MPSO based Model Order Formulation Technique for SISO Continuous Systems
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32845
MPSO based Model Order Formulation Technique for SISO Continuous Systems

Authors: S. N. Deepa, G. Sugumaran


This paper proposes a new version of the Particle Swarm Optimization (PSO) namely, Modified PSO (MPSO) for model order formulation of Single Input Single Output (SISO) linear time invariant continuous systems. In the General PSO, the movement of a particle is governed by three behaviors namely inertia, cognitive and social. The cognitive behavior helps the particle to remember its previous visited best position. In Modified PSO technique split the cognitive behavior into two sections like previous visited best position and also previous visited worst position. This modification helps the particle to search the target very effectively. MPSO approach is proposed to formulate the higher order model. The method based on the minimization of error between the transient responses of original higher order model and the reduced order model pertaining to the unit step input. The results obtained are compared with the earlier techniques utilized, to validate its ease of computation. The proposed method is illustrated through numerical example from literature.

Keywords: Continuous System, Model Order Formulation, Modified Particle Swarm Optimization, Single Input Single Output, Transfer Function Approach

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1737


[1] Z. Qian and Z. Meng, "Low order approximation for analog simulation of thermal processes", ACTA Automarica Sinica (in Chinese), Vol. 4, No.1, pp. 1-17. 1966.
[2] C.F. Chen and L.S. Shien, "A novel approach to linear model simplification", International Journal of Control System, Vol. 8, pp. 561-570, 1968.
[3] V. Zaliin, "Simplification of linear time-invariant system by moment approximation", International Journal of Control System, Vol. 1, No. 8, pp. 455-460, 1973.
[4] H. Xiheng, "Frequency-fitting and Pade-order reduction", Information and Control, Vol. 12, No. 2, 1983.
[5] An investigation on the methodology and technique of model reduction (in Preprints), 7th IFAC Symposium on Identification and System Parameter and Estimation, Vol. 2, pp.1700-1706, 1985.
[6] P. O. Gutman, C. F. Mannerfelt and P. Molander, "Contributions to the model reduction problem", IEEE Trans. Auto. Control, Vol. 27, pp. 454- 455, 1982.
[7] J. Pal, "System reduction by mixed method", IEEE Transaction on Automatic Control, Vol. 25, No. 5, pp. 973-976, 1980.
[8] Y. Shamash, "Truncation method of reduction: a viable alternative", Electronics Letters, Vol. 17, pp. 97-99, 1981.
[9] D. E. Goldberg, "Genetic Algorithms in Search, Optimization, and Machine Learning", Addison-Wesley, 1989.
[10] M.Gopal , "Control systems principle and design", Tata McGraw Hill Publications, New Delhi, 1997.
[11] R. C Eberhart and Y. Shi, "Particle Swarm Optimization: Developments applications and resourses", Proceedings Congress on Evolutionary Computation IEEE service, NJ, Korea, 2001.
[12] A. M. Abdelbar and S. Abdelshahid, "Swarm Optimization with instinct driven particles", Proceedings of the IEEE Congress on Evolutionary Computation, pp. 777-782, 2003.
[13] U. Baumgartner, C. Magele and W. Reinhart", Pareto optimality and particle swarm optimization" IEEE Transaction on Magnetics, Vol. 40, pp.1172-1175, 2004.
[14] S. N. Sivanandam and S. N. Deepa," A Genetic Algorithm and Particle Swarm Optimization approach for lower order modeling of linear time invariant discrete systems "Int. Conf. on Comp. Intelligent and Multimedia Application, Vol. 1, pp. 443- 447, Dec. 2007.
[15] A. Immanuel selvakumar and K. Thanushkodi "A New Particle Swarm Optimization solution to nonconvex economic dispath problem", IEEE Trans. On Power System, Vol. 22. No. 1, pp. 42- 51, Feb. 2007.
[16] R. Prasad and J. Pal, "Stable reduction of linear systems by continued fractions", Journal of Institution of Engineers IE(I) Journal, Vol. 72, pp. 113-116, October, 1991.
[17] Y. Shamash, "Linear system reduction using Pade approximation to allow retention of dominant modes", Int. J. Control, Vol. 21, No. 2, pp. 257-272, 1975.
[18] S. Mukherjee, Satakshi and R. C. Mittal, "Model order reduction using response-matching technique", Journal of Franklin Inst., Vol. 342 , pp. 503-519, 2005.
[19] S. K. Tomar and R. Prasad, "Conventional and PSO based approaches for Model order reduction of SISO Discrete systems", International journal of electrical and electronics Engineering, Vol. 2, pp. 45-50, 2009.
[20] S. Yadav, N. P. Patidar, J. Singhai, S. Panda and C. Ardil, "A combined conventional and differential evolution method for model order reduction", International Journal of Computational Intelligence, Vol. 5, No. 2, pp. 111-118, 2009.
[21] S. Panda, S. K. Tomar, R. Prasad and C. Ardil, "Reduction of linear time invariant systems using Routh - approximation and PSO", International Journal of Applied Mathematics and Computer Science, Vol. 5, No. 2, pp. 82- 89, 2009.
[22] S. Panda, S. K. Tomar, R. Prasad and C. Ardil, "Model reduction of linear systems by conventional and evolutionary techniques", International Journal of Computational and Mathematical Science, Vol.3, No.1, pp. 28-34, 2009.