Multivariable System Reduction Using Stability Equation Method and SRAM

Authors: D. Bala Bhaskar

Abstract:

An algorithm is proposed for the order reduction of large scale linear dynamic multi variable systems where the reduced order model denominator is obtained by using Stability equation method and numerator coefficients are obtained by using SRAM. The proposed algorithm produces a lower order model for an original stable high order multivariable system. The reduction procedure is easy to understand, efficient and computer oriented. To highlight the advantages of the approach, the algorithm is illustrated with the help of a numerical example and the results are compared with the other existing techniques in literature.

Keywords: Multi variable systems, order reduction, stability equation method, SRAM, time domain characteristics, ISE.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1317258

References:

[1] Y. Shamash (1974) Stable reduced order models using Pade type approximations, IEEE trans. On Automatic Control, Vol. 19, pp.615-616
[2] Y. Shamash (1973) Continued fraction methods for the reduction of Linear time invariant systems. In Proc.Conf. Computer Aided Control system Design, Cambridge, England, pp.220-227.
[3] E. Jonckheere and C. Ma (1989) Combined sequence of Markov parameter and moments in linear systems. IEEE Trans. Aufomuf. Confr.; vol. AC-34,pp.379-382.
[4] M. F. Hutton, B. Friendland (1999) Routh approximations for reducing order of linear time-varying systems. IEEE Trans. Automat. Control, vol.44, No.9, pp. 1782-1787
[5] Y. Shamash (1975) Model reduction using the Routh stability criterion and the Pade approximation technique. Int. J. Control, 21, pp. 475-484
[6] Hwang C (1984) Mixed method of Routh and ISE criterion approaches for reduced order modeling of continuous time systems. Trans ASME J Dyn Syst Meas Control 106: pp. 353-356
[7] B. Bandyopadhyay, O. Ismail, and R. Gorez (1994) Routh Pade approximation for interval systems. IEEE Trans. Automat. Contr., pp. 2454-2456.
[8] R. Genesio and M. Milanese, “A note on the derivation and use of reduced order models”, IEEE Trans. Automat. Control, Vol. AC-21, No. 1, pp. 118-122, February 1976.
[9] M. S. Mahmoud and M. G. Singh, Large Scale Systems Modelling, Pergamon Press, International Series on Systems and Control 1st ed.,Vol. 3, 1981.
[10] M. Jamshidi, Large Scale Systems Modelling and Control Series, New York, Amsterdam, Oxford, North Holland, Vol. 9, 1983.
[11] S. K. Nagar and S. K. Singh, “An algorithmic approach for system decomposition and balanced realized model reduction”, Journal of Franklin Inst., Vol. 341, pp. 615-630, 2004.
[12] V. Singh, D. Chandra and H. Kar, “Improved Routh Pade approximants: A computer aided approach”, IEEE Trans. Automat. Control, Vol. 49, No.2, pp 292-296, February 2004.
[13] S. Mukherjee, Satakshi and R.C.Mittal, “Model order reduction using response-matching technique”, Journal of Franklin Inst., Vol. 342, pp.503-519, 2005.
[14] B. Salimbahrami, and B. Lohmann, “Order reduction of large scale second-order systems using Krylov subspace methods”, Linear Algebra Appl., Vol.415, pp.385-405, 2006.
[15] S. Mukherjee and R.N. Mishra, “Reduced order modelling of linear multivariable systems using an error minimization technique”, Journal of Franklin Inst., Vol.325, No. 2, pp. 235-245, 1988.
[16] S. S. Lamba, R. Gorez and B. Bandyopadhyay, “New reduction technique by step error minimization for multivariable systems”, Int. J. Systems Sci., Vol. 19,No. 6, pp. 999-1009, 1988.
[17] R. Prasad and J. Pal, “Use of continued fraction expansion for stable reduction of linear multivariable systems”, Journal of Institution of Engineers, India,IE(I) Journal – EL, Vol. 72, pp. 43-47, June 1991.
[18] R. Prasad, A. K. Mittal and S. P. Sharma, “A mixed method for the reduction of multi-variable systems”, Journal of Institution of Engineers, India, IE(I) Journal– EL, Vol. 85, pp. 177-181, March 2005.
[19] S. Mukherjee, and R.N. Mishra, “Order reduction of linear systems using an error minimization technique”, Journal of Franklin Inst., Vol. 323,No. 1,pp. 23-32, 1987.
[20] A.K. Mittal, R. Prasad, and 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.
[21] J. Pal, “Improved Pade approximants using stability equation method”, Electronic Letters, Vol. 19, No.11, pp.426-427, May 1983.
[22] M. G. Safonov and R. Y. Chiang, “Model reduction for robust control: a Schur relative error method”, Int. J. Adaptive Cont. and Signal Proc., Vol. 2, pp. 259-272, 1988.
[23] Y. Bistritz and U. Shaked, “Minimal Pade model reduction for multivariable systems”, ASME Journal of Dynamic System Measurement and Control, Vol.106, pp.293-299, 1984.
[24] R. Prasad, J. Pal and A. K. Pant, “Multivariable system approximation using polynomial derivatives”, Journal of Institution of Engineers, India, IE(I)Journal – EL, Vol. 76, pp. 186-188, November 1995.
[25] L.S. Shieh and Y.J. Wei, “A mixed method for multivariable system reduction”, IEEE Trans. Automat. Control, Vol. AC-20, pp. 429-432, 1975.
[26] P. O. Gutman, C.F. Mannerfelt and P. Molander, “Contributions to the model reduction problem”, IEEE Trans. Automat. Control, Vol. AC-27, No.2, pp. 454-455, April 1982.
[27] G. Parmar, R. Prasad, and S. Mukherjee, “Order Reduction of Linear Dynamic Systems using Stability Equation Method and GA” Int Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering Vol:1, No:2, pp. 236-242, 2007.
[28] R. Prasad, J. Pal and A. K. Pant, “Multivariable system approximation using polynomial derivatives”, IE(I) Journal – EL, Vol. 76, pp. 186-188, November-1995, India.
[29] Sudhir Y. Kumar, Kritika, “a noble hybrid concept for mimo system modeling using bacterial foraging optimization technique”, Journal of Basic and Applied Engineering Research Print ISSN: 2350-0077; Online ISSN: 2350-0255; Volume 1, Number 7;October, 2014 pp. 101-104.
[30] Jasvir singh rana, Rajendra Prasad, R.P. Agarwal, “MIMO system order reduction using basic characteristics and factor division method”, International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084 Volume-4.