Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30077
Model Order Reduction of Discrete-Time Systems Using Fuzzy C-Means Clustering

Authors: Anirudha Narain, Dinesh Chandra, Ravindra K. S.


A computationally simple approach of model order reduction for single input single output (SISO) and linear timeinvariant discrete systems modeled in frequency domain is proposed in this paper. Denominator of the reduced order model is determined using fuzzy C-means clustering while the numerator parameters are found by matching time moments and Markov parameters of high order system.

Keywords: Model Order reduction, Discrete-time system, Fuzzy C-Means Clustering, Padé approximation.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2332


[1] L.Fortuna, G. Nunnari, and A. Gallo, “Model Order Reduction Techniques with applications in Electrical Engineering", Springer- Verlag, Lomndon, 1992.
[2] Y Shamash, “Stable reduced-order models using Padé type approximations”, IEEE Trans. Auto. Control, Vol. AC-19, No.5, pp. 615-616, October 1974.
[3] Y. Shamash, “Linear system reduction using Padé approximation to allow retention of dominant modes", Int. J. Contr., Vo. 21, Issue. 2, pp. 257-272, 1975.
[4] Maurice F.Hutton and Bernard Friedland, “Routh-approximation for reducing order of linear, time-invariant systems” IEEE Trans. Auto. Contr. Vol. AC-20, No.3, pp. 329-337, June 1975.
[5] Vimal Singh, Dinesh Chandra, and Harnath Kar, “Improved Routh - Padé Approximant: A Computer-aided approach” IEEE Trans. Auto. Contr. Vol. AC-49, No.2, pp. 292-296, February 2004.
[6] Vimal Singh, “Obtaining Routh-Padé approximants using the Luus- Jaakola algorithm”, IEE Proceedings, Control Theory Applications, vol.152,no.2, March 2005.
[7] T.N.Lucas, “Scaled Impulse Energy approximation for Model Reduction”, IEEE Trans. Auto. Contr. Vol. AC-33, No.8, pp. 791793, August 1988.
[8] W. Krajewski, A. Lepschy, and U. Viaro, “Model reduction by matching Markov parameters, time moments and impulse response energy”, IEEE Trans. Auto. Contr. Vol. AC-40, No.5, pp. 949-953, May 1995.
[9] B. Salimbahrami, B. Lohmann, T. Bechtold, and J. Korvink, “A Two- Sided Arnoldi-Algorithm with Stopping Criterion and an application in Order Reduction of MEMS”, Mathematical and Computer Modelling of Dynamical Systems, 11(1):79–93, 2005.
[10] W.H. Enright and M.S. Kamal, “On selecting a low order model using dominant mode concept”, IEEE Trans. Auto. Contr. Vol. AC-25, No.5, pp. 976-978, Oct. 1980.
[11] M.Gopal and S.I. Mehta, “On selection of eigen-values to be retained in the reduced order models”, IEEE Trans. Auto. Contr. Vol. AC-27, No.3, pp. 688-690, June 1982.
[12] Tai-Yih Chiu, “Model reduction by the low frequency approximation balancing method for unstable systems”, IEEE Trans. Auto. Contr. Vol. AC-41, No.7, pp. 995-997, July 1996.
[13] M. G. Safonov and R. Y. Chiang, “A Survey of model reduction by balanced truncation and some new results”, Int. J. Control, 77(8):748– 766, 2004.
[14] C.B.Vishwakarma and R. Prasad, “Clustering method for Reduction Order of Linear System using Pade approximation”, IETE Journal of Research, vol 54, issue5, Oct 2008.
[15] M. Srinivasan, A. Krishnan, “Transformer Linear Section Model Order Reduction with an Improved Pole Clustering”, European Journal of Scintific Research, Vol. 44, No.4, pp.541-549, 2010.
[16] D. Napoleon and S. Pavalakodi, “ A New Method for Dimensionality Reduction using K-Means Clustering Algorithm for high Dimensional Data Set”, International Journal of Computer Applications, Vol.13, No.7, January 2011.
[17] Y.P. Shih, and W.T. Wu., “Simplification of z-transfer functions by continued fraction” Int. J. Contr., Vo. 17, pp. 1089-1094, 1973.
[18] Chuang C., “Homographic transformation for the simplification of discrete-time functions by Padé approximation”, Int. J. Contr., Vo. 22, pp. 721-729, 1975.
[19] R.Y. Hwang, and Y.P. Shih, “ Combined methods of model reduction via discrete Laguerre polynomials” Int. J. Contr., Vo. 37, pp. 615-622, 1983.
[20] Khalid Hammouda, Fakhareddine Karray, “A Comparative Study of Data Clustering Techniques, University of Waterloo, Ontario, Canada.
[21] Jesus Gonzalez, Ignacio Rojas, Hector Pomares, Julio Ortega, & Alberto Prieto, “A New Clustering Technique for Function Approximation” IEEE Transaction on Neural Networks, Vol.13, NO.1, January, 2002.
[22] Kai-Ming Tse, Chen-Chien Hsu, and Chi-Hsu Wang, “Discrete-time model reduction of sampled systems using an enhanced multiresolutional dynamic genetic algorithm”, IEEE Conference Proc. On Systems, Man, and Cybernatics, Taipei, 2001.
[23] Chyi Hwang and Yen-Ping Shih, “On the time moments of discrete systems”, Int. J. Contr., Vo. 34, No. 6, pp. 1227-1228, 1981.
[24] Chyi Hwang and Ching-Shieh Hsieh, “A new canonical expansion of ztransfer function of reduced-order modeling of discrete-time systems”, IEEE Transactions circuits and systems, vol. 36, No., December 1989.
[25] N.N.Puri and M.T. Lim, “Stable optimal model reduction of linear discrete-time systems”, Transactions of the ASME, Measurement, and Control,vol.119, pp.300-304, June 1997.
[26] Vinay Pratap Singh, and Dinesh Chandra, “Reduction of discrete interval systems based on pole clustering and improved Pade approximation: a computer aided approach”, AMO-Advanced Modeling and Optimization, volume 14, Number 1, 2012.
[27] Shailendra K. Mittal, Dinesh Chandra, and Bhartiu Dwivedi, “VEGA based Routh-Padé approximants for discrete-time systems: a computer aided approach”, IACSIT International Journal of Engineering and Technology Vol.1, No.5, December, 2009.
[28] C.M. Liaw, C.T.Pan, and M.Quyang, “Model reduction of discrete system using the power decomposition method and the system identification method”, IEE Proceeding, vol. 133, No.1, January, 1986.
[29] G.Saraswathi, “A modified method for order reduction of large scale discrete systems”, International Journal of Advance Computer Science and Applications, vol.2, No.6, 2011.
[30] M.Farsi, K.Warwick and M. Guilandoust, “Stable reduced-order models for discrete-time system”, IEE proceedings, Vol. 133, pt D, No.3, pp137-141, May 1986.
[31] S. Mukherjee, Satakshi, R.C. Mittal, “Discrete system order reduction using multipoint step response matching”, Journal of Computational and Applied Mathematics, 461-466, 2004.
[32] S.N.Deepa, G. Sugumaran, “MPSO based Model Order Formulation Scheme for Discrete Time Linear System in State Space Form”, European Journal of Scientific Research, vol.58 No.4, pp 444-454, 2011.