A Combined Conventional and Differential Evolution Method for Model Order Reduction
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1074481Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1778
 M. J. Bosley and F. P. Lees, "A survey of simple transfer function derivations from high order state variable models", Automatica, Vol. 8, pp. 765-775, !978.
 M. F. Hutton and B. Fried land, "Routh approximations for reducing order of linear time- invariant systems", IEEE Trans. Auto. Control, Vol. 20, pp 329-337, 1975.
 R. K. Appiah, "Linear model reduction using Hurwitz polynomial approximation", Int. J. Control, Vol. 28, no. 3, pp 477-488, 1978.
 T. C. Chen, C. Y. Chang and K. W. Han, "Reduction of transfer functions by the stability equation method", Journal of Franklin Institute, Vol. 308, pp 389-404, 1979.
 Y. Shamash, "Truncation method of reduction: a viable alternative", Electronics Letters, Vol. 17, pp 97-99, 1981.
 P. O. Gutman, C. F. Mannerfelt and P. Molander, "Contributions to the model reduction problem", IEEE Trans. Auto. Control, Vol. 27, pp 454-455, 1982.
 Y. Shamash, "Model reduction using the Routh stability criterion and the Pade approximation technique", Int. J. Control, Vol. 21, pp 475-484, 1975.
 T. C. Chen, C. Y. Chang and K. W. Han, "Model Reduction using the stability-equation method and the Pade approximation method", Journal of Franklin Institute, Vol. 309, pp 473-490, 1980.
 Bai-Wu Wan, "Linear model reduction using Mihailov criterion and Pade approximation technique", Int. J. Control, Vol. 33, pp 1073-1089, 1981.
 V. Singh, D. Chandra and H. Kar, "Improved Routh-Pade Approximants: A Computer-Aided Approach", IEEE Trans. Auto. Control, Vol. 49. No. 2, pp292-296, 2004.
 Stron Rainer and Price Kennth, Differential Evolution - "A simple and efficient adaptive scheme forGlobal Optimization over continuous spaces", Journal of Global Optimization, Vol.11, pp. 341-359, 1997.
 Storn Rainer, Differential Evolution for Continuous Function Optimization," http://www.icsi.berkeley.edu/- storn/code.html,2005.
 DE bibliography, http://www.lut.fi/~jlampine/debiblio.htm
 S. Panda, S. K. Tomar, R. Prasad, 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, S.C.Swain and A.K.Baliarsingh, "Power System Stability Improvement by Differential Evolution Optimized TCSC-Based Controller", Proceedings of International Conference on Computing, (CIC 2008), Mexico City, Mexico, Held on Dec., 3-5, 2008.
 S. Panda, S. K. Tomar, R. Prasad, 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, 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.
 T. N. Lukas. "Linear system reduction by the modified factor division method" IEEE Proceedings Vol. 133 Part D No. 6, nov.-1986, pp-293-295.
 Gamperle R.,. Muller S. D. and Koumoutsakos P., "A Parameter Study for Differential Evolution," Advances in Intelligent Systems, Fuzzy Systems, Evolutionary Computation, pp. 293- 298, 2002.
 Zaharie D., "Critical values for the control parameters of differential evolution algorithms," Proc. of the8th International Conference on SoftComputing, pp. 62-67, 2002.