MPSO based Model Order Formulation Technique for SISO Continuous Systems
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62051", author = "S. N. Deepa and G. Sugumaran", title = "MPSO based Model Order Formulation Technique for SISO Continuous Systems", abstract = "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", volume = "5", number = "3", pages = "476-6", }