ROBUST AUTOMATIC VOLTAGE REGULATOR DESIGN USING BODE’S IDEAL TRANSFER FUNCTION
Mots-clés :
AVR, Bode’s ideal loop, fractional order operators, fractional order control, rational function approxim, boucle idéale de Bode, les opérateurs ordre fractionnaire, le contrôleur d'ordre fractionnaireRésumé
Robust control based on fractional order calculus is gaining more and more interests from the control community. In this paper, a robust automatic voltage regulator (AVR) design based on fractional order calculus is presented. The controller design strategy is drawn up such that the open loop transfer function of the AVR system is the Bode’s ideal transfer function that is widely used in the fractional order control domain because of its iso-damping property which is an important robustness feature. The controller design consists of choosing the poles and the zeros of the proposed controller to force the AVR open-loop transfer function to be the Bode’s ideal transfer function. The basic ideas and the derived formulations of the controller design are presented. Simulations were made to test the effectiveness and the usefulness of the proposed controller design approach. Performances analysis to variations of the gain and the time constant of the generator of the AVR were also presented. Comparisons are made with PID controllers to show the robustness efficiency of the proposed design with respect to the generator parameters uncertainties.
Références
A.Oustaloup, La Commande CRONE, Paris:Hermès, 1991.
C.A. Monje, Y.Q. Chen, B.M. Vinagre, D. Xue, V. Feliu, Fractional-Order Systems and Controls Fundamentals and Applications, London:Springer-Verlag, 2010.
R. Caponetto, G. Dongola, L. Fortuna, I. Petras, Fractional Order Systems: Modeling and Control Applications, Singapore: World Scientific, 2010.
Y. Luo, Y.Q. Chen, Fractional Order Motion Controls, Chichester, United Kingdom : John Wiley & Sons Ltd, 2012.
D.Valerio, J. Sa da Costa, An Introduction to Fractional Control, London: Institution of Engineering and Technology, 2013.
I. Pan, S. Das, Intelligent Fractional Order Systems and Control: An Introduction, Berlin : New York, Springer, 2013.
H.W. Bode, Network Analysis and Feedback Amplifier Design, New York: Van Nostrand, 1945.
A. Tustin et al, “The Design of Systems for Automatic Control of the Psition of Massive object, ” Proceedings of Institution of Electrical Engineers, vol. 105, no. 1, pp. 1-57, 1958.
S. Manabe, “The Non-Integer Integral and its Application to Control Systems, ”ETJ of Japan, vol. 6, no. 3-4, pp. 83-87, 1961.
A. Oustaloup, Systèmes Asservis Linéaires d’Ordre Fractionnaire: Théorie et Pratique, Paris: Editions Masson, 1983.
M. Axtell, E.M. Bise, Fractional Calculus Applications in Control Systems, Proceedings of the IEEE Nat. Aerospace and Electronics Conf., N.Y, pp. 563–566, 1990.
I. Podlubny, “Fractional Order Systems and PIλDμ Controllers,” IEEE Transactions on Automatic Control, vol.44, no. 1, pp. 208-214,1999.
B.M. Vinagre, I. Podlubny, L. Dorcak, V. Feliu, On Fractional PID Controllers: A Frequency Domain Approach, In: the IFAC Workshop on Digital Control, Past, Present and Future of PID Control, , Terrasa, Spain. April 5-7, 2000.
C.A. Monje, B.M. Vinagre, Y.Q. Chen, V. Feliu, P. Lanusse, J. Sabatier, Proposals for fractional PIλDμ tuning, In: Proceedings of the 1st IFAC Workshop on Fractional Differentiation and its Applications, Bordeaux, France, FDA’04, July 19-21, 2004.
R. Caponetto, L. Fortuna, A new tuning Strategy for a non integer order PID Controller, In: Proceedings of the 1st IFAC Workshop on Fractional Differentiation and its Applications, Bordeaux, France, FDA’04, July 19-21, 2004.
A. Djouambi, A. Charef, T. Bouktir, “Fractional Order Robust Control and PIλDμ Controllers, ” WSEAS Trans. on Circuits and Systems, vol. 4, no. 8, pp. 850-57, 2005.
D. Valério, J. Sà da Costa, “Tuning of fractional PID controllers with Ziegler-Nichols type rules, ” Signal Processing, vol. 86, pp. 2771-84, 2006.
C.A. Monje, and B.M. Vinagre, V. Feliu, Y.Q. Chen, “Tuning and auto-tuning of fractional order controllers for industry applications, ”Control Engineering Practice, vol. 16, pp. 798-12, 2008.
K. Bettou, and A. Charef, “Control Quality Enhancement using Fractional PIλDμ Controller, ” International Journal of System Sciences, Vol. 40, no. 8, pp. 875-88, 2009.
F. Merrikh-Bayat, and M. Karimi-Ghartemani, “Method for Designing PIλDμ Stabilizers for Minimum-Phase Fractional-Order Systems, ” IET Control Theory Appl, vol. 4, no. 1, pp. 61-70, 2010.
Y.Q. Chen, I. Petras, and D. Xue, Fractional Order Control - A Tutorial, In: Proceedings American Control Conference, St. Louis, MO, USA, pp. 1397-1411 , June 10-12, 2009.
H. Yoshida, K. Kawata, and Y. Fukuyama, “A Particle Swarm Optimization for Reactive Power and Voltage Control Considering Voltage Security Assessment, ” IEEE Trans. Power Systems, vol. 15, pp. 1232–39, 2000.
Z.L. Gaing,“A particle Swarm Optimization Approach for Optimum Design of PID Controller in AVR System,” IEEE Trans. Energy Conversion, vol. 19, no. 2, pp. 384-91, 2004.
V. Mukherjee, and S.P. Ghoshal, “Intelligent Particle Swarm Optimized Fuzzy PID Controller for AVR System,” Electric Power System Research, vol. 77, no. 12, pp. 1689-98, 2007.
L. Coelho, “Tuning of PID Controller for An Automatic Regulator Voltage System Using Chaotic Optimization Approach,” Chaos Solit. & Fractals, vol. 39, no. 4, pp. 1504-14, 2009.
H. Zhu, L. Li, Y. Zhao, Y. Guo, and Y. Yang, “CAS Algorithm-Based Optimum Design of PID Controller in AVR System,” Chaos, Solitons and Fractals, vol. 42, pp. 792-800, 2009.
D. Devaraj, and B. Selvabala,“Real-Coded Genetic Algorithm and Fuzzy Logic Approach for Real-Time Tuning of Proportional–Integral–Derivative controller In Automatic Voltage Regulator System,”IET Generation, Transmission & Distribution, vol. 3, no. 7, pp.641-49, 2009.
H. Gozde, M. C. Taplamacioglu, and I. Kocaarslan, “Application of Artificial Bees Colony Algorithm in Automatic Voltage Regulator (AVR) System,” International Journal on Technical and Physical Problems of Engineering (IJTPE), vol. 1, no. 3,pp. 88-92, 2010.
D.H. Kim, “Hybrid GA–BF Based Intelligent PID Controller Tuning for AVR System,” Applied Soft Computing, vol. 11, pp. 11–22, 2011.
M.N. Anwar, S. Pan, “A Frequency Domain Design of PID Controller for An AVR System,” Journal of Zhejiang University-SCIENCE, vol. 15, no. 4, pp. 293-299, 2014.
M. Zamani, M. Masoud Karimi-Ghartemani, N. Sadati, and M. Parniani, “Design of A Fractional Order PID Controller for An AVR Using Particle Swarm Optimization,” Control Engineering Practice, vol. 17, pp. 1380–87, 2009.
M.I. Alomoush, “Fractional Calculus-Based Optimal Controllers of Automatic Voltage Regulator in Power System, Control and intelligent systems, vol. 38, no. 1, pp. 40-48, 2010.
I. Pan, and S. Das, “Chaotic Multi-Objective Optimization Based Design of Fractional Order PIλDμ Controller in AVR System,” International Journal of Electrical Power & Energy Systems, vol. 43, no.1, pp. 393-407, 2012.
H. Ramezanian, S. Balochian, and A. Zarz, “Design of Optimal Fractional Order PID Controllers Using Particle Swarm Optimization Algorithm for Automatic Voltage Regulator (AVR) System,” Journal Control, Automation and Electrical Systems, vol. 24, pp. 601-611, 2013.
D.L. Zhang, Y.G. Tang, and X.P. Guan, “Optimum Design of Fractional Order PID Controller for an AVR System Using an Improved Artificial Bee Colony Algorithm,” Acta Automatica Sinica, vol. 40, no.5, pp. 973-979,2014.
I. Pan, and S. Das, “Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-Objective Optimization,” Electrical Power and Energy Systems, vol. 51, pp.106–118, 2013.
A. Djouambi, A. Charef, and A.V. Besançon, Fractional Order Controllers Based on Bode’s Ideal Transfer Function,” Inter. Journal of Control and Intelligent Systems, Vvol. 38, no. 2, pp. 67-73, 2010.
R.S. Barbosa, J.A. Machado, and I.M. Ferreira, “Tuning of PID Controllers Based on Bode’s Ideal Transfer Function,” Nonlinear Dynamics, vol. 38, no.1-4, pp. 305-21, 2004.
M. Assabaa, A. Charef, Z. Santouh, M. Benmalek, “Modeling and analysis of multiple fractional Order systems,” In : Proceedings de la 5ème Conférence sur le génie électrique, CGE’05, Algiers, Algeria, April 16-17, 2007.
A. Charef, “Analogue Realization of Fractional Order Integrator, Differentiator and Fractional PIλDμ Controllers,” IEE proceedings on Control Theory & Applications, vol. 153, no.6, pp. 714-20, 2006.
A. Charef, “Modeling and Analog Realization of the Fundamental Linear Fractional Order Differential Equation,” Nonlinear Dynamics, vol. 46,no. 1-2, pp. 195-210, 2006.
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