1.
ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 6, June 2013
2130
www.ijarcet.org
Abstract—This paper Present to design method for
determining the optimal proportional-integral-derivative
(PID) controller parameters of an Automatic Voltage
Regulator (AVR) system using the particle swarm
optimization (PSO) algorithm and Genetic Algorithm (GA).
The design goal is to minimize transient response by
minimizing overshoot, settling time and rise time of step
response. The proposed approach had superior features,
including easy implementation, stable convergence
characteristic, and good computational efficiency. Fast tuning
of optimum PID controller parameters yields high-quality
solution. First an objective function is defined, and then by
minimizing the objective functions using real-coded GA and
PSO, the optimal controller parameters can be assigned.
Compare the result of step response of AVR system by using
Particle Swarm Optimization (PSO) and Genetic Algorithm
(GA). The obtained result of the closed loop PSO-PID and
GA-PID controller response to the unit step input signal
shows excellent performance of the PID controller.
Keywords— AVR system, Feedback System, Optimization,
PID controller, PSO and GA.
1. INTRODUCTION
The task of an AVR system is to hold the terminal voltage
magnitude of a synchronous generator at a specified level.
Thus, the stability of the AVR system would seriously affect
the security of the power system. A simpler AVR system
contains five basic components such as amplifier, exciter,
generator, sensor and comparator. The real model of such a
system is shown in fig1. A unit step response of this system
without control has some oscillations which reduce the
performance of the regulation (1). Thus, a control technique
must be applied to the AVR system. For this reason, the PID
block is connected to amplifier seriously. The A small signal
model of this system including PID controller which is
constituted through the transfer functions of these
components is depicted in Fig, and the limits of the
parameters used in these transfer functions are presented(2) .
PID controllers have been widely used for speed and position
control of various system.
Several tuning methods have been proposed for the tuning of
process control loop. The most popular tuning methods are:
Ziegler- Nichols, Cohen-Coon, and Astra-Hagglund.
Unfortunately, in spite of this large range of tuning
techniques, the optimum performance cannot be achieved
[1].
Manuscript received June, 2013.
Anil kumar, ia a PG (control and instrumentation) student of University
College of engg. kota /RTU kota, ., From Nalanda, Bihar, India Mob
No8302029110
Dr. Rajeev Gupta is Professor & HOD Department of electronics
engineering, University College of engineering, Rajasthan technical
university, Kota ,(Mob.No. 9414596958;)
Several new intelligent optimization techniques have been
emerged in the past two decades like: Genetic Algorithm
(GA), Particle Swarm Optimization (PSO), Ant Colony
Optimization (ACO), Simulated Annealing (SA), and
bacterial Foraging (BF) [2]. Due to its high potential for global
optimization, GA has received great attention in control
system such as the search of optimal PID controller
parameters. The natural genetic operations would still result
in enormous computational efforts.
PSO is one of the modern Heuristics algorithms it was
developed through simulation of a simplified social system,
and has been found to be robust in solving continuous
non-linear optimization problems [2].
In this paper, a tradition method for tuning PID controller of
non-linear synchronous generator AVR system control is
represented. Then the GA and PSO based methods for tuning
the PID controller parameters are proposed as a modern
intelligent optimization algorithm.
The PSO technique can generate a high-quality solution
within shorter calculation time and stable convergence
characteristic than other stochastic methods. The integral
performance criteria in frequency domain were often used to
evaluate the controller performance, but these criteria have
their own advantages and disadvantages.
In this paper, a simple performance criterion in time domain
is proposed for evaluating the performance of a PSO-PID
controller that was applied to the complex control system.
GA is an iterative search algorithm based on natural selection
and genetic mechanism. However, GA is very fussy; it
contains selection, copy, crossover and mutation scenarios
and so on. Furthermore, the process of coding and decoding
not only impacts precision, but also increases the complexity
of the genetic algorithm. This project attempts to develop a
PID tuning method using GA algorithm. For example, ants
foraging, birds flocking, fish schooling, bacterial chemo taxis
are some of the well-known examples.
2. Linearized Model of an AVR System
There are five models:
(a) PID Controller Model,
The transfer function of PID controller is
(2.1)
Where kp, kd, and ki are the proportion coefficient,
differential coefficient, and integral coefficient, respectively.
The derivative controller adds a finite zero to the open-loop
plant transfer function and improves the transient response.
The integral controller adds a pole at the origin, thus
increasing system type by one and reducing the steady-state
error due to a step function to zero. Range of PID controller
parameters are shown in table (I).
Compare the results of Tuning of PID controller by using PSO and
GA Technique for AVR system
Anil Kumar1
,Dr. Rajeev Gupta2
2.
ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 6, June 2013
www.ijarcet.org
2131
TABLE I: RANGE OF THREE CONTROLLER PARAMETERS
Controller parameters Min. value Max. value
Kp 0 1.5
Ki 0 1
Kd 0 1
(b) Amplifier Model,
The transfer function of amplifier model is
(2.2)
where KA is an amplifier gain and τA is a time constant.
(c) Exciter Model,
The transfer function of exciter model is
(2.3)
Where KE is an amplifier gain and τE is a time constant.
(d) Generator Model,
The transfer function of generator model is
(2.4)
Where KG is an amplifier gain and τG is a time constant.
(e) Sensor Model
The transfer function of sensor model is
(2.5)
Where KR is an amplifier gain and τR is a time constant.
Fig 1. Block diagram of an AVR system with a PID
controller.
3. IMPLEMENTATION OF A PSO-PID CONTROLLER
In this paper, a PID controller using the PSO algorithm was
developed to improve the step transient response of AVR of a
generator. It was also called the PSO-PID controller. The PSO
algorithm was mainly utilized to determine three optimal
controller parameters Kp, Ki and Kd, such that the controlled
system could obtain a good step response output.
A. Individual String Definition
To apply the PSO method for searching the controller
parameters, we use the ―individual‖ to replace the ―particle‖
and the ―population‖ to replace the ―group‖ in this paper. We
defined three controller parameters kp, ki and kd , to compose
an individual by ; hence, there are three members in an
individual. These members are assigned as real values. If
there are n individuals in a population, then the dimension of
a population is nx3.
B. Evaluation Function Definition
In the meantime, we defined the evaluation function given in
(3.2) as the evaluation value of each individual in population.
The evaluation function is a reciprocal of the performance
criterion as in (3.1).
FF= (1-e-β)(Mp+Ess)+e-β(Ts-Tr) (3.1)
It implies the smaller the value of individual , the higher its
evaluation value
F=1/W (k) (3.2)
In order to limit the evaluation value of each individual of the
population within a reasonable range, the Routh–Hurwitz
criterion must be employed to test the closed-loop system
stability before evaluating the evaluation value of an
individual. If the individual satisfies the Routh–Hurwitz
stability test applied to the characteristic equation of the
system, then it is a feasible individual and the value of is
small. In the opposite case, the value of the individual is
penalized with a very large positive constant.
4. PARTICLE SWARM OPTIMIZATION
PSO is one of the optimization techniques first proposed by
Eberhart and Colleagues [5, 6]. This method has been found
to be robust in solving problems featuring non-linearity and
non-differentiability, which is derived from the
social-psychological theory. The technique is derived from
research on swarm such as fish schooling and bird flocking.
In the PSO algorithm, instead of using evolutionary operators
such as mutation and crossover to manipulate algorithms, the
population dynamics simulates a "bird flocks" behavior,
where social sharing of information takes place and
individuals can profit from the discoveries and previous
experience of all the other companions during the search for
food. Thus, each companion, called particle, in the
population, which is called swarm, is assumed to ―fly ―in
many direction over the search space in order to meet the
demand fitness function [2, 5, 6].
Fig 2. Concept of modification of a searching point by PSO
For n-variables optimization problem a flock of particles are
put into the n-dimensional search space with randomly
chosen velocities and positions knowing their best values, so
far (Pbest) and the position in the n-dimensional space [5, 6].
The velocity of each particle, adjusted accordingly to its own
experience and the other particles flying experience. For
example, the ith particle is represented, as:,
Xi = (xi1, xi2, xi3,..................xid) in the d-dimensional space,
the best previous positions of the ith particle is represented as:
Pbest = (Pbesti,1 , Pbesti,2 ,Pbesti,3..........Pbesti,d )
The index of the best particle among the group is gbest.
Velocity of the ith particle is represented as:
Vi = (Vi,1 Vi,2 Vi,3.......... Vi,d)
The updated velocity and the distance from Pbesti,d to
gbesti,d is given as ;
vi+1 = vi + c1R1 (pi,best − pi ) + c2 R2 (gi,best − pi ) (4.1)
3.
ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 6, June 2013
2132
www.ijarcet.org
and
(4.2)
where
pi and vi - are the position and velocity of particle i,
respectively;
pi,best and gi,best - is the position with the ‗best‘ objective
value found so far by particle i and the entire population
respectively;
w - is a parameter controlling the dynamics of flying;
R1 and R2 - are random variables in the range [0,1];
c1 and c2 - are factors controlling the related weighting of
corresponding terms. The random variables help the PSO
with the ability of stochastic searching.
4.1 PSO-PID Controller
PSO-PID controller for searching the optimal or near optimal
controller parameters kp, ki, and kd, with the PSO algorithm.
Each individual K contains three members kp, ki, and kd.
The searching procedures of the proposed PSO-PID
controller were shown as below.
Step 1) Specify the lower and upper bounds of the three
controller parameters and initialize randomly the individuals
of the population including searching points, velocities,
Pbests, and gbest.
Step 2) For each initial individual of the population, employ
the Routh-Hurwitz criterion to test the closed-loop system
stability and calculate the values of the four performance
criteria in the time domain, namely Mp, Ess, tr, and ts.
Step 3) Calculate the evaluation value of each individual in
the population using the evaluation function.
Step 4) Compare each individual‘s evaluation value with its
Pbest. The best evaluation value among the Pbest is denoted
as gbest.
Step 5) Modify the member velocity v of each individual K
According to
For i = 1,2,3.......n.
m = 1,2,3.....d.
Where w is weighting factor. When g is 1, represents the
change in velocity of kp controller Parameter. When g is 2,
vj,2 represents the change in velocity of ki controller
parameter.
Step 6)
. (4.3)
Step 7) Modify the member position of each individual
K according to
,
(4.4)
Where and represent the lower and upper bounds,
respectively, of member g of the individual K.
Step 8)If the number of iterations reaches the maximum,
then go to Step 9. Otherwise, go to Step 2.
Step 9) The individual that generates the latest gbest is an
optimal controller parameter.
Fig3: The block diagram of PID Controller with PSO algorithms
PSO parameters are used for verifying the performance of the
PSO-PID controller in searching the PID controller
parameters:
The member of each individual is Kp, Ki and Kd;
Population size = 100,
Inertia weight factor is set
Acceleration constant C1=1.8 and C2=1.8
We have to use the value of beta is 0.5 and 1.0
Through about 150 iterations (150 generations), the PSO
method can prompt convergence and obtain good evaluation
value. These results show that the PSO-PID controller can
search optimal PID controller parameters quickly and
efficiently.
5. Result of PID controller by using PSO technique
Terminal Voltage Step Response
Time (sec)
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
TerminalVoltage
Fig 4: Terminal voltage step response of an AVR system with
PSO (β = 0.5, generations (iterations) = 20).
S
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal voltage step response
Time (sec)
Terminalvoltage
Fig 5: Terminal voltage step response of an AVR system with
PSO (β = 0.5, generations (iterations) = 50).
Terminal voltage Step Response
Time (sec)
Terminalvoltage
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Fig 6: Terminal voltage step response of an AVR system with PSO
(β = 0.5, generations (iterations) = 100).
4.
ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 6, June 2013
www.ijarcet.org
2133
Terminal Voltage Step Response
Time (sec)
TerminalVoltage
0 0.5 1 1.5 2 2.5 3 3.5 4
0
0.2
0.4
0.6
0.8
1
1.2
Fig 7: Terminal voltage step response of an AVR system with PSO
(β = 0.5, generations (iterations) = 150).
Terminal Voltage Step Response
Time (sec)
TerminalVoltage
0 2 4 6 8 10 12 14 16 18
0
0.2
0.4
0.6
0.8
1
1.2
Fig 8: Terminal voltage step response of an AVR system with PSO
(β = 1.0, generations (iterations) = 20).
Terminal Voltage Step Response
Time (sec)
TerminalVoltage
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.2
0.4
0.6
0.8
1
1.2
Fig 9: Terminal voltage step response of an AVR system with PSO
(β = 1.0, generations (iterations) = 50).
Terminal Voltage Step Response
Time (sec)
TerminalVoltage
0 0.5 1 1.5 2 2.5 3 3.5 4
0
0.2
0.4
0.6
0.8
1
1.2
Fig 10: Terminal voltage step response of an AVR system with PSO
(β = 1.0, generations (iterations) = 100).
Terminal Voltage Step Response
Time (sec)
TerminalVoltage
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
Fig 11: Terminal voltage step response of an AVR system with PSO
(β = 1.0, generations (iterations) = 150).
We present a comparative study of the performance of the
initial global best position out of randomly initialized swarm
particles to the performance of the final global best position
which comes after the application of ―particle swarm
optimization‖ algorithm.
The result in the tabular format:
TableII: Performance of gbest and fbest position of PSO
Beta No. of
Iteratio
n
fbest Gbest
0.5 20 1.219
3
[0.0041 0.0057 0.0083]
0.5 50 0.656
5
[0.0046 0.0002 0.0092]
0.5 100 0.7128 [0.0103 0.0043 0.0139]
0.5 150 1.065
7
1.0e-004*[0.1631 0.7006 0.8990]
1.0 20 0.630
5
[0.0125 0.0012 0.0116]
1.0 50 1.162
0
[0.0015 0.0009 0.0077]
1.0 100 1.186
9
1.0e-003 *[ 0.7018 0.6370
0.7526]
1.0 150 0.500
3
[0.0048 0.0082 0.0122]
6. Genetic Algorithm Optimization
Artificial intelligent techniques have come to be the most
widely used tool for solving many optimization problems.
Genetic Algorithm (GA) is a relatively new approach of
optimum searching, becoming increasing popular in science
and engineering disciplines [7]. The basic principles of GA
were first proposed by Holland, it is inspired by the
mechanism of natural selection where stronger individuals
would likely be the winners in a competing environment [8].
In this approach, the variables are represented as genes on a
chromosome. Gas features a group of candidate solutions
(population) on the response surface. Through natural
selection and genetic operators, mutation and crossover,
chromosomes with better fitness are found. Natural selection
guarantees the recombination operator, the GA combines
genes from two parent chromosomes to form two
chromosomes (children) that have a high probability of
having better fitness that their parents [7, 9]. Mutation allows
new area of the response surface to be explored. In this paper,
a GA process is used to find the optimum tuning of the PID
controller, by forming random of population of 50 real
numbers double precision chromosomes is created
representing the solution space for the PID controller
parameters (KP, KI and KD), which represent the genes of
chromosomes. The GA proceeds to find the optimal solution
through several generations, the mutation function is the
adaptive feasible, and the crossover function is the scattered.
6.1 Fitness Function
In PID controller design methods, the most common
performance criteria are Integrated Absolute Error (IAE),
Integrated of Time weight Square Error (ITSE) and Integrated
of Square Error (ISE) that can be evaluated analytically in
frequency domain [2]. Each criterion has its own advantage
and disadvantage. For example, disadvantage of IAE and ISE
criteria is that its minimization can result in a response with
relatively small overshot but a long settling time, because the
ISE performance criteria weights all errors equally
independent of time. Although, ITSE performance criterion
can overcome this is the disadvantage of ISE criterion. The
IAE, ISE, and ITSE performance criterion formulas are as
follows:
5.
ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 6, June 2013
2134
www.ijarcet.org
IAE Index: IAE = (6.1)
ISE Index: ISE = (6.2)
ITSE Index: ITSE = (6.3)
ITAE Index: ITAE = (6.4)
A set of good control parameters can yield a good step
response that will result in performance criteria minimization
in the time domain, this performance criterion is called
Fitness Function (FF) which can be formulated as follows [2]:
FF= (1-e-β)(Mp+Ess)+e-β(Ts-Tr) (6.5)
To illustrate the working process of genetic algorithm, the
steps to realize a basic GA are listed:
Step 1: Represent the problem variable domain as a
chromosome of fixed length; choose the size of the
chromosome population N, the crossover probability Pc and
the mutation probability Pm.
Step 2: Define a fitness function to measure the performance
of an individual chromosome in the problem domain. The
fitness function establishes the basis for selecting
chromosomes that will be mated during reproduction.
Step 3: Randomly generate an initial population of size N:
X1, X2, X3, …………., XN
Step 4: Calculate the fitness of each individual chromosome:
f(X1), f(X2),…………....., f(XN).
Step 5: Select a pair of chromosomes for mating from the
current population. Parent chromosomes are selected with a
probability related to their fitness. High fit chromosomes
have a higher probability of being selected for mating than
less fit chromosomes.
Step 6: Create a pair of offspring chromosomes by applying
the genetic operators.
Step 7: Place the created offspring chromosomes in the new
population.
Step 8: Repeat Step 5 until the size of the new population
equals that of initial population, N.
Step 9: Replace the initial (parent) chromosome population
with the new (offspring) population.
Step 10: Go to Step 4, and repeat the process until the
termination criterion is satisfied.
Fig 12: Block-diagram of AVR system with GA-PID controller
GA parameters are used for verifying the performance of the
GA-PID controller in searching the PID controller
parameters: the member of each individual is Kp, Ki and Kd;
We have to use initial population is random function.
Population size = 100, crossover fraction=0.8
7. Result of PID controller by using PSO technique
0 1 2 3 4 5 6 7 8 9
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal Voltage step response
time (sec)
TerminalVoltage
Fig 13: Terminal voltage step response of an AVR system with
Genetic Algorithm (β = 0.5, generations = 20).
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
Terminal voltage step response of ga tune pid controller system
time in seconds
Terminalvoltage
Fig 14: Terminal voltage step response of an AVR system with
Genetic Algorithm (β = 0.5, generations = 50).
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal voltage step response of ga tune pid controller system
time in seconds
Terminalvoltage
Fig15: Terminal voltage step response of an AVR system with
Genetic Algorithm (β = 0.5, generations = 100).
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
Terminal voltage step response of ga tune pid controller system
time in seconds
Terminalvoltage
Fig 16: Terminal voltage step response of an AVR system with
Genetic Algorithm (β = 0.5, generations = 150).
0 2 4 6 8 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal Voltage step response
time (sec)
TerminalVoltage
Fig 17: Terminal voltage step response of an AVR system with
Genetic Algorithm (β = 1.0, generations = 20).
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
Terminal voltage step response of ga tune pid controller system
time in seconds
Terminalvoltage
Fig 18: Terminal voltage step response of an AVR system with
Genetic Algorithm (β = 1.0, generations = 50).
6.
ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 6, June 2013
www.ijarcet.org
2135
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
Terminal voltage step response
time (sec)
Terminalvoltage
Fig 19: Terminal voltage step response of an AVR system with
Genetic Algorithm (β = 1.0, generations = 100).
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
Terminal voltage step response of ga tune pid controller system
time in seconds
Terminalvoltage
Fig 20: Terminal voltage step response of an AVR system with
Genetic Algorithm (β = 1.0, generations = 150).
8. Comparison of Two Proposed Controllers
In order to emphasize the advantages of the proposed
PSO-PID controller, we also implemented the GA-PID
controller derived from the real-value GA method with the
Elitism scheme [5], [6]. We have compared the characteristics
of the two controllers using the same valuation function and
individual definition. The following real-value GA parameters
have been used:
Two proposed controllers and their performance evaluation
criteria in the time domain were implemented by Matlab and
control system toolbox.
7.1 Terminal Voltage Step Response: There were eight
simulation examples to evaluate the performance of both the
PSO-PID and the GA-PID controllers. In each simulation
example, the weighting factor in the performance criterion
and the number of iterations (generations) were set as
follows:
The simulation results that showed the best solution were
summarized in Table I. As can be seen, both controllers could
give good PID controller parameters in each simulation
example, providing good terminal voltage step response of
the AVR system. Table I also shows the four performance
criteria in the time domain of each example. As revealed by
the above four performance criteria, the PSO-PID controller
has better performance than the GA-PID controller.
There are eight simulation examples of terminal voltage step
response of the AVR system. As can be seen, the PSO-PID
controller could create very perfect step response of the AVR
system, indicating that the PSO-PID controller is better than
the GA-PID controller.
7.2 Convergence Characteristic: Under the same
conditions, we performed simulations using the two
proposed controllers to compare their convergence
characteristics. Fig. 12 showed their convergence properties.
As can be seen, the PSO-PID controller has better evaluation
value than the GA-PID controller. The results showed that the
PSO-PID controller could obtain higher quality solution,
indicating the drawbacks of GA method mentioned in [10]
and [14].
We also performed 100 trials for both proposed controllers
with different random number to observe the variation in
their evaluation values. In addition, the maximum, minimum,
and average evaluation values were obtained by the two
methods. The PSO-PID controller has better convergence
characteristic.
7.3 Computation Efficiency: The comparison of
computation efficiency of both methods is shown in Table 1.
As can be seen, because the PSO method does not perform
the selection and crossover operations in evolutionary
processes, it can save some computation time compared with
the GA method, thus proving that the PSO-PID controller is
more efficient than the GA-PID controller.
8. Simulation and result
Transfer function of AVR system without using PSO & GA
0.2 s + 10
------------------------------------------------------------ (7.1)
0.00128 s^4 + 0.08288 s^3 + 0.9816 s^2 + 1.9 s + 11
0 2 4 6 8 10 12
0
0.5
1
1.5
Terminal Voltage Step Response
Time (sec)
TerminalVoltage
Fig21: step response of AVR system without using PSO &
GA
0 1 2 3 4 5 6 7
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal Voltage Step Response
Time (sec)
TerminalVoltage
PSO-PID
GA-PID
n=20, Beta=0.5
Fig 22: Terminal voltage step response of an AVR system with different
Controllers (β = 0.5, generations = 20).
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal Voltage step response
Time (sec)
TerminalVoltage
PSO-PID
GA-PID
n=50 & Beta=0.5
Fig 23: Terminal voltage step response of an AVR system with different
Controllers (β = 0.5, generations = 50).
7.
ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 6, June 2013
2136
www.ijarcet.org
0 1 2 3 4 5 6 7 8
0
0.2
0.4
0.6
0.8
1
1.2
Terminal Voltage step response
Time (sec)
TerminalVoltage
PSO-PID
GA-PID
n=100 & Beta=0.5
Fig24: Terminal voltage step response of an AVR system with different
Controllers (β = 0.5, generations = 100)
0 0.5 1 1.5 2 2.5 3 3.5 4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal Voltage step response
Time (sec)
TerminalVoltage
PSO-PID
GA-PID
n=150 & Beta=0.5
Fig 25: Terminal voltage step response of an AVR system with different
Controllers (β = 0.5, generations = 150).
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal Voltage step response
Time (sec)
TerminalVoltage
PSO-PID
GA-PID
n=20 & Beta=1.0
Fig 26: Terminal voltage step response of an AVR system with different
Controllers (β = 1.0, generations = 20)
0 1 2 3 4 5 6 7
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal Voltage step response
Time (sec)
TerminalVoltage
PSO-PID
GA-PID
n=50 & Beta=1.0
Fig 27: Terminal voltage step response of an AVR system with different
Controllers (β = 1.0, generations = 50).
0 1 2 3 4 5 6 7
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Terminal Voltage step response
Time (sec)
TerminalVoltage
PSO-PID
GA-PID
n=50 & Beta=1.0
Fig 28: Terminal voltage step response of an AVR system with different
Controllers (β = 1.0, generations = 100).
0 1 2 3 4 5 6 7
0
0.2
0.4
0.6
0.8
1
1.2
Terminal Voltage step response
Time (sec)
TerminalVoltage
PSO-PID
GA-PID
n=150 & Beta=1.0
Fig 29: Terminal voltage step response of an AVR system with different
Controllers (β = 1.0, generations = 150).
0 50 100 150
0
0.5
1
1.5
2
Generation
EvaluationValue
PSO
GA
Fig 30: Convergence tendency of the evaluation value of PSO & GA methods.
Fig.21 shows the original terminal voltage step response of
the AVR system without a PID controller. To simulate this
case, we found that Mp=61.6388%, Tr = 0.3417sec, Ts =
7.4798 sec.
TableIII: comparison of the parameters of PID by using PSO & GA
8.
ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 6, June 2013
www.ijarcet.org
2137
Β N0. Of
generations
Type of
controller
Kp Ki Kd Mp(%) ts tr Ess Evaluation
value
0.5 20 GA-PID 0.4370 0.2353 0.2391 0.0165 2.0316 0.7267 0 0.9387
PSO-PID 0.4315 0.2356 0.1557 2.4064 1.7284 0.6801 0 1.0868
0.5 50 GA-PID 0.5395 0.2645 0.2466 0 1.2828 0.5225 0 1.3952
PSO-PID 0.5846 0.2987 0.2438 0.4566 0.7555 0.4762 0 1.3837
0.5 100 GA-PID 0.3002 0.1682 0.1524 0.2869 2.3165 1.1758 0 1.4044
PSO-PID 0.4497 0.2370 0.2636 0.2100 2.2400 0.7258 0 1.8399
0.5 150 GA-PID 0.6233 0.3728 0.2820 0.7377 0.6696 0.4207 0 1.3996
PSO-PID 0.5374 0.3096 0.2572 0.1548 0.9808 0.5076 0 1.8398
1.0 20 GA-PID 0.3371 0.1656 0.2489 0.3370 3.4780 1.6281 0 0.7054
PSO-PID 0.1035 0.0667 0.0228 0 4.0772 2.4701 0 0.7511
1.0 50 GA-PID 0.4373 0.2164 0.1865 0 1.3584 0.6969 0 1.4815
PSO-PID 0.6938 0.3780 0.3216 0.0846 0.5772 0.3653 0 0.7689
1.0 100 GA-PID 0.6235 0.3212 0.2865 0 0.7266 0.4242 0 1.4847
PSO-PID 0.3741 0.1864 0.1367 0 1.2991 0.8182 0 0.7600
1.0 150 GA-PID 0.5684 0.3148 0.2579 0 0.8192 0.4786 0 1.4860
PSO-PID 0.5959 0.2745 0.2998 0 2.1816 0.4407 0 0.7678
9. DISCUSSION AND CONCLUSION
From this table it represents the better performance of
PSO-PID as compared to GA-PID technique. The no. of
generation is increased the performance is increased in
both methods. It is clear from the results that the proposed
PSO method can avoid the shortcoming of premature
convergence of GA method and can obtain higher quality
solution with better computation efficiency. The proposed
method integrates the PSO algorithm with the new
time-domain performance criterion into a PSO-PID
controller. Through the simulation of a practical AVR
system, the results show that the proposed controller can
perform an efficient search for the optimal PID controller
parameters. In addition, in order to verify it being superior to
the GA
method, many performance estimation schemes are
performed, such as
multiple simulation examples for their terminal
voltage step responses;
convergence characteristic of the best evaluation
value;
dynamic convergence behavior of all individuals in
population during the evolutionary processing;
Computation efficiency.
The amount of overshoot for the output response was
successfully decreased using the above two techniques.
Genetic algorithm and Particle Swarm Optimization enabled
the PID controller to get an output which is robust and has
faster response. As the number of iterations (generations) in
PSO Algorithm and also the no. of generations in GA went
on increasing the performance of
the system also went on improving. The performance
characteristics of the PID controller by using PSO Algorithm
give the better results as compared to Genetic Algorithm.
8. REFERENCES
[1] Astrom, K. J. and T., Hagglund, PID Controllers: Theory,
Design and Tuning, ISA, Research Triangle, Par, NC, (1995)
[2] R. C. Eberhart and Y. Shi, ―Comparison between genetic
algorithms and particle swarm optimization,‖ in Proc. IEEE
Int. Conf. Evol. Comput., Anchorage, AK, May 1998, pp.
611–616.
[3] Adel A. A. El-Gammal1 Adel A. El-Samahy A Modified
Design of PID Controller For DC Motor Drives Using Particle
Swarm Optimization PSO 1Energy
Research Centre, University of Trinidad and Tobago UTT
(Trinidad and Tobago), Lisbon, Portugal, March 18-20, 2009
[4] Gaing, Z.L. (2004). A particle swarm optimization
approach for optimum design of PID controller in AVR
system. IEEE Transaction on Energy Conversion, Vol.19 (2),
pp.384-391.
[5] Zhao, J., Li, T. and Qian, J. (2005). Application of particle
swarm optimization algorithm on robust PID controller
tuning. Advances in Natural Computation: Book Chapter.
Springer Berlin Heidelberg, pp. 948-957.
[6] Mahmud Iwan Solihin, Lee Fook Tack and Moey Leap
Kean‖ Tuning of PID Controller Using Particle Swarm
Optimization (PSO)‖ Proceeding of the International
Conference on Advanced Science, Engineering and
Information Technology 2011.
[7] Wen-wen Cai , Li-xin Jia , Yan-bin Zhang , Nan Ni‖
Design and simulation of intelligent PID controller based on
particle swarm optimization‖ School of Electrical
Engineering Xi'an Jiao Tong University Xi'an, Shaanxi,
710049, P. R. China Caiwenwen0533@yahoo.com.cn
[8] G. Cheng, Genetic Algorithms & Engineering Design.
New York: Wiley, 1997.
[13] Y. Shi and R. C. Eberhart, ―Empirical study of particle
swarm optimization,‖ in Proc. IEEE Int. Conf. Evol.
Comput., Washington, DC, July 1999, pp. 1945–1950.
[14] R. C. Eberhart and Y. Shi, ―Comparison between genetic
algorithms and particle swarm optimization,‖ in Proc. IEEE
9.
ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 6, June 2013
2138
www.ijarcet.org
Int. Conf. Evol. Comput., Anchorage, AK, May 1998, pp.
611–616.
[15] P. J. Angeline, ―Using selection to improve particle
swarm optimization,‖ in Proc. IEEE Int. Conf. Evol.
Comput., Anchorage, AK, May 1998, pp. 84–89.
[16] H. Yoshida, K. Kawata, and Y. Fukuyama, ―A particle
swarm optimization for reactive power and voltage control
considering voltage security assessment,‖ IEEE Trans.
Power Syst., vol. 15, pp. 1232–1239, Nov. 2000.
[17] S. Naka, T. Genji, T. Yura, and Y. Fukuyama, ―Practical
distribution state estimation using hybrid particle swarm
optimization,‖ in Proc. IEEE Power Eng. Soc. Winter
Meeting, vol. 2, 2001, pp. 815–820.
AUTHOR BIOGRAPHY
1 Anil Kumar
PG (M.TECH, Control & Instrumentation) student,
Department of electronics engineering
University College of engineering,
Rajasthan technical university, Kota.
(Mob.No.8302029110;
2. Dr. Rajeev Gupta
Professor & HOD
Department of electronics engineering
University College of engineering,
Rajasthan technical university, Kota
(Mob.No.9414596958;
Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.
Be the first to comment