Controller Design of Discrete Systems by Order Reduction Technique Employing Differential Evolution Optimization Algorithm

Authors: J. S. Yadav, N. P. Patidar, J. Singhai

Abstract:

One of the main objectives of order reduction is to design a controller of lower order which can effectively control the original high order system so that the overall system is of lower order and easy to understand. In this paper, a simple method is presented for controller design of a higher order discrete system. First the original higher order discrete system in reduced to a lower order model. Then a Proportional Integral Derivative (PID) controller is designed for lower order model. An error minimization technique is employed for both order reduction and controller design. For the error minimization purpose, Differential Evolution (DE) optimization algorithm has been employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the desired response and actual response pertaining to a unit step input. Finally the designed PID controller is connected to the original higher order discrete system to get the desired specification. The validity of the proposed method is illustrated through a numerical example.

Keywords: Discrete System, Model Order Reduction, PIDController, Integral Squared Error, Differential Evolution.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085776

References:

[1] J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, and C. Ardil "A Combined Conventional and Differential Evolution Method for Model Order Reduction", International Journal of Computational Intelligence, Vol. 5, No. 2, pp. 111-118, 2009.
[2] S. Panda, J. S. Yadav, N. P. Patidar and C. Ardil, "Evolutionary Techniques for Model Order Reduction of Large Scale Linear Systems", International Journal of Applied Science, Engineering and Technology, Vol. 5, No. 1, pp. 22-28, 2009.
[3] Y. Shamash, "Continued fraction methods for the reduction of discrete time dynamic systems", Int. Journal of Control, Vol. 20, pages 267-268, 1974.
[4] C.P. Therapos, "A direct method for model reduction of discrete system", Journal of Franklin Institute, Vol. 318, pp. 243-251, 1984.
[5] J.P. Tiwari, and S.K. Bhagat, "Simplification of discrete time systems by improved Routh stability criterion via p-domain", Journal of IE (India), Vol. 85, pp. 89-192, 2004.
[6] J.S. Yadav, N.P. Patidar and J. Singhai, S. Panda, "Differential Evolution Algorithm for Model Reduction of SISO Discrete Systems", Proceedings of World Congress on Nature & Biologically Inspired Computing (NaBIC 2009) 2009, pp. 1053-1058.
[7] D.A. Wilson and R.N. Mishra, "Design of low order estimators using reduced models", Int. J. Control, Vol. 29, pp. 267-278, 1979.
[8] J.A. Davis and R.E. Skelton, "Another balanced controller reduction algorithm" Systems and Controller Letters, Vol. 4, pp. 79-83, 1884.
[9] R Stron. And K. Price, "Differential Evolution - A simple and efficient adaptive scheme for Global Optimization over continuous spaces, Journal of Global Optimization, Vol. 11, pp. 341-359, 1995.
[10] Sidhartha Panda, "Differential Evolutionary Algorithm for TCSC-based Controller Design", Simulation Modelling Practice and Theory, Vol. 17, pp. 1618-1634, 2009.
[11] S. Mukhrjee and R.N. Mishra, "Optimal order reduction of discrete systems", Journal of Institution of Engineers, Vol. 68, pp. 142-149, 1988.
[12] K. Ramesh, A. Nirmalkumar and G. Gurusamy, "Design of discrete controller via a novel model order reduction technique", International Journal of Electrical Power and Engineering, Vol. 3, pp. 163-168, 2009.