MPSO based Model Order Formulation Scheme for Discrete PID Controller Design
This paper proposes the novel model order
formulation scheme to design a discrete PID controller for higher
order linear time invariant discrete systems. Modified PSO (MPSO)
based model order formulation technique has used to obtain the
successful formulated second order system. PID controller is tuned to
meet the desired performance specification by using pole-zero
cancellation and proposed design procedures. Proposed PID
controller is attached with both higher order system and formulated
second order system. System specifications are tabulated and closed
loop response is observed for stabilization process. The proposed
method is illustrated through numerical examples from literature.
[1] T. L. Seng, M. B. Khalid and R. Yusof, "Tuning of a neuro-fuzzy
controller by genetic algorithm", IEEE Transaction on Systems
Manufacturing Cybernetics, Vol. 29. pp. 226-236, 1999.
[2] A. Visioli, "Tuning of PID controllers with fuzzy logic", Proceedings of
Industrial Electrical Engineering Control Theory Application, Vol. 148,
pp.1-8, 2001.
[3] R. A. Krohling and J. P. Rey, "Design of optimal disturbance rejection
PID controllers using genetic algorithm", IEEE Transaction on
Evolutionary Computation. Vol.5, pp.78-82, 2001.
[4] G. J. Silva, A. Datta, "New results on the synthesis of PID controllers",
IEEE Transactions on Automatic Control, Vol. 47, No. 2, pp. 241-252,
2002.
[5] 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.
[6] V. Zaliin, "Simplification of linear time-invariant system by moment
approximation", International Journal of Control System, Vol. 1, No. 8,
pp. 455-460, 1973.
[7] 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.
[8] S. Mukherjee, Satakshi and R. C. Mittal, "Model order reduction using
response-matching technique", Journal of Franklin Inst., Vol. 342, pp.
503-519, 2005.
[9] J. Tschauner, "A General Formulation of the Stability Constraints for
Sampled Data Control System", IEEE Proceedings, Vol. 51, pp. 613-
621, 1963.
[10] K. S. Yeung, K. Q. Chaid and D. X. Tien, "Bode design charts for
continuous- time and discrete- time compensators", IEEE Transaction
on Education", Vol. 38, No. 3, pp. 252-257, 1995.
[11] M. Zhuang, D. P. Atherton "Automatic tuning of optimum PID
controllers", IEEE Proceedings of Control Theory and Applications,
Vol. 140, No. 3, pp. 216-224, 1993.
[12] K. Rattan, "Digitalization of existing continuous control system", IEEE
Trans. Auto. Control, Vol. 29, pp. 282- 285, 1984.
[13] H. Inooka, G. Obinata and M. Takeshima, "Design of a digital controller
based on series expansions of pulse transfer functions", Journal of
Dynamic systems, Measurement and Control, Vol. 105, No. 3, pp. 204-
207, 1983.
[14] L. A. Aguirre, "PID tuning based on model matching", IEEE Electronics
Letter, Vol. 28, No. 25, pp. 2269-2271, 1992.
[15] A. Varsek, T. Urbacic and B. Filipic, "Genetic Algorithms in Controller
Design and Tuning", IEEE Transaction on Sys. Man and Cyber, Vol. 23,
No.5, pp.1330-1339, 1993.
[16] Z. L. Gaing, "A particle swarm optimization approach for optimum
design of PID controller in AVR system", IEEE Transaction on Energy
Conversion, Vol.19, No.2, pp.384-391, 2004.
[17] J. Zhao, T. Li, J. Qian, "Application of particle swarm optimization
algorithm on robust PID controller tuning", Advances in Natural
Computation - Springer, pp.948-957, 2005.
[18] M. Gopal , "Control systems principle and design", Tata McGraw Hill
Publications, New Delhi, 1997.
[19] B. C. Kuo and F. Golnaraghi, "Automatic control system", John Wiley,
2003.
[20] R. C Eberhart and Y. Shi, "Particle Swarm Optimization: Developments
applications and resourses", Proceedings Congress on Evolutionary
Computation IEEE service, NJ, Korea, 2001.
[21] S. N. Deepa and G. Sugumaran, "MPSO based model order formulation
technique for SISO continuous system", International Journal of
Engineering and Applied Science, Vol. 7, No. 3, pp. 125-130,2011.
[22] O. A. Sebakhy and M.N. Aly, "Discrete-time Model Reduction with
Optimal Zero Locations by Non-minimization," IEEE Proceeding of
Control Theory and Application, Vol. 145, No. 6, pp. 499-506,
November 1998.
[23] R. Prasad, "Order reduction of discrete time using stability equation
method and weighted time moments", IE (I) journal, Vol.74, pp.94-99,
1993.
[24] 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.
[25] S.Panda, S.K. Tomar, R.Prasad, 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] T. L. Seng, M. B. Khalid and R. Yusof, "Tuning of a neuro-fuzzy
controller by genetic algorithm", IEEE Transaction on Systems
Manufacturing Cybernetics, Vol. 29. pp. 226-236, 1999.
[2] A. Visioli, "Tuning of PID controllers with fuzzy logic", Proceedings of
Industrial Electrical Engineering Control Theory Application, Vol. 148,
pp.1-8, 2001.
[3] R. A. Krohling and J. P. Rey, "Design of optimal disturbance rejection
PID controllers using genetic algorithm", IEEE Transaction on
Evolutionary Computation. Vol.5, pp.78-82, 2001.
[4] G. J. Silva, A. Datta, "New results on the synthesis of PID controllers",
IEEE Transactions on Automatic Control, Vol. 47, No. 2, pp. 241-252,
2002.
[5] 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.
[6] V. Zaliin, "Simplification of linear time-invariant system by moment
approximation", International Journal of Control System, Vol. 1, No. 8,
pp. 455-460, 1973.
[7] 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.
[8] S. Mukherjee, Satakshi and R. C. Mittal, "Model order reduction using
response-matching technique", Journal of Franklin Inst., Vol. 342, pp.
503-519, 2005.
[9] J. Tschauner, "A General Formulation of the Stability Constraints for
Sampled Data Control System", IEEE Proceedings, Vol. 51, pp. 613-
621, 1963.
[10] K. S. Yeung, K. Q. Chaid and D. X. Tien, "Bode design charts for
continuous- time and discrete- time compensators", IEEE Transaction
on Education", Vol. 38, No. 3, pp. 252-257, 1995.
[11] M. Zhuang, D. P. Atherton "Automatic tuning of optimum PID
controllers", IEEE Proceedings of Control Theory and Applications,
Vol. 140, No. 3, pp. 216-224, 1993.
[12] K. Rattan, "Digitalization of existing continuous control system", IEEE
Trans. Auto. Control, Vol. 29, pp. 282- 285, 1984.
[13] H. Inooka, G. Obinata and M. Takeshima, "Design of a digital controller
based on series expansions of pulse transfer functions", Journal of
Dynamic systems, Measurement and Control, Vol. 105, No. 3, pp. 204-
207, 1983.
[14] L. A. Aguirre, "PID tuning based on model matching", IEEE Electronics
Letter, Vol. 28, No. 25, pp. 2269-2271, 1992.
[15] A. Varsek, T. Urbacic and B. Filipic, "Genetic Algorithms in Controller
Design and Tuning", IEEE Transaction on Sys. Man and Cyber, Vol. 23,
No.5, pp.1330-1339, 1993.
[16] Z. L. Gaing, "A particle swarm optimization approach for optimum
design of PID controller in AVR system", IEEE Transaction on Energy
Conversion, Vol.19, No.2, pp.384-391, 2004.
[17] J. Zhao, T. Li, J. Qian, "Application of particle swarm optimization
algorithm on robust PID controller tuning", Advances in Natural
Computation - Springer, pp.948-957, 2005.
[18] M. Gopal , "Control systems principle and design", Tata McGraw Hill
Publications, New Delhi, 1997.
[19] B. C. Kuo and F. Golnaraghi, "Automatic control system", John Wiley,
2003.
[20] R. C Eberhart and Y. Shi, "Particle Swarm Optimization: Developments
applications and resourses", Proceedings Congress on Evolutionary
Computation IEEE service, NJ, Korea, 2001.
[21] S. N. Deepa and G. Sugumaran, "MPSO based model order formulation
technique for SISO continuous system", International Journal of
Engineering and Applied Science, Vol. 7, No. 3, pp. 125-130,2011.
[22] O. A. Sebakhy and M.N. Aly, "Discrete-time Model Reduction with
Optimal Zero Locations by Non-minimization," IEEE Proceeding of
Control Theory and Application, Vol. 145, No. 6, pp. 499-506,
November 1998.
[23] R. Prasad, "Order reduction of discrete time using stability equation
method and weighted time moments", IE (I) journal, Vol.74, pp.94-99,
1993.
[24] 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.
[25] S.Panda, S.K. Tomar, R.Prasad, 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 Electrical, Electronic and Communication Sciences:57900", author = "S. N. Deepa and G. Sugumaran", title = "MPSO based Model Order Formulation Scheme for Discrete PID Controller Design", abstract = "This paper proposes the novel model order
formulation scheme to design a discrete PID controller for higher
order linear time invariant discrete systems. Modified PSO (MPSO)
based model order formulation technique has used to obtain the
successful formulated second order system. PID controller is tuned to
meet the desired performance specification by using pole-zero
cancellation and proposed design procedures. Proposed PID
controller is attached with both higher order system and formulated
second order system. System specifications are tabulated and closed
loop response is observed for stabilization process. The proposed
method is illustrated through numerical examples from literature.", keywords = "Discrete PID controller, Model Order Formulation,
Modified Particle Swarm Optimization, Pole-Zero Cancellation", volume = "5", number = "12", pages = "1762-8", }
