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• 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;