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Order Reduction of LTIV Continuous MIMO System using Stability Preserving Approximation Method

by K. Ramesh, Dr. A. Nirmalkumar, Dr. G. Gurusamy
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 36 - Number 8
Year of Publication: 2011
Authors: K. Ramesh, Dr. A. Nirmalkumar, Dr. G. Gurusamy
10.5120/4508-5822

K. Ramesh, Dr. A. Nirmalkumar, Dr. G. Gurusamy . Order Reduction of LTIV Continuous MIMO System using Stability Preserving Approximation Method. International Journal of Computer Applications. 36, 8 ( December 2011), 1-8. DOI=10.5120/4508-5822

@article{ 10.5120/4508-5822,
author = { K. Ramesh, Dr. A. Nirmalkumar, Dr. G. Gurusamy },
title = { Order Reduction of LTIV Continuous MIMO System using Stability Preserving Approximation Method },
journal = { International Journal of Computer Applications },
issue_date = { December 2011 },
volume = { 36 },
number = { 8 },
month = { December },
year = { 2011 },
issn = { 0975-8887 },
pages = { 1-8 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume36/number8/4508-5822/ },
doi = { 10.5120/4508-5822 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:22:36.266838+05:30
%A K. Ramesh
%A Dr. A. Nirmalkumar
%A Dr. G. Gurusamy
%T Order Reduction of LTIV Continuous MIMO System using Stability Preserving Approximation Method
%J International Journal of Computer Applications
%@ 0975-8887
%V 36
%N 8
%P 1-8
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In modeling physical systems, the order of the system gives an idea of the measure of accuracy of the modeling of the system. The higher the order, the more accurate the model can be in describing the physical system. But in several cases, the amount of information contained in a complex model may obfuscate simple, insightful behaviors, which can be better captured and explored by a model with a much lesser order. In this paper, stability preserving method is proposed for the Multiple Input Multiple Output linear time invariant system to obtain the stable reduced order system. The genetic algorithm is used at the tail end of the proposed scenarios to get error minimized reduced model.

References
  1. Wan Bai-Wu. 1981. Linear Model Reduction using Mihailov Criterion and Pade Approximation Technique, Int. J. of Cont. 33(6), pp. 1073-1081.
  2. Prasad, R.,Sharma, S.P. and Mittal, A.K. 2003. Linear Model Reduction Using the Advantages of Mihailov Criterion and Factor Division, J. of Inst. of Engg. (India), 84, pp. 7-10.
  3. Mittal, A.K., Sharma, S. P. and Prasad, R. 2002. Reduction of Multi-variable Systems using the Advantages of Mihailov Criterion and Factor Division, Proceedings of Int. Conf. of CERA, IIT Roorkee, pp. 477-481.
  4. Lucas, T.N. 1983. Factor division: A useful algorithm in model reduction, IEE proceedings, 130(6).
  5. Lucas, T.N. 1978. Frequency domain approximation of linear systems, Ph.D thesis, UWIST, Cardiff, Wales.
  6. Lal, M. and Mitra, R. 1974. Simplification of large scale system dynamics using a moment evaluation algorithm, IEEE transactions, AC-19, pp. 602-603.
  7. Shamash, Y. 1975. Model Reduction using the Routh Stability Criterion and the Pade Approximation Technique, Int. J. of Cont., 21(3), pp. 475-484.
  8. Chen, T.C., Chang, C.Y. and Han, K.W. 1980. Model Reduction using Stability equation Method and the Pade Approximation Method, J. of Fran. Inst., 309, pp. 473-490.
  9. Chen, T.C., Chang, C.Y. and Han, K.W. 1980. Model Reduction using Stability equation Method and Continued Fraction Method, Int. J. of Cont., 32(1), pp. 81-94.
  10. Pal, J., Sinha, A.K. and Sinha, N.K. 1995. Reduced-order Modelling using Pole Clustering and Time-moment Matching, J. of Ins. of Engg.(India), Pt El, 76, pp. 1-6.
  11. Gupta, D.K., Bhagat, S.K. and Tewari, J.P. 2002. A Mixed Method for the Simplification of Linear Dynamic Systems, Proc. of Int. Conf. on Comp. Appl. in Elec. Engg. Recent Advances, IIT, Roorkee, February 21-23, pp. 455-459.
  12. Bhagat, S.K., Tewari, J.P. and Srinivasan, T. 2004. Some mixed methods fro the simplification of higher order single input single output system, IE(I) Journal- EL,85.
  13. Ramar, K. and Ramaswamy, B. 1968. Transformation to the Phase Variable Canonical Form, IEEE Trans. on Auto. Cont., 13, pp. 746-747.
  14. Gutman,P.O., Mannerfelt, C.F. and Molander, P. 1982. Contributions to the Model Reduction Problems, IEEE Trans. on Auto.Cont. 27(2), pp. 454-455.
  15. Chen, T.C., Chang, C.Y. and Han, K.W. 1979. Reduction of Transfer Functions by the Stability-equation Method. J. of Frank. Ins., 308(4), pp. 389-404.
  16. Hwang, C.1984. Mixed method of Routh and ISE criterion approaches for reduced order modelling of continuous time systems, Trans. ASME, J. Dyn. Syst. Meas. Cont., Vol. 106, pp. 353-356, 1984.
  17. Mukherjee, S. and Mishra, R.N. 1987. Order reduction of linear systems using an error minimization technique, J. of Frank. Ins., 323(1), pp. 23-32.
  18. Lamba, S.S., Gorez, R. and Bandyopadhyay, B. 1988. New reduction technique by step error minimization for multivariable systems, Int. J. Sys. Sci., 19(6), pp. 999-1009.
  19. Mukherjee, S. and Mishra, R.N. 1988. Reduced order modeling of linear multivariable systems using an error minimization technique, J. of Frank. Ins., 325(2), pp. 235-245.
  20. Puri, N.N. and Lan, D.P. 1988. Stable model reduction by impulse response error minimization using Mihailov criterion and Pade’s approximation, Trans. ASME, J. Dyn. Syst. Meas. Cont., 110, pp. 389-394.
  21. Vilbe, P. and Calvez, L.C. 1990. On order reduction of linear systems using an error minimization technique, J. of Frank. Inst., 327, pp. 513-514.
  22. Mittal, A.K., Prasad, R. and Sharma, S.P. 2004. Reduction of linear dynamic systems using an error minimization technique, J. of IE(I)– EL, 84, pp. 201-206.
  23. Howitt, G.D. and Luus, R.1990. Model reduction by minimization of integral square error performance indices, J. of Frank. Inst., 327, pp. 343-357.
  24. Vishwakarma, C.B. and Prasad, R. 2009. MIMO system reduction using Modified pole clustering and Genetic algorithm, Modeling and simu. in Engg. Hindawi Publishing Corporation, pp-1-5.
  25. Sivanandam, S.N., Venkatesan, R. and Suganthi, J. 2007. A rule-based approach for second order model formulation of linear time invariant multivariable systems, J. of Elec. Engg., Springer-Verilog, 89, pp. 319-331.Available: DOI 10.1007/s00202-006-0010-x.
  26. Parmar, G., Prasad, R. and Mukherjee, S. 2007. Order reduction of linear dynamic systems using stability equation method and GA, Int. J. of Comp. Inf. and Sys. Sci. and Engg., 1(1), pp. 26–32.
  27. Prasad, R. and Pal, J. 1991. Use of continued fraction expansion for stable reduction of linear multivariable systems, J. of IE(I), 72, pp. 43–47.
  28. Prasad, R., Pal, J. and Pant, A.K. 1995.Multivariable system approximation using polynomial derivatives,” J. of IE(I), 76, pp. 186–188.
  29. Safonov, M. G. and Chiang, R.Y. 1988. Model reduction for robust control: a schur relative error method, Int. J. of Adap. Cont. and Sig. Proc., 2(4), pp. 259– 272.
  30. Swadhin Ku. Mishra, Sidhartha Panda, Simanchala Padhy and Ardil, C. 2010. MIMO System Order Reduction Using Real-Coded Genetic Algorithm, Int. J. of Elec. and Comp. Engg, 6(1), pp 10-14.
  31. Prasad.R, Sharma, S.P. and Mittal, A.K. 2003. Improved Pade approximants for multivariable systems using stability equation method, J. of IE (I), EL, 86, pp 161–165.
  32. Prasad.R. 2000. Pade type model order reduction for multivariable systems using Routh approximation, Int. J. of Comp. and Elec. Engg., 26, pp 445-450.
Index Terms

Computer Science
Information Sciences

Keywords

Model order reduction Integral Square Error (ISE) Genetic Algorithm (GA) Transient gain Steady state gain

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