuned <strong>PID</strong> <strong>controller</strong> may work better in open<br />
loop, but can’t guarantee when loop is closed.<br />
So the closed loop stability method can be used<br />
<strong>for</strong> <strong>tuning</strong> <strong>of</strong> <strong>PID</strong> <strong>controller</strong>. Various methods like<br />
Ziegler Nichol’s method, <strong>Relay</strong> feedback method can<br />
be used <strong>for</strong> <strong>tuning</strong> <strong>of</strong> <strong>PID</strong> <strong>controller</strong>. <strong>Relay</strong> feedback<br />
method can be used <strong>for</strong> online <strong>tuning</strong> <strong>of</strong> <strong>PID</strong><br />
<strong>controller</strong> also. In open loop method the control loop<br />
is required to be separated from the process, which is<br />
not required in <strong>Relay</strong> feedback method.<br />
As shown in figure 2, a relay can be placed in<br />
parallel with <strong>PID</strong> <strong>controller</strong>. For <strong>tuning</strong> relay is used<br />
in series with the plant. For <strong>tuning</strong> <strong>of</strong> <strong>PID</strong> <strong>controller</strong><br />
the gain <strong>of</strong> relay is slowly increased till the closed<br />
loop produces sustained oscillations. Once sustained<br />
oscillations are produced, the frequency and<br />
amplitude <strong>of</strong> oscillation are measured which are<br />
called ultimate (critical) frequency and ultimate<br />
(critical) gain. After this various <strong>tuning</strong> rules like<br />
Ziegler Nichol, Cohen Coon can be used <strong>for</strong> <strong>tuning</strong><br />
<strong>of</strong> <strong>PID</strong> <strong>controller</strong>.<br />
“Figure 1: Non-linear Feedback System”<br />
.In a scalar case, if the process transfer function<br />
is G(jw), the condition <strong>for</strong> oscillation is simply given<br />
by N(a)G(jw) = -1.This equation is obtained by<br />
requiring that the sine wave <strong>of</strong> frequency w should<br />
propagate around the feedback loop with the same<br />
amplitude and phase. If the negative inverse <strong>of</strong> the<br />
DF is drawn in the complex plane together with the<br />
Nyquist curve <strong>of</strong> the linear system, an oscillation may<br />
occur if there is an intersection between the two<br />
curves. The amplitude and the frequency <strong>of</strong><br />
oscillation are determined at the intersection point.<br />
There<strong>for</strong>e, measuring the amplitude and the period <strong>of</strong><br />
“ Figure 2: Schematic <strong>of</strong> <strong>tuning</strong> <strong>of</strong> <strong>PID</strong> <strong>controller</strong>”<br />
The advantages <strong>of</strong> this method are the <strong>tuning</strong> can be<br />
done online and less chance <strong>of</strong> getting the system<br />
unstable during <strong>tuning</strong> <strong>of</strong> <strong>PID</strong> <strong>controller</strong>. We will test<br />
this method <strong>for</strong> various order <strong>of</strong> plant with and<br />
without time delay system.<br />
So given the tedious and possibly dangerous<br />
plant trials that result in poorly damped responses, it<br />
behaves one to speculate why it is <strong>of</strong>ten the only<br />
<strong>tuning</strong> scheme many instrument engineers are<br />
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familiar with, or indeed ask if it has any concrete<br />
redeeming features at all. In fact the ZN <strong>tuning</strong><br />
scheme, where the <strong>controller</strong> gain is experimentally<br />
determined to just bring the plant to the brink <strong>of</strong><br />
instability is a <strong>for</strong>m <strong>of</strong> model identification. All<br />
<strong>tuning</strong> schemes contain a model identification<br />
component, but the more popular ones just streamline<br />
and disguise that part better. The entire tedious<br />
procedure <strong>of</strong> trial and error is simply to establish the<br />
value <strong>of</strong> the gain that introduces half a cycle delay<br />
when operating under feedback. This is known as the<br />
ultimate gain Ku and is related to the point where the<br />
Nyquist curve <strong>of</strong> the plant in Fig. 3 first cuts the real<br />
axis. The problem is <strong>of</strong> course, is that we rarely have<br />
the luxury <strong>of</strong> the Nyquist curve on the factory floor,<br />
hence the experimentation required.<br />
After experimenting with the ZN scheme a few<br />
times, if we can establish the ultimate gain where<br />
the key is to temporarily swap a simple relay <strong>for</strong> the<br />
<strong>PID</strong> <strong>controller</strong> in the feedback loop. This was first<br />
proposed in the early 1990s, and a very readable<br />
summary <strong>of</strong> <strong>PID</strong> control in general, and relay based<br />
<strong>tuning</strong> in specific, is given in table 1.<br />
For a certain class <strong>of</strong> process plants, the socalled<br />
“auto <strong>tuning</strong>" procedure <strong>for</strong> the automatic<br />
<strong>tuning</strong> <strong>of</strong> <strong>PID</strong> <strong>controller</strong>s can be used. Such a<br />
procedure is based on the idea <strong>of</strong> using an on/<strong>of</strong>f<br />
<strong>controller</strong> (called a relay <strong>controller</strong>) whose dynamic<br />
behavior resembles to that shown in Figure 4(a).<br />
Starting from its nominal bias value (denoted as 0 in<br />
the Figure) the control action is increased by an<br />
amount denoted by h and later on decreased until a<br />
value denoted by -h.<br />
The closed-loop response <strong>of</strong> the plant, subject to<br />
the above described actions <strong>of</strong> the relay <strong>controller</strong>,<br />
will be similar to that depicted in Figure 4(b).<br />
Initially, the plant oscillates without a definite pattern<br />
around the nominal output value (denoted as 0 in the<br />
Figure) until a definite and repeated output response<br />
can be easily identified. When we reach this closedloop<br />
plant response pattern the oscillation period (Pu)<br />
and the amplitude (A) <strong>of</strong> the plant response can be<br />
measured and used <strong>for</strong> <strong>PID</strong> <strong>controller</strong> <strong>tuning</strong>. In fact,<br />
the ultimate gain can be computed as: Kcu =<br />
4h/pi*A.<br />
“Figure 3: Polar plot <strong>of</strong> plant and relay”<br />
As it turns out, under relay feedback, most plants<br />
oscillate with modest amplitude <strong>for</strong>tuitously at the<br />
critical frequency. The procedure is now the<br />
following:<br />
1. Substitute a relay with amplitude d <strong>for</strong> the <strong>PID</strong><br />
<strong>controller</strong> as shown in Fig. 2.<br />
2. Kick into action and record the plant output<br />
amplitude a and period P.<br />
3. The ultimate period is the observed period, Pu = P,<br />
while the ultimate gain is inversely proportional to<br />
the observed amplitude (Describing function).<br />
“Figure 4: The closed-loop response <strong>of</strong> the plant”<br />
Having established the ultimate gain and period<br />
with a single succinct experiment, we can use the ZN<br />
<strong>tuning</strong> rules (or equivalent) to establish the <strong>PID</strong><br />
<strong>tuning</strong> constants.<br />
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3 “Methodology followed”:<br />
The Methodology Followed is given below:<br />
Consider the linear system without time delay.<br />
Generate the simulink diagram as shown in figure 1.<br />
Apply step input to the simulink diagram.<br />
Find the ultimate gain (Ku) and ultimate period (Tu)<br />
<strong>of</strong> the closed loop system.<br />
Find the <strong>tuning</strong> parameters <strong>of</strong> the <strong>PID</strong> <strong>controller</strong>s<br />
using various methods like ZN, Cohen Coon method.<br />
Replace the <strong>Relay</strong> block in the simulink using the<br />
tuned <strong>PID</strong> <strong>controller</strong> and test <strong>for</strong> the per<strong>for</strong>mance <strong>of</strong><br />
the closed loop system by applying step as test input<br />
to the system.<br />
Tuning <strong>of</strong> <strong>PID</strong> <strong>controller</strong> <strong>for</strong> linear systems with time<br />
delay.<br />
4 “Conclusion & future scope”:<br />
[5] Somanath Majhi and Lothar Litz, Department <strong>of</strong><br />
Process Control, Kaiserslautern University Erwin-<br />
Schrodinger-Str., 67653 Kaiserslautern Germany, “On line<br />
<strong>tuning</strong> <strong>of</strong> <strong>PID</strong> <strong>controller</strong>s” Proceedings <strong>of</strong> the American<br />
Control Conference, Denver, Colorado June 4.6.2003<br />
[6] YangQuan Chen, ChuanHua Hu and Kevin L. Moore,<br />
Center <strong>for</strong> Self-organizing and Intelligent Systems<br />
(CSOIS), Dept. <strong>of</strong> Electrical and Computer Engineering,<br />
UMC 4160, College <strong>of</strong> Engineering, 4160 Old Main Hill,<br />
Utah State University, Logan, UT 84322-4160, USA.<br />
“<strong>Relay</strong> Feedback Tuning <strong>of</strong> Robust <strong>PID</strong> Controllers with<br />
Iso-Damping Property” Proceedings <strong>of</strong> the 4th IEEE<br />
Conference on Decision and Control, 2003<br />
[7] Myung-Hyun Yoon and Chang-Hoon Shin, System and<br />
Communication Research Laboratory Korea Electric Power<br />
Research Institute 103-16 Munji-dong Yusung-ku, Taejon<br />
305-380, Korea, “Design <strong>of</strong> on line <strong>tuning</strong> <strong>PID</strong> <strong>controller</strong><br />
<strong>for</strong> power plant process control” SCE '97 July 29-31,<br />
Tokushima.<br />
This paper gives a brief overview <strong>of</strong> the various<br />
<strong>PID</strong> Auto-<strong>tuning</strong> methods <strong>for</strong> single input single<br />
output available in literature. The main objective <strong>of</strong><br />
this work has been to demonstrate relay <strong>PID</strong> auto<strong>tuning</strong><br />
method. For SISO <strong>PID</strong> <strong>controller</strong>, two<br />
different <strong>tuning</strong> <strong>for</strong>mulae can be used. The responses<br />
<strong>of</strong> the closed loop systems <strong>for</strong> various control action<br />
shows that the <strong>controller</strong> are perfectly tuned <strong>for</strong> the<br />
given application. Since it is a closed loop method <strong>of</strong><br />
<strong>tuning</strong>, the per<strong>for</strong>mance is guaranteed.<br />
References:<br />
[1] H.-P.Huang, M.-L.Roan and J.-C.Jeng, The authors are<br />
with the Department <strong>of</strong> chemical Engineering, National<br />
Taiwan University, Taipei, Taiwan 10617, “On-line<br />
adaptive <strong>tuning</strong> <strong>for</strong> <strong>PID</strong> <strong>controller</strong>s” IEE Proceedings<br />
online no. 20020099 DOI: 10.1049/ip-cta: 20020099, 12th<br />
November 2001.<br />
[2] Tor Steinar Schei ,SINTEF Automatic Control 1992<br />
ACC/FA127034 Trondheim –NTH Norway, “Closed-loop<br />
Tuning <strong>of</strong> PLD Controllers”.<br />
[3] C. C. Hang and Kok Kee Sin, “On-Line Auto Tuning <strong>of</strong><br />
<strong>PID</strong> Controllers Based on the Cross-Correlation<br />
Technique” IEEE Transactions on industrial electronics,<br />
Vol. 38.No.6, December 1991.<br />
[4] Jing-Chug Shen Huann-Keng Chiang* Department <strong>of</strong><br />
Automation Engineering National Huwei Institute <strong>of</strong><br />
Technology, Huwei, Yunlin, Taiwan, National Yunlin<br />
University <strong>of</strong> Science and Technology, Toulou, Yunlin,<br />
Taiwan, “<strong>PID</strong> Tuning Rules <strong>for</strong> Second Order Systems”<br />
2004 5th Asian Control Conference.<br />
IJCTA | MAY-JUNE 2012<br />
Available online@www.ijcta.com<br />
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