Design Of Multivariable Fractional Order Pid Controller Using Covariance Matrix Adaptation Evolution Strategy

Open access


This paper presents an automatic tuning of multivariable Fractional-Order Proportional, Integral and Derivative controller (FO-PID) parameters using Covariance Matrix Adaptation Evolution Strategy (CMAES) algorithm. Decoupled multivariable FO-PI and FO-PID controller structures are considered. Oustaloup integer order approximation is used for the fractional integrals and derivatives. For validation, two Multi-Input Multi- Output (MIMO) distillation columns described byWood and Berry and Ogunnaike and Ray are considered for the design of multivariable FO-PID controller. Optimal FO-PID controller is designed by minimizing Integral Absolute Error (IAE) as objective function. The results of previously reported PI/PID controller are considered for comparison purposes. Simulation results reveal that the performance of FOPI and FO-PID controller is better than integer order PI/PID controller in terms of IAE. Also, CMAES algorithm is suitable for the design of FO-PI / FO-PID controller.

[1] R.S. BARBOSA, J.A.T. MACHADO and I.S.JESUS: Fractional PID control of an experimental servo system. Computers & Mathematics with Applications, 59(5), (2010), 1679-1686.

[2] A.BISWAS, S. DAS, A. ABRAHAM and S. DASGUPTA: Design of fractional-order PID controllers with an improved differential evolution. Engineering Applications of Artificial Intelligence, 22 (2009), 343-350.

[3] J.Y. CAO, J. LIANG and B.G.CAO: Optimization of fractional order PID controllers based on genetic algorithms. Proc. Int. Conf. Machine Learning and Cybernetics, 9 (2005), 5686-5689.

[4] J.Y. CAO and B.G.CAO: Design of fractional order controller based on particle swarm optimization. Int. J. of Control, Automation, and Systems, 4(6), (2006), 775-781.

[5] Y.Q.CHEN, I.PETRAS and D.XUE: Fractional order control - A Tutorial. Proc.American Control Conf., St. Louis, MO, USA. (2009), 1397-1411.

[6] MA.CHENGBIN and Y. HORI: Fractional order control: Theory and applications in motion control [past and present]. IEEE. Industrial Electronics Magazine, 1(4), (2007), 6-16.

[7] N.HANSEN: The CMA evolution strategy: A comparing eeview. Studies in fuzziness and soft computing, 192 (2006a), 75-102.

[8] N.HANSEN: CMA-ES in MATLAB. Available from : , (2006b).

[9] M.W.IRUTHAYARAJAN and S.BASKAR: Evolutionary algorithms based design of multivariable PID controller. Expert Systems with Applications, 36(5), (2009), 9159-9167.

[10] M.W.IRUTHAYARAJAN and S.BASKAR: Covariance matrix adaptation evolution strategy based design of centralized PID controller. Expert systems with Applications, 37(8), (2010), 5775-5781.

[11] C.A. MONJE, Y.Q.CHEN, B.M.VINAGRE, D.XUE and V.FELIU: Fractional Order Systems and Controls - Fundamentals and Applications. Springer-Verlag, London Ltd. 2010.

[12] F.PADULA and A.VISIOLI: Tuning rules for optimal PID and fractional-order PID controllers. J. of Process Control, 21(1), (2011), 69-81.

[13] I.PETRAS: The fractional order controllers: methods for their synthesis and application.J. of Electrical Engineering, 50(9), (1999), 284-288.

[14] I.PODLUBNY: Fractional-order systems and PIλDμ-controllers. IEEE Trans. Automatic Control, 44(1), (1999), 208-214.

[15] B.M.VINAGRE, I.PODLUBNY, L.DORCAK and V.FELIU: On fractional PID controllers: a frequency domain approach. Proc. IFAC Workshop on Digital Control, Terrassa, Spain. (2000).

[16] M.ZAMANI, M.K.GHARTEMANI, N.SADATI and M.PARNIANI: Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Engineering Practice, 179(12), (2009), 1380-1387.

Archives of Control Sciences

The Journal of Polish Academy of Sciences

Journal Information

IMPACT FACTOR 2016: 0.705

CiteScore 2016: 3.11

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.565


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 55 55 3
PDF Downloads 14 14 2