{"title":"A Combined Conventional and Differential Evolution Method for Model Order Reduction","authors":"J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, C. Ardil","volume":57,"journal":"International Journal of Electrical and Computer Engineering","pagesStart":1289,"pagesEnd":1297,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10034","abstract":"
In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE 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. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.<\/p>\r\n","references":"[1] M. J. Bosley and F. P. Lees, \"A survey of simple transfer\r\nfunction derivations from high order state variable models\",\r\nAutomatica, Vol. 8, pp. 765-775, !978.\r\n[2] M. F. Hutton and B. Fried land, \"Routh approximations for\r\nreducing order of linear time- invariant systems\", IEEE Trans.\r\nAuto. Control, Vol. 20, pp 329-337, 1975.\r\n[3] R. K. Appiah, \"Linear model reduction using Hurwitz\r\npolynomial approximation\", Int. J. Control, Vol. 28, no. 3, pp\r\n477-488, 1978.\r\n[4] T. C. Chen, C. Y. Chang and K. W. Han, \"Reduction of transfer\r\nfunctions by the stability equation method\", Journal of Franklin\r\nInstitute, Vol. 308, pp 389-404, 1979.\r\n[5] Y. Shamash, \"Truncation method of reduction: a viable\r\nalternative\", Electronics Letters, Vol. 17, pp 97-99, 1981.\r\n[6] P. O. Gutman, C. F. Mannerfelt and P. Molander, \"Contributions\r\nto the model reduction problem\", IEEE Trans. Auto. Control,\r\nVol. 27, pp 454-455, 1982.\r\n[7] Y. Shamash, \"Model reduction using the Routh stability\r\ncriterion and the Pade approximation technique\", Int. J. Control,\r\nVol. 21, pp 475-484, 1975.\r\n[8] T. C. Chen, C. Y. Chang and K. W. Han, \"Model Reduction\r\nusing the stability-equation method and the Pade approximation\r\nmethod\", Journal of Franklin Institute, Vol. 309, pp 473-490,\r\n1980.\r\n[9] Bai-Wu Wan, \"Linear model reduction using Mihailov criterion\r\nand Pade approximation technique\", Int. J. Control, Vol. 33, pp\r\n1073-1089, 1981.\r\n[10] V. Singh, D. Chandra and H. Kar, \"Improved Routh-Pade\r\nApproximants: A Computer-Aided Approach\", IEEE Trans.\r\nAuto. Control, Vol. 49. No. 2, pp292-296, 2004.\r\n[11] Stron Rainer and Price Kennth, Differential Evolution - \"A\r\nsimple and efficient adaptive scheme forGlobal Optimization\r\nover continuous spaces\", Journal of Global Optimization,\r\nVol.11, pp. 341-359, 1997.\r\n[12] Storn Rainer, Differential Evolution for Continuous Function\r\nOptimization,\" http:\/\/www.icsi.berkeley.edu\/-\r\nstorn\/code.html,2005.\r\n[13] DE bibliography, http:\/\/www.lut.fi\/~jlampine\/debiblio.htm\r\n[14] S. Panda, S. K. Tomar, R. Prasad, C. Ardil, \"Model Reduction\r\nof Linear Systems by Conventional and Evolutionary\r\nTechniques\", International Journal of Computational and\r\nMathematical Sciences, Vol. 3, No. 1, pp. 28-34, 2009.\r\n[15] S. Panda, S.C.Swain and A.K.Baliarsingh, \"Power System\r\nStability Improvement by Differential Evolution Optimized\r\nTCSC-Based Controller\", Proceedings of International\r\nConference on Computing, (CIC 2008), Mexico City, Mexico,\r\nHeld on Dec., 3-5, 2008.\r\n[16] S. Panda, S. K. Tomar, R. Prasad, C. Ardil, \"Reduction of\r\nLinear Time-Invariant Systems Using Routh-Approximation and\r\nPSO\", International Journal of Applied Mathematics and\r\nComputer Sciences, Vol. 5, No. 2, pp. 82-89, 2009.\r\n[17] S. Panda, J. S. Yadav, N. P. Patidar and C. Ardil, \"Evolutionary\r\nTechniques for Model Order Reduction of Large Scale Linear\r\nSystems\", International Journal of Applied Science, Engineering\r\nand Technology, Vol. 5, No. 1, pp. 22-28, 2009.\r\n[18] T. N. Lukas. \"Linear system reduction by the modified factor\r\ndivision method\" IEEE Proceedings Vol. 133 Part D No. 6,\r\nnov.-1986, pp-293-295.\r\n[19] Gamperle R.,. Muller S. D. and Koumoutsakos P., \"A Parameter\r\nStudy for Differential Evolution,\" Advances in Intelligent\r\nSystems, Fuzzy Systems, Evolutionary Computation, pp. 293-\r\n298, 2002.\r\n[20] Zaharie D., \"Critical values for the control parameters of\r\ndifferential evolution algorithms,\" Proc. of the8th International\r\nConference on SoftComputing, pp. 62-67, 2002.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 57, 2011"}