Order Reduction using Modified Pole Clustering and Pade Approximations

Authors: C.B. Vishwakarma

Abstract:

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.

Keywords: Modified pole clustering, order reduction, padeapproximation, stability, transfer function.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1059535

References:

[1] V. Singh, D. Chandra and H. Kar, "Improved Routh Pade approximants: A Computer aided approach", IEEE Trans. Autom. Control, 49(2), pp.292-296, 2004.
[2] S.Mukherjee and R.N. Mishra, "Reduced order modeling of linear multivariable systems using an error minimization technique", Journal of Franklin Inst., 325 (2), pp.235-245, 1988.
[3] Sastry G.V.K.R Raja Rao G. and Mallikarjuna Rao P., "Large scale interval system modeling using Routh approximants", Electronic Letters, 36(8), pp.768-769, 2000.
[4] R. Prasad, "Pade type model order reduction for multivariable systems using Routh approximation", Computers and Electrical Engineering, 26, pp.445-459, 2000.
[5] G. Parmar, S. Mukherjee and R. Prasad, "System reduction using factor division algorithm and eigen spectrum analysis", Applied Mathematical Modelling, Elsevier, 31, pp.2542-2552, 2007.
[6] R. Prasad and J. Pal, "Stable reduction of linear systems by continued fractions", Journal of Institution of Engineers IE(I) Journal-EL, 72, pp.113-116, 1991.
[7] R. Prasad, S.P. Sharma and A.K. Mittal, "Improved Pade approximation for multivariable systems using stability equation method", Journal of Institution of Engineers IE (I) Journal-EL, 84, pp.161-165, 2003.
[8] A.K. Sinha, J. Pal, Simulation based reduced order modeling using a clustering technique, Computer and Electrical Engg., 16(3), 1990, 159-169.
[9] J. Pal, A.K. Sinha and N.K. Sinha, Reduced-order modelling using pole clustering and time-moments matching, Journal of The Institution of Engineers (India), Pt El, 76,1995, 1-6.
[10] Pade H, "Sur La representation approaches dune function pardes fraction vationnellers", 9, pp.1-32, 1892.
[11] Shamash Y, "Stable reduced order models using Pade type approximants", IEEE Trans. Autom. Control, Vol.AC-19, No.5, pp.615-616, October 1974.
[12] Shamash Y, "Linear system reduction using Pade approximation to allow retention of dominant modes", Int. J. Control, Vol.21, No. 2, pp.257-272, 1975.
[13] C.B. Vishwakarma & R. Prasad, "MIMO system reduction using modified pole clustering and Genetic algorithm", Modelling and Simulation in Engineering, Hindawi Pub. Corp., USA, Volume 2009, pp. 1-6, 2009.
[14] A.K Mittal, R. Prasad, S.P Sharma, "Reduction of linear dynamic systems using an error minimization technique", Journal of Institution of Engineers IE(I) Journal-EL, Vol.84, pp.201-206, March 2004.
[15] S. Mukherjee, Satakshi, R.C Mittal, "Model order reduction using response matching", Journal of Franklin Inst., Vol.342, pp.503-519, 2005.
[16] Bistritz Y. and Langholz G., "Model reduction by Chebyshev polynomial techniques", IEEE Trans. Automatic Control, Vol-AC-25, No.5, pp. 741-747.