Compare the results of Tuning of PID controller by using PSO and GA Technique for AVR system Anil Kumar 1,Dr. Rajeev Gupta 2

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1 ISSN: Volume 2, Issue 6, June 23 Compare the results of Tuning of PID controller by using PSO and GA Technique for AVR system Anil Kumar,Dr. Rajeev Gupta 2 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 and 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.. 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 fig. A unit step response of this system without control has some oscillations which reduce the performance of the regulation (). 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 []. Manuscript received June, 23. Anil kumar, ia a PG (control and instrumentation) student of University College of engg. kota /RTU kota,., From Nalanda, Bihar, India Mob No83229 Dr. Rajeev Gupta is Professor & HOD Department of electronics engineering, University College of engineering, Rajasthan technical university, Kota,(Mob.No ;) 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 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.) 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). 23

2 ISSN: Volume 2, Issue 6, June 23 TABLE I: RANGE OF THREE CONTROLLER PARAMETERS Controller parameters Min. value Max. value Kp.5 Ki Kd (b) Amplifier Model, The transfer function of amplifier model is (2.2) where K A is an amplifier gain and τ A is a time constant. (c) Exciter Model, The transfer function of exciter model is (2.3) Where K E is an amplifier gain and τ E is a time constant. (d) Generator Model, The transfer function of generator model is (2.4) Where K G is an amplifier gain and τ G is a time constant. (e) Sensor Model The transfer function of sensor model is (2.5) Where K R is an amplifier gain and τ R is a time constant. FF= (-e-β)(mp+ess)+e-β(ts-tr) (3.) It implies the smaller the value of individual, the higher its evaluation value F=/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. Block diagram of an AVR system with a PID controller. 3. IMPLEMENTATION OF A 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 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.). 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 = (xi, xi2, xi3,...xid) in the d-dimensional space, the best previous positions of the ith particle is represented as: Pbest = (Pbesti,, 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, Vi,2 Vi,3... Vi,d) The updated velocity and the distance from Pbesti,d to gbesti,d is given as ; v i+ = vi + c R (pi,best pi ) + c 2 R 2 (gi,best pi ) (4.) 23

3 ISSN: Volume 2, Issue 6, June 23 and where (4.2) 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; R and R2 - are random variables in the range [,]; c and c2 - are factors controlling the related weighting of corresponding terms. The random variables help the PSO with the ability of stochastic searching. 4. Controller 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 controller were shown as below. Step ) 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, t r, and t s. 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 Fig3: The block diagram of PID Controller with PSO algorithms PSO parameters are used for verifying the performance of the controller in searching the PID controller parameters: The member of each individual is Kp, Ki and Kd; Population size =, Inertia weight factor is set Acceleration constant C=.8 and C2=.8 We have to use the value of beta is.5 and. Through about 5 iterations (5 generations), the PSO method can prompt convergence and obtain good evaluation value. These results show that the controller can search optimal PID controller parameters quickly and efficiently. 5. Result of PID controller by using PSO technique Step Response Fig 4: step response of an AVR system with PSO (β =.5, generations (iterations) = 2). step response S For i =,2,3...n. m =,2,3...d. Where w is weighting factor. When g is, represents the change in velocity of kp controller Parameter. When g is 2, v j,2 represents the change in velocity of ki controller parameter. Step 6) Fig 5: step response of an AVR system with PSO (β =.5, generations (iterations) = 5)..4 Step Response.2. (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., Time 5 (sec) Fig 6: step response of an AVR system with PSO (β =.5, generations (iterations) = ). 232

4 ISSN: Volume 2, Issue 6, June Step Response Fig 7: step response of an AVR system with PSO (β =.5, generations (iterations) = 5) Step Response Fig 8: step response of an AVR system with PSO (β =., generations (iterations) = 2) Step Response Fig 9: step response of an AVR system with PSO (β =., generations (iterations) = 5) Step Response Fig : step response of an AVR system with PSO (β =., generations (iterations) = ) Step Response Fig : step response of an AVR system with PSO (β =., generations (iterations) = 5). 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 fbest Gbest Iteratio n [ ] [ ] [ ] e-4*[ ] [ ] [ ] e-3 *[ ] [ ] 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 5 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. 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: 233

5 ISSN: Volume 2, Issue 6, June 23 IAE Index: IAE = (6.) ISE Index: ISE = (6.2).4.2 step response 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= (-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 : 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: X, X 2, X 3,., XN Step 4: Calculate the fitness of each individual chromosome: f(x ), f(x 2 ),..., f(x N ). 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 : Go to Step 4, and repeat the process until the termination criterion is satisfied time (sec) Fig 3: step response of an AVR system with Genetic Algorithm (β =.5, generations = 2) step response of ga tune pid controller system Fig 4: step response of an AVR system with Genetic Algorithm (β =.5, generations = 5) step response of ga tune pid controller system Fig5: step response of an AVR system with Genetic Algorithm (β =.5, generations = ) step response of ga tune pid controller system Fig 6: step response of an AVR system with Genetic Algorithm (β =.5, generations = 5)..4.2 step response time (sec) Fig 7: step response of an AVR system with Genetic Algorithm (β =., generations = 2). step response of ga tune pid controller system.8 Fig 2: Block-diagram of AVR system with controller GA parameters are used for verifying the performance of the 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 =, crossover fraction=.8 7. Result of PID controller by using PSO technique Fig 8: step response of an AVR system with Genetic Algorithm (β =., generations = 5). 234

6 ISSN: Volume 2, Issue 6, June step response time (sec) Fig 9: step response of an AVR system with Genetic Algorithm (β =., generations = ) step response of ga tune pid controller system Fig 2: step response of an AVR system with Genetic Algorithm (β =., generations = 5). 8. Comparison of Two Proposed Controllers In order to emphasize the advantages of the proposed controller, we also implemented the 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. Step Response: There were eight simulation examples to evaluate the performance of both the and the 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 controller has better performance than the controller. There are eight simulation examples of terminal voltage step response of the AVR system. As can be seen, the controller could create very perfect step response of the AVR system, indicating that the controller is better than the controller. 7.2 Convergence Characteristic: Under the same conditions, we performed simulations using the two proposed controllers to compare their convergence characteristics. Fig. 2 showed their convergence properties. As can be seen, the controller has better evaluation value than the controller. The results showed that the controller could obtain higher quality solution, indicating the drawbacks of GA method mentioned in [] and [4]. We also performed 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 controller has better convergence characteristic. 7.3 Computation Efficiency: The comparison of computation efficiency of both methods is shown in Table. 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 controller is more efficient than the controller. 8. Simulation and result Transfer function of AVR system without using PSO & GA.2 s (7.).28 s^ s^ s^2 +.9 s Step Response Fig2: step response of AVR system without using PSO & GA Step Response n=2, Beta= Fig 22: step response of an AVR system with different Controllers (β =.5, generations = 2) step response n=5 & Beta= Fig 23: step response of an AVR system with different Controllers (β =.5, generations = 5). 235

7 Evaluation Value ISSN: Volume 2, Issue 6, June 23.2 step response n= & Beta= step response n=5 & Beta= Fig24: step response of an AVR system with different Controllers (β =.5, generations = ) step response n=5 & Beta= Fig 25: step response of an AVR system with different Controllers (β =.5, generations = 5)..4.2 step response n=2 & Beta= Fig 28: step response of an AVR system with different Controllers (β =., generations = ) step response n=5 & Beta= Fig 29: step response of an AVR system with different Controllers (β =., generations = 5) PSO GA Fig 26: step response of an AVR system with different Controllers (β =., generations = 2) step response n=5 & Beta=. 5 5 Generation Fig 3: Convergence tendency of the evaluation value of PSO & GA methods Fig.2 shows the original terminal voltage step response of the AVR system without a PID controller. To simulate this case, we found that Mp=6.6388%, Tr =.347sec, Ts = sec Fig 27: step response of an AVR system with different Controllers (β =., generations = 5). TableIII: comparison of the parameters of PID by using PSO & GA 236

8 ISSN: Volume 2, Issue 6, June 23 Β N. Of generations Type of controller K p K i K d Mp(%) t s t r Ess Evaluation value DISCUSSION AND CONCLUSION From this table it represents the better performance of as compared to 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 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 [] Astrom, K. J. and T., Hagglund, PID Controllers: Theory, Design and Tuning, ISA, Research Triangle, Par, NC, (995) [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 998, pp [3] Adel A. A. El-Gammal Adel A. El-Samahy A Modified Design of PID Controller For DC Motor Drives Using Particle Swarm Optimization PSO Energy Research Centre, University of Trinidad and Tobago UTT (Trinidad and Tobago), Lisbon, Portugal, March 8-2, 29 [4] Gaing, Z.L. (24). A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Transaction on Energy Conversion, Vol.9 (2), pp [5] Zhao, J., Li, T. and Qian, J. (25). Application of particle swarm optimization algorithm on robust PID controller tuning. Advances in Natural Computation: Book Chapter. Springer Berlin Heidelberg, pp [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 2. [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, 749, P. R. China Caiwenwen533@yahoo.com.cn [8] G. Cheng, Genetic Algorithms & Engineering Design. New York: Wiley, 997. [3] Y. Shi and R. C. Eberhart, Empirical study of particle swarm optimization, in Proc. IEEE Int. Conf. Evol. Comput., Washington, DC, July 999, pp [4] R. C. Eberhart and Y. Shi, Comparison between genetic algorithms and particle swarm optimization, in Proc. IEEE 237

9 Int. Conf. Evol. Comput., Anchorage, AK, May 998, pp [5] P. J. Angeline, Using selection to improve particle swarm optimization, in Proc. IEEE Int. Conf. Evol. Comput., Anchorage, AK, May 998, pp [6] 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. 5, pp , Nov. 2. [7] 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, 2, pp ISSN: Volume 2, Issue 6, June 23 AUTHOR BIOGRAPHY Anil Kumar PG (M.TECH, Control & Instrumentation) student, Department of electronics engineering University College of engineering, Rajasthan technical university, Kota. (Mob.No.83229; 2. Dr. Rajeev Gupta Professor & HOD Department of electronics engineering University College of engineering, Rajasthan technical university, Kota (Mob.No ; 238