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Design of Robust Optimal Fractional-Order Pid Controllers
Using Particle Swarm Optimization Algorithm for
Automatic Voltage Regulator (AVR) System

 

Saeed Balochian1, Hossein Baloochin2 and Hadi Ramezanian3

1,3Department of Electrical Engineering, Gonabad Branch,
Islamic Azad University, Gonabad, Iran
2Department of Electrical Engineering, Ferdows Branch,
Islamic Azad University, Ferdows, Iran


corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

 

ABSTRACT

In this paper, a fractional order controller with a first-order low pass filter in derivative was designed. Since disturbance rejection is more common than set point tracking in industrial processes, the performance of the system was evaluated by its ability to reject disturbance. Morever, a method for robust optimum tuning of fractional PID controllers for AVR system using Particle swarm optimization (PSO) algorithm was presented. Using the H∞-norm of a SISO linear system, condition for disturbance rejection was determined and constrained optimization problem was solved. The proposed approach with new defined fitness function has very easy implementation and has the most control performance. The influence and efficiency of the proposed method were illustrated in simulations.

 

INTRODUCTION

In the last decade, fractional-order dynamic systems and controllers had been widely studied in many areas of engineering and science (Baleanu et al. 2012a, Baleanu et al. 2012b, Pan and Das 2013). The concept of fractional-order PID (FOPID) controllers was proposed by Podlubny in 1999. Hardware and digital realizations of fractional-order systems can be followed in Valerio and Sada (2011). Biswas et al. (2009) presented an FOPID design method based on differential evolution (DE) technique. Moreover, Yeroglu and Tan (2011) presented a method based on the Ziegler–Nichols and the Astrom–Hagglund methods. Luo et al. (2011a) also designed a fractional order (PI)λ controller to improve the flight control performance of a small fixed-wing unmanned aerial . . . . read more

 

REFERENCES

AMER ML, HASSAN HH, YOUSSEF HM. 2008. Modified Evolutionary Particle Swarm Optimization for AVR-PID tuning.  Communications and Information Technology Systems and Signals, 2008 Marathon Beach, Attica, Greece. 164-173.
BALEANU D, DIETHELM K, SCALAS E, TRUJILLO JJ. 2012a. Fractional Calculus: Models and Numerical Methods. Singapore: World Scientific Publishing Company. 428p.
BALEANU D, TENREIRO MJA, LUO ACJ. 2012b. Fractional Dynamics and Control. New York, USA: Springer Science+Business Media. 310 pp.
BARBOSA RS, TENREIRO MJA, JESUS IS. 2010. Effect of fractional orders in the velocity control of a servo system. Comput Math Appl, 59, 1679-1686.
BINGUL Z, KARAHAN O. 2011. Tuning of fractional PID controllers using PSO algorithm for robot trajectory control. In: Proceedings of the IEEE International Conference on Mechatronics; 13-15 April 2011; Istanbul, Turkey: IEEE. p13-15.
BISWAS A, DAS S, ABRAHAM A, DASGUPTA S. 2009. Design of fractional-order PID controllers with an improved differential evolution. Engineering Applications of Artificial Intelligence 22:343-350.
CAPONETTO R, DONGOLA G, FORTUNA L, PETRAS I. 2010. Fractional order systems, modeling and control applications. World scientific series on nonlinear science, series A (World Scientific Publishing Co. Pvt. Ltd.).
COELHO LDS. 2009. Tuning of PID Controller for an Automatic Regulator Voltage System Using chaotic Optimization Approach. Chaos Solitons & Fractals, 39(4):1504-1514.
CVETKOVSKI G, PETKOVSKA L. 2013. Efficiency Improvement of Axial Flux PM Motor Using Particle Swarm Optimisation. PrzeglÄ…d Elektrotechniczny (2b): 38-42.
DAS S. 2011. Functional Fractional Calculus. Berlin, Germany: Springer. 612p.
DAS S, PAN I. 2012. Chaotic multi-objective optimization based design of fractional order PIλ Dµ controller in AVR system. International Journal of Electrical Power & Energy Systems 43(1), 393-407.
DAS S, PAN I. 2013. Frequency domain design of fractional order PID controller for AVR system using chaotic multi-objective optimization. Electrical Power and Energy Systems, 51, 106-118.
DEVARAJ D, SELVABALA B. 2009. Real-coded genetic algorithm and fuzzy logic approach for real-time tuning of proportional-integral-derivative controller in automatic voltage regulator system. IET Gener. Transm. Distrib 3(7):641-649.
DOMINGUES J, VALERIO D, DA CJS. 2009. Rule-based fractional control of an irrigation canal.  In: 35th annual conference of IEEE industrial electronics IECON ’09; 3-5 November 2009; Porto, Portugal: IEEE. p1712-1717.
GAING ZLA. 2004. Particle Swarm Optimization Approach for Optimum Design of PID Controller in AVR System.  IEEE Transactions on Energy Conversion, 2004. 384-391.
GOZDE H, TAPLAMACIOGLU MC. 2010. Application Of artificial bee colony algorithm in an automatic voltage regulator (AVR) system. International Journal on Technical and Physical Problems of Engineering, 1(3), 88-92.
KENNEDY  J, EBERHART RC. 1995. Particle swarm optimization.  In: Proceedings of IEEE International Conference on Neural Networks; Nov/Dec 1995; Perth, Australia: IEEE. p1942-1948.
KROHLING RA, REY JP. 2001. Design of optimal disturbance rejection PID controllers using genetic algorithm. IEEE Trans. Evol. Comput, 5, 78-82.
LUO Y, CHAO H, DI L, CHEN YQ. 2011a. Lateral directional fractional order (PI)a control of a small fixed-wing unmanned aerial vehicles: controller designs and flight tests. IET Control Theory Appl 5: 2156-2167.
LUO Y, CHEN YQ. 2009. Fractional-order [proportional derivative] controller for a class of fractional order systems. Automatica 45 (10): 2446-2450.
LUO Y, CHEN YQ, PI Y. 2011b. Experimental study of fractional order proportional derivative controller synthesis for fractional order systems. Mechatronics 21: 204-214.
PAN I, DAS S. 2013. Intelligent Fractional Order Systems and Control. Berlin, Germany: Springer-Verlag Berlin Heidelberg. 298p.
PODLUBNY I. 1999. Fractional-order systems and PIλ Dµ controllers. IEEE Transactions on Automatic Control  44:208-214.
RAHIMIAN M, RAAHEMIFAR K. 2011. Optimal PID controller design for AVR system using particle swarm optimization algorithm. In: IEEE 24th Canadian Conference on Electrical and Computer Engineering (CCECE); 8-11 May 2011; Niagara Falls, Canada: IEEE. p337-340.
TANG Y, CUI M, HUA C, LI L, YANG Y. 2012. Optimum design of fractional order PIλ Dµ controller for AVR system using chaotic ant swarm. Expert Systems with Applications 39: 6887-6896.
VALERIO D, SADA CJ. 2011. Introduction to single-input, single-output fractional control IET Control Theory Appl 5(8):1033-1057.
WONG CC, LI L, WANG HY. 2009. Optimal PID Controller Design for AVR System. Tamkang Journal of Science and Engineering 12(3): 259-270.
YEROGLU C, TAN N. 2011. Note on fractional-order proportional integral differential controller design. IET Control Theory Appl 5(17): 1978-1989.
ZAMANI M, KARIMI-GHARTEMANI M, SADATI N, PARNIANI M. 2009. Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Engineering Practice 17(12): 1380-1387.