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Real-coded genetic algorithm and fuzzy logic approach for real-time tuning of
proportional-integral - derivative controller in automatic voltage regulator
system
Article in IET Generation Transmission & Distribution · August 2009
DOI: 10.1049/iet-gtd.2008.0287 · Source: IEEE Xplore
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Published in IET Generation, Transmission & Distribution
Received on 19th June 2008
Revised on 10th February 2009
doi: 10.1049/iet-gtd.2008.0287
ISSN 1751-8687
Real-coded genetic algorithm and fuzzy
logic approach for real-time tuning of
proportional –integral – derivative controller
in automatic voltage regulator system
D. Devaraj B. Selvabala
Power System Automation Laboratory, Kalasalingam University, Krishnankoil 626190, Tamilnadu, India
E-mail: [email protected]
Abstract: Optimal tuning of proportional – integral – derivative (PID) controller parameters is necessary for the
satisfactory operation of automatic voltage regulator (AVR) system. This study presents a combined genetic
algorithm (GA) and fuzzy logic approach to determine the optimal PID controller parameters in AVR system.
The problem of obtaining the optimal PID controller parameters is formulated as an optimisation problem and
a real-coded genetic algorithm (RGA) is applied to solve the optimisation problem. In the proposed RGA, the
optimisation variables are represented as floating point numbers in the genetic population. Further, for
effective genetic operation, the crossover and mutation operators which can deal directly with the floating
point numbers are used. The proposed approach has resulted in PID controller with good transient response.
The optimal PID gains obtained by the proposed GA for various operating conditions are used to develop the
rule base of the Sugeno fuzzy system. The developed fuzzy system can give the PID parameters on-line for
different operating conditions. The suitability of the proposed approach for PID controller tuning has been
demonstrated through computer simulations in an AVR system.
Nomenclature
Kp
Ki
proportional gain of PID controller
integral gain of PID controller
Kd
derivative gain of PID controller
Ka
Ke
amplifier gain
exciter gain
Kg
Ks
generator gain
sensor gain
ta
te
tg
ts
DVt
DVref
amplifier time constant
exciter time constant
generator time constant
sensor time constant
incremental change in terminal voltage
incremental change in reference voltage
IET Gener. Transm. Distrib., 2009, Vol. 3, Iss. 7, pp. 641 – 649
doi: 10.1049/iet-gtd.2008.0287
Osh
Ess
overshoot
steady-state error
Ts
Tr
settling time
rising time
1
Introduction
The main objective of the automatic voltage regulator
(AVR) is to control the terminal voltage by adjusting the
generator exciter voltage. The AVR must keep track of the
generator terminal voltage all the time and under any load
condition, working in order to keep the voltage within
pre-established limits. Despite significant studies in the
development of advanced control schemes, the classical
proportional – integral – derivative (PID) controllers [1 – 5]
remain the controllers of choice to control the AVR
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because of its simple structure and robustness to variations of
the system parameters.
applied to obtain the optimal PID parameters of an AVR
system.
Proper selection of the PID controller parameters is
necessary for the satisfactory operation of the AVR.
Traditionally, the PID controller parameters are evaluated
using Ziegler–Nichols (ZN) [1, 2] and Cohen Coon
methods [6, 7]. In both these methods, the parameters of the
controller are obtained for an operating point where the
model can be considered linear. This implies that there is
sub-optimal tuning when a process operates outside the
validity zone of the model. Internal model control [8]
overcomes the above said problem but its design calculations
could be complicated for higher order process.
2 Modelling of automatic voltage
regulator system
Alternatively, numerical optimisation techniques like
gradient descent technique can be applied to obtain the
parameters of the PID controllers. They are computationally
fast, but with a non-monotonic solution surface these
methods are highly sensitive to starting points and frequently
converge to local optimum solutions or diverge altogether. In
[9], an optimal PID controller for a general second-order
system has been developed using linear-quadratic regulator
(LQR) technique. This approach requires the proper selection
of weighting functions for satisfactory performance. Recently,
evolutionary computation techniques such as genetic
algorithm (GA) [10–13] and particle swarm optimisation
[14] have been applied to obtain the optimal controller
parameters. GA is a global search algorithm based on the
principle of ‘survival of the fittest’. Devaraj et al. [12]
proposed an enhanced genetic algorithm (GA) for PI
controller tuning in pH process. A hybrid GA and bactorial
foraging approach was proposed in [13] to tune the PID
controller of an AVR. Gaing [14] has proposed a novel
design method for determining the PID controller
parameters of the AVR system using the particle swarm
optimisation (PSO) method. PSO is a population-based
optimisation algorithm which is inspired by social behaviour
patterns of organisms such as bird flocking and fish schooling.
Both GA and PSO suffer from computational burden and
memory requirement and so they are not suitable for on-line
applications. To overcome the above difficulties, this paper
proposes Sugeno fuzzy model [15] for on-line tuning of
PID controller. The optimal PID parameters required to
formulate the fuzzy rule table are generated by employing
the real-coded genetic algorithm (RGA). In the RGA, the
optimisation variables are represented as floating point
numbers instead of the binary string which is followed in
the conventional binary-coded GA. Further, crossover and
mutation operators which can deal directly with the
floating point numbers are used. The proposed approach is
In a synchronous generator, the terminal voltage is maintained
constant at various levels by using an AVR. The AVR system
consists of four major components, namely amplifier, exciter,
generator and sensor. Fig. 1 illustrates the block diagram
representation of the AVR system. The transfer functions of
the individual components are given in Table 1 along with
the limits of the parameters.
An increase in the reactive power load of the generator is
accompanied by a drop in the terminal voltage magnitude.
The voltage magnitude is sensed by a sensor. This voltage
is compared with a dc set point signal to generate the error
signal. A PID controller is used to reduce the error and to
improve the dynamic response. The PID controller is a
combination of the proportional, integral and derivative
control mechanisms that when used together effectively
stabilise the manipulated variable at the set point. The PID
controller transfer function is given by
G(s) ¼ Kp þ
Ki
þ Kd s
s
The transfer function of AVR system with PID control is
given by (as shown in (2))
The AVR quality influences the voltage level during
steady-state operation and also reduces the voltage
oscillations during transient periods, affecting the overall
system stability.
3 Optimisation of controller
parameters
Proper selection of PID controller parameters is necessary for
the satisfactory operation of the system. In this work, the
problem of PID controller parameter selection is
formulated as an optimisation problem, the objective
function of which is given by
Min F (Kp , Ki , Kd ) ¼ (1 eb )(Osh þ Ess ) þ eb (ts tr )
(3)
The above objective function uses a combination of transient
response including rise time, overshoot, settling time and
steady-state error. By selecting the proper value of the
weighting factor b, the performance criterion can be made
to satisfy the designer requirements. The above optimisation
(s2 Kd þ sKp þ Ki )(Ka Ke Kg )(1 þ sts )
DVt (s)
¼
DVref (s) s(1 þ sta )(1 þ ste )(1 þ stg )(1 þ sts ) þ (Ka Ke Kg Ks )(s2 Kd þ sKp þ Ki )
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(1)
(2)
IET Gener. Transm. Distrib., 2009, Vol. 3, Iss. 7, pp. 641– 649
doi: 10.1049/iet-gtd.2008.0287
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Figure 1 Block diagram of AVR system along with PID controller
problem is subjected to the following constraints
4.1 Reproduction
Kpmin Kp Kpmax
Kimin Ki Kimax
(4)
Kdmin Kd Kdmax
A RGA is applied to the above optimisation problem to search
for the optimum value of the controller parameters. The
details of the proposed GA are given in the next section.
4
Proposed GA
GAs [16] are search algorithms based on the mechanics of
natural selection and genetics. They combine solution
evaluation with randomised, structured exchange of
information between solutions to obtain optimality.
Starting with an initial population, the GA exploits the
information contained in the present population and
explores new individuals by generating offspring using the
three genetic operators namely, reproduction, crossover and
mutation which can then replace the members of the old
generation. After several generations, the algorithm
converges to the best chromosome, which hopefully
represents the optimum or near optimal solution. In the
traditional binary-coded GA, the decision variables of the
problem are represented by a fixed-length string of binary
bits (0, 1). In this representation, the resolution of the
solution depends on the number of bits used to represent
the variables. Further, the coding of real-valued variables in
finite-length strings causes a number of difficulties. To
overcome these difficulties, in this paper, the decision
variables are represented in their natural form. Also,
crossover and mutation operators which can operate directly
with floating point numbers are used. The details of the
genetic operators used in the proposed GA are given below.
Reproduction is a method that stochastically selects the
individuals from the population according to their fitness;
higher the fitness, more chance an individual has to be
selected for the next generation. There are three main types
of selection methods: fitness proportionate selection, ranking
method and tournament selection. Tournament selection [17]
is used in this work. In tournament selection, ‘n’ individuals
are selected randomly from the population, and the best of
the ‘n’ is inserted into the new population for further genetic
processing. This procedure is repeated until the mating pool
is filled. Tournaments are often held between pairs of
individuals, although larger tournaments can be used.
4.2 Crossover operation
The crossover operator is mainly responsible for the global
search property of the GA. Crossover basically combines
substructures of two parent chromosomes to produce new
structures, with the selected probability typically in the
range of 0.6– 1.0. The Blend crossover operator (BLX-a)
[17] is applied in this work.
Fig. 2 illustrates the BLX-a crossover operation for the
one-dimensional case. In the BLX-a crossover, the off
spring y is sampled from the space [e1 , e2] as follows
y¼
where
where
e1 þ r(e2 e1 )
repeat sampling
if
umin y umax
otherwise
(5)
e1 ¼ u1 a(u2 u1 )
(6)
e2 ¼ u2 þ a(u2 u1 )
(7)
r is the uniform random number [ [0, 1].
Table 1 Transfer function of AVR components
Component
amplifier
exciter
generator
sensor
Transfer function
Parameter limits
TFamplifier ¼ Ka/1 þ tas
10 , Ka , 40; 0.02 s , ta , 1 s
TFexciter ¼ Ke/1 þ tes
1 , Ke , 10; 0.4 s , te ,1 s
TFgenerator ¼ Kg/1 þ tgs
Kg depends on load (0.7 – 1.0); 1 s , tg ,2 s
TFsensor ¼ Ks/1 þ tss
0.001 s , ts , 0.06 s
IET Gener. Transm. Distrib., 2009, Vol. 3, Iss. 7, pp. 641 – 649
doi: 10.1049/iet-gtd.2008.0287
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Figure 2 Schematic representation of BLX-a crossover
It is to be noted that e1 and e2 will lie between umin and
umax , the variable’s lower and upper bounds, respectively. In
a number of test problems, it was observed that a ¼ 0.5
provides good results. One interesting feature of this type
of crossover operator is that the created point depends on
the location of both parents. If both parents are close to
each other, the new point will also be close to the parents.
On the other hand, if parents are far from each other, the
search is more like a random search.
4.3 Mutation operation
The mutation operator is used to inject new genetic material
into the population. Mutation randomly alters a variable with
a small probability. ‘Uniform mutation’ operator is used in
this work. In uniform mutation, the variable is set to a
uniform random number between the variable’s lower and
upper limits.
5 GA implementation for PID
controller tuning
While applying GA to obtain the optimal PID controller
parameters, two main issues need to be addressed:
† representation of the decision variables and
† formation of the fitness function.
5.1 Variable representation
Each individual in the genetic population represents a
candidate solution. For the PID controller tuning problem,
the elements of the solution consist of proportional gain
(Kp), integral gain (Ki) and derivative gain (Kd). These
variables are represented as floating point numbers in the
proposed GA population. With floating point
representation, an individual in the GA population for
computing the optimal PID gains will look like the following
0:937
|fflffl{zfflffl}
Kp
0:242
|fflffl{zfflffl}
Ki
0:320
|fflffl{zfflffl}
Kd
With the direct representation of the solution variables, the
computer space required to store the population is reduced.
Moreover, the efficiency of the GA is increased as there is
no need to convert the solution variables to the binary string.
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5.2 Fitness function
The performance of each individual in the population is
evaluated according to its ‘fitness’, which is defined as the
non-negative figure of merit to be maximised. It is
associated directly with the objective function value.
Evaluation of the individual is accomplished by calculating
the performance criteria given by (3) for the problem
using the parameter set. The result of the performance
criteria calculation is used to calculate the fitness value of
the individual. The fitness function is the reciprocal of the
performance criterion F(Kp ,Ki ,Kd) given in (3). Hence,
the minimisation of performance criteria given by (3) is
transformed to a fitness function to be maximised as
Fitness ¼
k
F (Kp , Ki , Kd )
(8)
where k is a constant. This is used to amplify (1/F ), the value
of which is usually small, so that the fitness value of the
chromosome will be in a wider range.
6
Review of Sugeno fuzzy model
Fuzzy logic was first developed by Zadeh in the mid-1960s to
provide a mathematical basis for human reasoning. Fuzzy logic
[15] uses fuzzy set theory, in which a variable is a member of
one or more sets, with a specified degree of membership.
The degree of membership in a set is expressed by a number
between 0 and 1. 0 means entirely not in the set, 1 means
completely in the set, and a number in between means
partially in the set. Mathematically, a fuzzy set A in the
universe of discourse X is defined to be a set of ordered pairs
A ¼ {(x, mA (x))jx [ X }
(9)
where mA(x) is called the membership function of x in A. The
parameterisable membership functions most commonly used
in practice are the triangular membership function and the
trapezoidal membership function. Fuzzy logic when applied
to computers allows them to emulate the human reasoning
process, quantify imprecise information, make decisions
based on vague and incomplete data, yet by applying a
‘defuzzification’ process, arrive at definite conclusions.
There are three main types of fuzzy logic systems, namely,
Mamdani, Sugeno and Tsukamoto fuzzy logic systems. In
IET Gener. Transm. Distrib., 2009, Vol. 3, Iss. 7, pp. 641– 649
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the Sugeno fuzzy model, which is followed in this work, the
fuzzy rule is expressed as
If x is A and y is B then z ¼ f (x, y)
(10)
where x and y are input variables, A and B are fuzzy sets in the
antecedent and f (x, y) is a crisp function in the consequent.
The fuzzy sets of each variable are described by appropriate
membership functions. A set of such rules form the heart
of the fuzzy logic system.
For a specific input signal condition, the fuzzy system
determines the rules to be fired and then computes the
effective output. For this, first the minimum of the
membership functions of the inputs (wi) is obtained for
each of the rules. This value is the firing value for a
particular rule. Then the overall output is determined by
weighted average of individual rule outputs given by
PM
wi zi
z ¼ Pi¼1
M
i¼1 wi
(11)
In the present work, the Sugeno fuzzy system is used to
estimate the parameters of the PID controller under various
operating conditions.
7
Simulation results
The proposed methodology for PID controller tuning was
tested on an AVR system. The AVR system consists of
amplifier, exciter, generator and sensor. The parameters of the
AVR system are chosen as Ka ¼ 10, Ke ¼ Kg ¼ Ks ¼ 1.0,
ta ¼ 0.1, te ¼ 0.4, ts ¼ 0.01 and tg ¼ 1.0. Only Kg and tg
are load dependent. The AVR system was simulated in
MATLAB Simulink. The MATLAB-Simulink model of
AVR system along with PID controller is shown in Fig. 3.
The PID controller was tuned using the ZN method. A step
reference voltage of 0.01 p.u. is applied and the step response
of change in terminal voltage of AVR system in the presence
Figure 4 Step response of change in terminal voltage with
ZN PID controller
of PID controller is shown in Fig. 4. From the figure, it is
observed that the response of the AVR system with PID
controller tuned using ZN method posses more than one
oscillatory mode and has large settling time. This shows that
the system has not been tuned to its optimum.
7.1 Performance of RGA–PID controller
Next, the proposed GA was applied to obtain the optimal
PID controller parameters. The software for the proposed
GA was written in MATLAB and executed on a PC with
2.4 MHZ and 256 MB RAM. Proportional gain (Kp),
Integral gain (Ki) and derivative gain (Kd) are taken as the
optimisation variables. They are represented as floating
point numbers in the GA population. The initial
population is generated randomly between the variable’s
lower and upper limits. The fitness function given by (8) is
used to evaluate the fitness value of each set of controller
parameters. Simulation was conducted with different values
of b. The performance of GA for various values of
crossover and mutation probabilities in the ranges 0.6– 1.0
and 0.001 – 0.1, respectively, was evaluated. The best results
are obtained with the following control parameters.
Figure 3 MATLAB-Simulink model of AVR system along with PID controller
IET Gener. Transm. Distrib., 2009, Vol. 3, Iss. 7, pp. 641 – 649
doi: 10.1049/iet-gtd.2008.0287
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Number of generations: 50
population size: 30
crossover probability: 0.8
mutation probability: 0.05
The proposed GA took 72 s to reach the optimal solution.
Fig. 5 shows the convergence characteristics of GA
algorithm. It can be seen that the fitness value increases
rapidly in the first 15 generations of the GA. During this
stage, the GA concentrates mainly on finding feasible
solutions to the problem. Then the value increases slowly
and settles down near the optimum value with most of the
individuals in the population reaching that point.
Figure 6 Step response of RGA – PID change in terminal
voltage
Table 3. The terminal voltage responses with these
methods are also given in Fig. 6. On comparing these
results, it is found that the proposed GA approach has
resulted in minimum values of rise time, settling time and
overshoot are less when compared with the results obtained
using LQR method and binary-coded GA. In addition, the
steady-state error with RGA – PID is low compared to
other two methods. Also the proposed algorithm took less
time for convergence compared to the binary-coded GA.
The optimal values of the controller parameters obtained
using the proposed GA for different values of b are given in
Table 2. The time-domain performance indices of the
system, namely rise time, settling time, steady-state error and
overshoot are also given in Table 2. The system response with
optimal values of PID parameters is given in Fig. 6. The
transient response of the AVR system has improved
significantly and the response is faster than the one shown in
Fig. 4. These results show that the proposed approach is able
to search the optimal values of the PID controller.
To analyse the performance of the AVR system under severe
disturbances, a three phase fault is applied at the generator
terminal and the response of the system was observed. Fig. 7
shows the system response for the above contingency with
PID controller tuned using the RGA. It can be observed
that the controller is able to suppress the oscillations in the
terminal voltage and provide good damping characteristics.
For comparison, LQR technique and a binary-coded GA
were applied to obtain the parameters of the PID controller.
The results obtained by these methods are also given in
7.2 Development of Sugeno fuzzy model
for online tuning
A Sugeno fuzzy logic model was developed to obtain the optimal
PID parameters during real-time operation. Kg and tg are the
input to the fuzzy model and the values of Kp , Ki and Kd are
the output. Four fuzzy sets, namely, ‘low (L)’, ‘medium low
(ML)’, ‘medium high (MH)’ and ‘high (H)’ are defined for the
variable Kg . Similarly, the fuzzy sets defined for the variable tg
are ‘very low (VL)’, ‘low (L)’, ‘medium low (ML)’, ‘medium
high (MH)’, ‘high (H)’ and ‘very high (VH)’. They are
associated with overlapping triangular membership functions.
To formulate the fuzzy rule table the value of Kg is varied from
0.7 to 1.0 in steps of 0.1 and tg is varied from 1 to 2 in steps
Figure 5 Convergence characteristics of the RGA
Table 2 Optimal PID gains and transient response parameters
Kp
Ki
Kd
Ts(s)
Tr(s)
Osh
Ess(1025)
0.5
1.000
0.1448
0.7019
2.5595
1.9511
0.0158
46.911
1.0
1.000
0.1448
0.7019
2.5595
1.9511
0.0158
46.911
1.5
0.682
0.266
0.179
1.2682
1.0668
0.0004
b
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4.3386
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Table 3 Comparison of PID gains and transient response parameters
Method
Ki
Kp
Kd
Ts(s)
Tr(s)
Osh
Ess(1025)
15.007
LQR
1.01
0.5
0.1
2.3354
0.5004
0.3605
GA
0.5692
0.2484
0.1258
1.7019
0.8093
0.0586
8.2941
RGA
0.682
0.266
0.179
1.2682
1.0668
0.0004
4.3386
Figure 7 Terminal voltage response under three phase fault
of 0.2. For each combination of Kg and tg, , the proposed GA is
applied to obtain the optimal values of Kp , Ki and Kd. The fuzzy
rule table formulated for Kp , Ki and Kd using the above approach
is given in Table 4 as (a), (b) and (c), respectively.
During real-time operation, corresponding to the present
operating condition, the values of Kg and tg are found out.
For this value of Kg and tg , the optimal values of Kp , Ki
and Kd can be computed using the fuzzy rule table and the
Sugeno inference system explained in Section 5. The
optimal gains and transient response parameters obtained
using the Sugeno model for a new set of operating
condition (off-nominal) are given in Table 5. To validate
the results obtained by the fuzzy model, RGA was applied
for the same values of Kg and tg and the results are given
in Table 6. From the table, it is observed that the values of
controller parameters obtained are almost same in all cases.
Fig. 8 shows the response of the system with PID
controller values obtained using the fuzzy model and RGA
for Kg ¼ 0.77 and tg ¼ 1.5. From the figure, it is observed
that the terminal voltage response is similar in both cases.
This demonstrates the suitability of the proposed approach
to obtain the optimal PID gains during real-time operation
of the system.
Table 4 Sugeno fuzzy rule table
tg
Very low
Low
Medium low
Medium high
High
Very high
1
1.2
1.4
1.6
1.8
2
low (0.7)
0.8574
0.8574
0.7246
0.5408
0.6102
0.6102
medium low (0.8)
0.4752
0.7246
0.6848
0.7246
0.5864
0.6030
medium high (0.9)
0.5321
0.7246
0.8080
0.7379
0.5864
0.5864
high (1.0)
0.5408
0.8574
0.7246
0.7246
0.7379
0.5864
low (0.7)
0.2862
0.3601
0.3601
0.3601
0.3107
0.3107
medium low (0.8)
0.1719
0.2862
0.3601
0.3601
0.3601
0.3107
medium high (0.9)
0.1719
0.2505
0.3601
0.3601
0.3601
0.3601
high (1.0)
0.1719
0.2862
0.2862
0.3601
0.3601
0.3601
low (0.7)
0.2187
0.2078
0.1643
0.1643
0.3578
0.4207
medium low (0.8)
0.2078
0.1643
0.1643
0.1643
0.2049
0.3547
medium high (0.9)
0.1351
0.1643
0.1757
0.1643
0.1643
0.2049
high (1.0)
0.1351
0.2049
0.1643
0.1643
0.1643
0.1757
Kg
(a) For proportional gain Kp
(b) For integral gain Ki
(c) For derivative gain Kd
IET Gener. Transm. Distrib., 2009, Vol. 3, Iss. 7, pp. 641 – 649
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Table 5 Optimal gains and transient parameters for off-nominal operating condition
tg
Kp
Ki
Kd
Ts(s)
Tr(s)
Osh(1024)
Ess(1025)
0.77
1.50
0.723
0.36
0.164
1.1100
0.9699
1.1670
8.7792
0.79
1.15
0.682
0.266
0.179
1.1404
0.9698
0.4262
8.4564
0.85
1.30
0.736
0.314
0.167
0.8628
0.8356
8.3670
6.2673
0.75
1.67
0.621
0.361
0.205
1.6344
1.3304
0.0109
1.5927
0.99
1.45
0.731
0.31
0.165
0.8353
0.8082
2.2541
5.3307
0.99
1.96
0.614
0.36
0.176
1.4373
0.9671
0.0051
9.7682
Kg
Table 6 Optimal PID gains and transient response using RGA and SFL techniques
Kg
0.77
0.79
0.85
0.75
0.99
0.99
tg
Type
Kp
Ki
Kd
Ts(s)
Tr(s)
Osh(1024)
Ess(1025)
1.50
RGA
0.7246
0.3601
0.1643
1.1960
0.8083
2.157
6.1102
SFL
0.723
0.36
0.164
1.1100
0.9699
1.1670
8.7792
RGA
0.6598
0.2927
0.1743
1.1103
0.9404
0.2889
7.5400
SFL
0.682
0.266
0.179
1.1404
0.9698
0.4262
8.4564
RGA
0.7379
0.2862
0.1643
0.9031
0.8354
6.3345
8.0084
SFL
0.736
0.314
0.167
0.8628
0.8356
8.3670
6.2673
RGA
0.6321
0.3601
0.2643
1.8021
1.0740
0.0592
2.0006
SFL
0.621
0.361
0.205
1.6344
1.3304
0.0109
1.5927
RGA
0.7080
0.3601
0.1652
0.7646
0.7646
1.960
4.8988
SFL
0.731
0.31
0.165
0.8353
0.8082
2.2541
5.3307
RGA
0.6030
0.3601
0.1757
1.4093
0.9997
0.0416
1.3932
SFL
0.614
0.36
0.176
1.4373
0.9671
0.0051
9.7682
1.15
1.30
1.67
1.45
1.96
8
Figure 8 Step response of change in terminal voltage for
off-nominal values
648
& The Institution of Engineering and Technology 2009
Conclusion
This paper has proposed a RGA and Sugeno fuzzy logic
approach for obtaining the optimal gains of PID controller
in AVR system. In this paper, the problem of discretisation
in the representation of the decision variables in the binarycoded GA has been alleviated by employing floating point
numbers to represent the PID parameters. Blend crossover
and uniform mutation which can directly deal with the real
variables have been applied. The proposed GA approach
has resulted in better dynamic performance of the AVR.
Further the proposed GA occupies less computer space and
takes less time for convergence compared with the
conventional binary-coded GA. The optimal gains
produced by the GA-based approach were used to develop
the Sugeno fuzzy system. The performance of the
algorithm in obtaining the optimal values of PID controller
parameters under various operating conditions has been
IET Gener. Transm. Distrib., 2009, Vol. 3, Iss. 7, pp. 641– 649
doi: 10.1049/iet-gtd.2008.0287
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analysed through computer simulation. The simulation result
shows that the Sugeno fuzzy system can produce the optimal
PID values accurately in a fraction of the second and this
solves the problems associated with evolutionary
computation techniques in applying to on-line application.
9
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