MIMO System Order Reduction Using Real-Coded Genetic Algorithm
In this paper, real-coded genetic algorithm (RCGA) optimization technique has been applied for large-scale linear dynamic multi-input-multi-output (MIMO) system. The method is based on error minimization technique where the integral square error between the transient responses of original and reduced order models has been minimized by RCGA. The reduction procedure is simple computer oriented and the approach is comparable in quality with the other well-known reduction techniques. Also, the proposed method guarantees stability of the reduced model if the original high-order MIMO system is stable. The proposed approach of MIMO system order reduction is illustrated with the help of an example and the results are compared with the recently published other well-known reduction techniques to show its superiority.
[1] S. Mukherjee and R.N. Mishra,"Reduced order modelling of linear
multivariable systems using an error minimization technique", Journalof
Franklin Inst., Vol. 325, No. 2 , pp. 235-245,1998.
[2] 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.
[3] R. Prasad, A. K. Mittal and S. P. Sharma " A mixed method for the
reduction of multivariable systems", Journal of Institute of Engineers,
India, IE(I) Journal-EL, Vol. 85, pp 177-181,2005.
[4] 4. C. Hwang " Mixed method of Routh and ISE criterion approaches for
reduced order modelling of continuous time systems", Trans. ASME, J.
Dyn. Syst. Meas. Control, Vol. 106,pp. 353-356. 1984.
[5] S. Mukherjee, and R.N. Mishra, "Order reduction of linear systems
using an error minimization technique", Journalof Franklin Inst., Vol.
323, No. 1, pp. 23-32, 1987.
[6] N.N. Puri, and D.P. Lan, "Stable model reduction by impulse response
error minimization using Mihailov criterion and Pade-s approximation",
Trans. ASME, J. Dyn. Syst. Meas. Control, Vol. 110, pp. 389-394, 1988.
[7] P. Vilbe, and L.C. Calvez, "On order reduction of linear systems using
an error minimization technique", Journal of Franklin Inst., Vol. 327,
pp. 513-514, 1990.
[8] G.D. Howitt, and R. Luus, "Model reduction by minimization of
integral square error performance indices", Journal of Franklin Inst.,
Vol. 327, pp. 343-357, 1990.
[9] Vishwakarma and Prasad, "MIMO System Reduction Using Modified
Pole Clustering and Genetic Algorithm", Hindawi Pub. Corp. Mod. and
Sim. in Engineering,
[10] G. Parmar, R. Prasad, and S. Mukherjee, "Order reduction of linear
dynamic systems using stability equation method and GA,"
International Journal of Computer, Information, and Systems Science,
and Engineering, vol. 1, no. 1, pp. 26-32, 2007.
[11] R. Prasad and J. Pal, "Use of continued fraction expansion for stable
reduction of linearmultivariable systems," Journal of the Institution of
Engineers, vol. 72, pp. 43-47, 1991.
[12] M. G. Safonov and R. Y. Chiang, "Model reduction for robust control: a
schur relative errormethod," International Journal of Adaptive Control
and Signal Processing, vol. 2, no. 4, pp. 259-272, 1988.
[13] R. Prasad, J. Pal, and A. K. Pant, "Multivariable system approximation
using polynomial derivatives," Journal of the Institution of Engineers,
vol. 76, pp. 186-188, 1995.
[1] S. Mukherjee and R.N. Mishra,"Reduced order modelling of linear
multivariable systems using an error minimization technique", Journalof
Franklin Inst., Vol. 325, No. 2 , pp. 235-245,1998.
[2] 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.
[3] R. Prasad, A. K. Mittal and S. P. Sharma " A mixed method for the
reduction of multivariable systems", Journal of Institute of Engineers,
India, IE(I) Journal-EL, Vol. 85, pp 177-181,2005.
[4] 4. C. Hwang " Mixed method of Routh and ISE criterion approaches for
reduced order modelling of continuous time systems", Trans. ASME, J.
Dyn. Syst. Meas. Control, Vol. 106,pp. 353-356. 1984.
[5] S. Mukherjee, and R.N. Mishra, "Order reduction of linear systems
using an error minimization technique", Journalof Franklin Inst., Vol.
323, No. 1, pp. 23-32, 1987.
[6] N.N. Puri, and D.P. Lan, "Stable model reduction by impulse response
error minimization using Mihailov criterion and Pade-s approximation",
Trans. ASME, J. Dyn. Syst. Meas. Control, Vol. 110, pp. 389-394, 1988.
[7] P. Vilbe, and L.C. Calvez, "On order reduction of linear systems using
an error minimization technique", Journal of Franklin Inst., Vol. 327,
pp. 513-514, 1990.
[8] G.D. Howitt, and R. Luus, "Model reduction by minimization of
integral square error performance indices", Journal of Franklin Inst.,
Vol. 327, pp. 343-357, 1990.
[9] Vishwakarma and Prasad, "MIMO System Reduction Using Modified
Pole Clustering and Genetic Algorithm", Hindawi Pub. Corp. Mod. and
Sim. in Engineering,
[10] G. Parmar, R. Prasad, and S. Mukherjee, "Order reduction of linear
dynamic systems using stability equation method and GA,"
International Journal of Computer, Information, and Systems Science,
and Engineering, vol. 1, no. 1, pp. 26-32, 2007.
[11] R. Prasad and J. Pal, "Use of continued fraction expansion for stable
reduction of linearmultivariable systems," Journal of the Institution of
Engineers, vol. 72, pp. 43-47, 1991.
[12] M. G. Safonov and R. Y. Chiang, "Model reduction for robust control: a
schur relative errormethod," International Journal of Adaptive Control
and Signal Processing, vol. 2, no. 4, pp. 259-272, 1988.
[13] R. Prasad, J. Pal, and A. K. Pant, "Multivariable system approximation
using polynomial derivatives," Journal of the Institution of Engineers,
vol. 76, pp. 186-188, 1995.
@article{"International Journal of Electrical, Electronic and Communication Sciences:53680", author = "Swadhin Ku. Mishra and Sidhartha Panda and Simanchala Padhy and C. Ardil", title = "MIMO System Order Reduction Using Real-Coded Genetic Algorithm", abstract = "In this paper, real-coded genetic algorithm (RCGA) optimization technique has been applied for large-scale linear dynamic multi-input-multi-output (MIMO) system. The method is based on error minimization technique where the integral square error between the transient responses of original and reduced order models has been minimized by RCGA. The reduction procedure is simple computer oriented and the approach is comparable in quality with the other well-known reduction techniques. Also, the proposed method guarantees stability of the reduced model if the original high-order MIMO system is stable. The proposed approach of MIMO system order reduction is illustrated with the help of an example and the results are compared with the recently published other well-known reduction techniques to show its superiority.
", keywords = "Multi-input-multi-output (MIMO) system.Modelorder reduction. Integral squared error (ISE). Real-coded geneticalgorithm", volume = "5", number = "3", pages = "313-5", }
