Model Order Reduction by Legendre Expansion Using Harmony Search Algorithm

Majlesi Journal of Electrical Engineering

مقاله 4، دوره 9، شماره 1، خرداد 2015، صفحه 25-35   

نوع مقاله: Review Article

نویسندگان

Hasan Nasiri Soloklo^* ؛ Malihe Maghfoori Farsangi

Shahid bahonar University of Kerman

چکیده

In this paper, a new approach is investigated for order reduction based on Legendre expansion. Harmony Search is used in this approach, to determine the reduced order model's parameters. The Routh criterion is applied to specify the stability conditions. Then, the stability conditions are constraints in optimization problem. To present the efficiency of the proposed method, three test systems are reduced. The obtained results were compared to other existing techniques. The comparison showed that the proposed approach performs well. 

کلیدواژه‌ها

harmony search algorithm؛ en؛ Legendre Expansion؛ Order reduction؛ Routh Array؛ Stability Constraints

مراجع

[1] E.J. Davison, “A method for simplifying linear dynamic systems”, IEEE Trans. Automat. Contr. Vol.11, No.1, pp.93–101, 1996.

[2] M.R. Chidambara, “Further comments by M.R. Chidambara”, IEEE Trans. Automat. Cont. Vol.AC-12, No.1, pp. 799–800, 1967.

[3] E.J. Davison, “Further reply by E.J. Davison”, IEEE Trans. Automat. Control. Vol.12, No.1, p. 800, 1967.

[4] M.R. Chidambara, “Two simple techniques for the simplification of large dynamic systems”, Proc. Conf. joint automatic control, JAC, pp. 669–674, 1969.

[5] Z. Elrazaz, N.K. Sinha, “On the selection of dominant poles of a system to be retained in a low-order model”, IEEE Trans. Automat. Contr., Vol.24, No.5, pp.792-793, 1979.

[6] M. Hutton, B. Friedland, “Routh approximations for reducing order of linear, time-invariant systems”, IEEE Trans. Automat. Control., Vol.20, No.3 pp.329–337, 1975.

[7] R.K. Appiah, “Linear model reduction using Hurwitz polynomial approximation”, Int. J. Control, Vol.28, No.3, pp. 477-488, 1978.

[8] R.K. Appiah, “Pade methods of Hurwitz polynomial with application to linear system reduction”, Int. J. Control. 29, No.1 pp. 39-48, 1979.

[9] T.C. Chen, C.Y. Chang and K.W. Han, “Reduction of transfer functions by the stability equation method”, J. Franklin Inst. Vol.308, No.4, pp. 389-404, 1979.

[10] T.C. Chen, C.Y. Chang and K.W. Han, “Model reduction using the stability equation method and the continued fraction method”, Int. J. Control. Vol.32, No.1, pp. 81-94, 1980.

[11] L.G. Gibilaro, F.P. Lees, “The reduction of complex transfer function models to simple models using the method of moments”, Chemical Engineering Science. 24, No.1, pp. 85–93, 1969.

[12] F.P. Lees, “The derivation of simple transfer function models of oscillating and inverting process from the basic transformed equation using the method of moments”, Chemical Engineering Science. Vol.26, No.8, pp. 1179-1186, 1971.

[13] Y.P. Shih, C.S. Shieh, “Model reduction of continuous and discrete multivariable systems by moments matching”, Computer & Chemical Engineering. Vol.2, No.4, pp. 127-132, 1978.

[14] V. Zakian, “Simplification of linear time-variant system by moment approximation”, Int. J. Control. Vol.18, No.8, pp. 455-460, 1973.

[15] C.F. Chen, L.S. Shieh, “A novel approach to linear model simplification”, Int. J. Control. Vol.8, No.6, pp. 561–570, 1968.

[16] C.F. Chen, “Model reduction of multivariable control systems by means matrix continued

Majlesi Journal of Electrical Engineering Vol. 9, No. 1, March 2015

35

fractions”, Int. J. Control. Vol.20, No.2, pp. 225-238, 1974.

[17] D.J. Wright, “The continued fraction representation of transfer functions and model simplification”, Int. J. Control. Vol.18, No.3, pp. 449-454, 1973.

[18] Y. Shamash, “Stable reduced-order models using Pade type approximation”, IEEE Trans. Automat. Control. Vol.19, No.5, pp.615-616, 1974.

[19] D.A. Wilson, “Optimal solution of model reduction problem”, Proc. Institute of Electrical Engineering. Vol.117, No.6, p. 1161-1165.

[20] D.A. Wilson, “Model reduction for multivariable systems”, Int. J. Control Vol.20, No.1, pp. 57–64, 1974.

[21] G. Obinata, H. Inooka, “A method of modeling linear time-invariant systems by linear systems of low order”, IEEE Trans Automat. Contr. Vol.21, No.4, pp.602–603, 1976.

[22] G. Obinata, H. Inooka, “Authors reply to comments on model reduction by minimizing the equation error”, IEEE Trans Automat Control. 28, No.1, pp.124–125, 1983.

[23] E. Eitelberg, “Model reduction by minimizing the weighted equation error”, Int. J. Control. Vol.34, No.6, pp. 1113-1123, 1981.

[24] R.A. El-Attar, M. Vidyasagar, “Order reduction by L1 and L∞ Norm minimization”, IEEE Trans Automat Control. Vol.23, No.4, pp.731–734, 1978.

[25] B.C. Moore, “Principal component analysis in linear systems: controllability”, observability and model reduction, IEEE Trans Automat Control Vol.26, No.1, pp. 17–32, 1981.

[26] L. Pernebo, L. M. Silverman, “Model reduction via balanced state space representation”, IEEE Trans Automatic Control. Vol.27, No.2, pp. 382–387, 1982.

[27] D. Kavranoglu, M. Bettayeb, “Characterization of the solution to the optimal H∞ model reduction problem”, System & Control Letters. Vol.20, No.2, pp. 99–107, 1993.

[28] L. Zhang, J. Lam, “On H2 model reduction of bilinear system”, Automatica. Vol.38, No.2, pp. 205–216, 2002.

[29] W. Krajewski, A. Lepschy, G.A. Mian and U. Viaro, “Optimality conditions in multivariable L2 model reduction, J. Franklin Inst. Vol.330, No.3, pp.431–439, 1993.

[30] D. Kavranoglu, M. Bettayeb, “Characterization and computation of the solution to the optimal L∞ approximation problem, IEEE Trans Automat Control. Vol.39, No.9, pp.1899–1904, 1994.

[31] G. Parmar, S. Mukherjee and R. Prasad, “Reduced Order Modeling of Linear Dynamic Systems using Particle Swarm Optimized Eigen Spectrum Analysis”, Int. J. Computer and Mathematical Science. Vol.1, No.31, pp.45-52, 2007.

[32] G. Parmer, R. Prasad and S. Mukherjee, “Order Reduction of Linear Dynamic Systems using Stability Equation Method and GA”, W