Fractional Order PID Controller Design for Level Control of Three Tank System Based on Improved Cuckoo Optimization Algorithm

Subject Areas : Fractional order systems

Meysam Gheisarnezhad ¹ ( In Charge of Control Room, Khazar Steel Complex, Rasht )
Hamed Mojallali ² ( University of Guilan )

Received: 2014-07-04 Accepted : 2015-02-04 Published : 2015-02-20

Keywords: fractional order PID controller, Cuckoo Optimization Algorithm, three tank system,

Abstract :

Fractional-order PID (FOPID) controller is a generalization of standard PID controller using fractional calculus. Compared with the Standard  PID controller, two adjustable variables “differential order” and “integral order” are added to the PID controller.Three tank system is a nonlinear multivariable process that is a good prototype of chemical industrial processes. Cuckoo Optimization Algorithm (COA), that was recently introduced has shown its good performance in optimization problems. In this study, Improved Cuckoo Optimization Algorithm (ICOA) has been presented. The aim of the paper is to compare different controllers tuned with a Improved Cuckoo Optimization Algorithm (ICOA) for Three Tank System. In order to compare the performance of the optimized FOPID controller with other controllers, Genetic Algorithm(GA), Particle swarm optimization (PSO), Cuckoo Optimization Algorithm (COA) and Imperialist Competitive Algorithm (ICA).

References:

[1] J.G. Ziegler, N.B. Nicholas, “Optimum settings for automatic controllers”, Trans. of the ASME, No. 64, pp.759_768, Nov. 1942.
[2] A.A. Zamani, S.M. Kargar-Dehnavi, “Compensation of actuator’s saturation by using fuzzy logic and imperialist competitive algorithm in a system with PID Controller”, Journal of Intelligent Procedures in Electrical Technology, Vol. 3, No. 11, pp. 21-26, summer 2013. (in Persian)
[3] K.J. Aström, T. Hägglund, “The future of PID control”, Control Engineering Practice, Vol. 9, No. 11, pp. 1163-1175, Nov. 2001.
[4] K.B. Oldhum, J. Spanier, “The fractional calculus: Theory and applications of differentiation and integration to arbitrary order”, Academic Press, 1974.
[5] M. Safaei, S. Hosseinia, M.H osseini-Toodeshki “A general method for designing fractional order PID controller”, Journal of Intelligent Procedures in Electrical Technology, Vol. 3, No. 12, pp. 25-34, Winter 2013 (in Persian).
[6] K.S. Miller, B. Ross, “An introduction to the fractional calculus and fractional differential equations”, Wiley, New York, 1993.
[7] I. Podlubny, “Fractional-order systems and PIλDµ controllers”, IEEE Trans. on Automatic Control, Vol. 44, No. 1, pp. 208-213, Jan. 1999.
[8] M.S. Tavazoei, M. Haeri, “Choas control via a simple fractional order controller”, Physics Letter A, Vol. 372, pp. 798-807, Feb. 2008.
[9] Amira, “DTS200 – laboratory setup three tank system”, Documentation, Amira GmbH, Duisburg, Germany, 2000.
[10] I. Mosicat, “Iterative feedback tuning techniques: applications to control or three-tank system”, B.Sc, Thesis, Politehnica Univ. of Timisoara, Romania, 2009.
[11] E.M. Mellouli, S. Sefriti, I. Boumhidi, ”Direct adaptive fuzzy control for an uncertain three-tank-system”, International Journal of Research and Reviews in Artificial intelligence, Vol. 1, No. 4, 2011.
[12] M. Axtel, E.M. Bise, ”Fractional calculus applications in control systems”, Proceedings of the IEEE/NAECON, Vol. 2, pp. 563–566, Dayton, OH, May 1990.
[13] L.Y. Chang, H.C. Chen, “Tuning of fractional PID controllers using adaptive genetic algorithm for active Magnetic bearing system”, WSEAS Trans. on Systems, Vol. 8, pp. 226–236, 2009.
[14] Z. Majid, K.G. Masoud, S. Nasser, P. Mostafa, “Design of a fractional order PID controller for an AVR using particle swarm optimization”, Control Engineering Practice, Vol. 17, No. 12, pp. 1380-1387, Dec. 2009.
[15] X.S. Yang, S. Deb, “Cuckoo search via Lévy Flights”, Proceeding of the IEEE/NABIC, pp. 210–214, Coimbatore, Dec. 2009.
[16] R. Rajabioun, “Cuckoo Optimization Algorithm”, Applied Soft Computing Journal, Vol. 11, No. 8, pp. 5508_5518, Dec. 2011.
[17] H. Kahramanli, ”A modified cuckoo optimization algorithm for engineering optimization”, International Journal of Future Computer and Communication, Vol. 1, No. 2, pp. 199-201, 2012.
[18] M. Rabiee, H. Sajedi, “Job scheduling in grid computing with combination of cuckoo and genetic algorithms”, Payame Noor University National Conference on Information Technology and Networking, 2013.
[19] G. Vinagre, D. Valério, J. Sá da Costa, “Ruletuned PIDs and fractional PIDs for a three-tank liquid system”, In Fractional Signals and Systems, Caparica, 2009.
[20] C.Y. Quan, “Applied fractional calculus in controls and signal processing”, Proceeding of the IEEE/ACC, Atlanta, USA, Dec. 2010.
[21] A. Oustaloup, “La commande CRONE: CommandeRobuste d'Ordre non entier”, Hermès, Paris, 1991.
[22] D. Valério, J. Sá da Costa, “NINTEGER: A non-integer control toolbox for MATLAB”, Proceedings of the Fractional Differentiation and its Applications, Bordeaux, 2004.
[23] G. Hu, S. Zho, J. Guan, X. Hu, ”Towards effective document clustering: A constrained K-means based approach”, Information Processing and Management, Vol. 44, No. 4, pp. 1397–1409, 2008.

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