Conventional and PSO Based Approaches for Model Reduction of SISO Discrete Systems
Reduction of Single Input Single Output (SISO) discrete systems into lower order model, using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Modified Cauer Form (MCF) and differentiation are used. In this method the original discrete system is, first, converted into equivalent continuous system by applying bilinear transformation. The denominator of the equivalent continuous system and its reciprocal are differentiated successively, the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. The reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.
Keywords: Discrete System, Single Input Single Output (SISO), Bilinear Transformation, Reduced Order Model, Modified CauerForm, Polynomial Differentiation, Particle Swarm Optimization, Integral Squared Error.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1059907Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1702
 R. Genesio and M. Milanese, "A note on the derivation and use of reduced-order models", IEEE Transactions on Automatic Control, Vol. 21, pages 118-122, 1976.
 S. Panda, S. K. Tomar, R. Prasad and C. Ardil, "Reduction of Linear Time-Invariant Systems Using Routh-Approximation and PSO", International Journal of Applied Mathematics and Computer Sciences, Vol. 5, No. 2, pp. 82-89, 2009.
 S. Panda, S. K. Tomar, R. Prasad and C. Ardil, "Model Reduction of Linear Systems by Conventional and Evolutionary Techniques", International Journal of Computational and Mathematical Sciences, Vol. 3, No. 1, pp. 28-34, 2009.
 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.
 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.
 Y. Shamash, "Continued fraction methods for the reduction of discrete time dynamic systems", Int. Journal of Control, Vol. 20, pages 267-268, 1974.
 C.P. Therapos, "A direct method for model reduction of discrete system", Journal of Franklin Institute, Vol. 318, pp. 243-251, 1984.
 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.
 J. Kennedy and R. C. Eberhart, "Particle swarm optimization", IEEEInt.Conf. on Neural Networks, IV, 1942-1948, Piscataway, NJ, 1995.
 Sidhartha Panda and N. P. Padhy, "Comparison of Particle Swarm Optimization and Genetic Algorithm for FACTS-based Controller Design", Applied Soft Computing, Vol. 8, Issue 4, pp. 1418-1427, 2008.
 A.C. Davies, "Bilinear transformation of polynomials," IEEE Transaction on Circuits and systems, CAS-21, pp 792-794, 974.
 R. Parthasarthy and K.N. Jaysimha, "Bilinear Transformations by Synthetic Division," IEEE Transaction on Automatic Control. Vol. 29, No. 6, pp. 575-576, 1984.
 P.Gutman, C.F.Mannerfelt and P.Molandar, "Contribution to the model reduction problem," IEEE Transaction on.Automatic Control, Vol. 27, pp 454-455,1982.
 R. Parthasarthy and Sarasu John, "System reduction by Routh approximation and modified Cauer continued fraction," Electronics Letters, Vol. 5, No. 21, pp 691-692. 1979.
 Sunita Devi and Rajendra Prasad, "Reduction of Discrete time systems by Routh approximation, National System Conference," IIT Kharagpur, NSC 2003, pp 30-33, Dec 17-19, 2003.
 R. Parthasarthy and Sarasu John, "System Reduction using Cauer Continued Fraction Expansion about s=0 and s= ∞," Electronics Letters, Vol. 14, No. 8, pp .261-262, 1978.
 Ching-Shieh Hsieh and Chyi Hwang,"Model reduction of linear discrete-time systems using bilinear Schwartz approximation," International Journal of System & Science, Vol .21, No 1, pp. 33-49, 1990.