{"title":"Conventional and PSO Based Approaches for Model Reduction of SISO Discrete Systems","authors":"S. K. Tomar, R. Prasad, S. Panda, C. Ardil","volume":78,"journal":"International Journal of Electrical and Computer Engineering","pagesStart":790,"pagesEnd":796,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/4815","abstract":"<p>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.<\/p>\r\n","references":"[1] R. Genesio and M. Milanese, \"A note on the derivation and use of\r\nreduced-order models\", IEEE Transactions on Automatic Control, Vol.\r\n21, pages 118-122, 1976.\r\n[2] S. Panda, S. K. Tomar, R. Prasad and C. Ardil, \"Reduction of Linear\r\nTime-Invariant Systems Using Routh-Approximation and PSO\",\r\nInternational Journal of Applied Mathematics and Computer Sciences,\r\nVol. 5, No. 2, pp. 82-89, 2009.\r\n[3] S. Panda, S. K. Tomar, R. Prasad and C. Ardil, \"Model Reduction of\r\nLinear Systems by Conventional and Evolutionary Techniques\",\r\nInternational Journal of Computational and Mathematical Sciences,\r\nVol. 3, No. 1, pp. 28-34, 2009.\r\n[4] S. Panda, J. S. Yadav, N. P. Patidar and C. Ardil, \"Evolutionary\r\nTechniques for Model Order Reduction of Large Scale Linear Systems\",\r\nInternational Journal of Applied Science, Engineering and Technology,\r\nVol. 5, No. 1, pp. 22-28, 2009.\r\n[5] J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda and C. Ardil \"A\r\nCombined Conventional and Differential Evolution Method for Model\r\nOrder Reduction\", International Journal of Computational Intelligence,\r\nVol. 5, No. 2, pp. 111-118, 2009.\r\n[6] Y. Shamash, \"Continued fraction methods for the reduction of discrete\r\ntime dynamic systems\", Int. Journal of Control, Vol. 20, pages 267-268,\r\n1974.\r\n[7] C.P. Therapos, \"A direct method for model reduction of discrete\r\nsystem\", Journal of Franklin Institute, Vol. 318, pp. 243-251, 1984.\r\n[8] J.P. Tiwari, and S.K. Bhagat, \"Simplification of discrete time systems by\r\nimproved Routh stability criterion via p-domain\", Journal of IE (India),\r\nVol. 85, pp. 89-192, 2004.\r\n[9] J. Kennedy and R. C. Eberhart, \"Particle swarm optimization\",\r\nIEEEInt.Conf. on Neural Networks, IV, 1942-1948, Piscataway, NJ,\r\n1995.\r\n[10] Sidhartha Panda and N. P. Padhy, \"Comparison of Particle Swarm\r\nOptimization and Genetic Algorithm for FACTS-based Controller\r\nDesign\", Applied Soft Computing, Vol. 8, Issue 4, pp. 1418-1427, 2008.\r\n[11] A.C. Davies, \"Bilinear transformation of polynomials,\" IEEE\r\nTransaction on Circuits and systems, CAS-21, pp 792-794, 974.\r\n[12] R. Parthasarthy and K.N. Jaysimha, \"Bilinear Transformations by\r\nSynthetic Division,\" IEEE Transaction on Automatic Control. Vol. 29,\r\nNo. 6, pp. 575-576, 1984.\r\n[13] P.Gutman, C.F.Mannerfelt and P.Molandar, \"Contribution to the model\r\nreduction problem,\" IEEE Transaction on.Automatic Control, Vol. 27,\r\npp 454-455,1982.\r\n[14] R. Parthasarthy and Sarasu John, \"System reduction by Routh\r\napproximation and modified Cauer continued fraction,\" Electronics\r\nLetters, Vol. 5, No. 21, pp 691-692. 1979.\r\n[15] Sunita Devi and Rajendra Prasad, \"Reduction of Discrete time systems\r\nby Routh approximation, National System Conference,\" IIT Kharagpur,\r\nNSC 2003, pp 30-33, Dec 17-19, 2003.\r\n[16] R. Parthasarthy and Sarasu John, \"System Reduction using Cauer\r\nContinued Fraction Expansion about s=0 and s= \u221e,\" Electronics Letters,\r\nVol. 14, No. 8, pp .261-262, 1978.\r\n[17] Ching-Shieh Hsieh and Chyi Hwang,\"Model reduction of linear\r\ndiscrete-time systems using bilinear Schwartz approximation,\"\r\nInternational Journal of System & Science, Vol .21, No 1, pp. 33-49,\r\n1990.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 78, 2013"}