Design of PID Controller for Higher Order Continuous Systems using MPSO based Model Formulation Technique
This paper proposes a new algebraic scheme to design a PID controller for higher order linear time invariant continuous systems. Modified PSO (MPSO) based model order formulation techniques have applied to obtain the effective formulated second order system. A controller is tuned to meet the desired performance specification by using pole-zero cancellation method. Proposed PID controller is attached with both higher order system and formulated second order system. The closed loop response is observed for stabilization process and compared with general PSO based formulated second order system. The proposed method is illustrated through numerical example from literature.
[1] 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.
[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] 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.
[5] 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.
[6] S. Mukherjee, Satakshi and R. C. Mittal, "Model order reduction using
response-matching technique", Journal of Franklin Inst., Vol. 342 , pp.
503-519, 2005.
[7] J. G. Ziegler, N. B. Nichols, "Optimum settings for automatic
controllers", Transaction of the AMSE, Vol. 64, pp. 759-768, 1942.
[8] C. C. Hang, K. J. Astrom and W. K. Ho "Refinements of the Ziegler-
Nichols tuning formula", IEEE Proceedings of Control Theory and
Applications, Vol. 138, No. 2, pp. 111-118, 1991.
[9] 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.
[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] K. Rattan, "Digitalization of existing continuous control system", IEEE
Trans. Auto. Control, Vol. 29, pp. 282- 285, 1984.
[12] J. Tschauner, "A General Formulation of the Stability Constraints for
Sampled Data Control System", IEEE Proceedings, Vol. 51, pp. 613-
621, 1963.
[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] R. C Eberhart and Y. Shi, "Particle Swarm Optimization: Developments
applications and resourses", Proceedings Congress on Evolutionary
Computation IEEE service, NJ, Korea, 2001.
[20] 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. 125-130,2011V.
[21] Krishnamurthy and V. Seshadri, "Model reduction using Routh stability
criterion", IEEE Trans. Auto. Control, Vol. 23, pp. 729 731, Aug.1978.
[1] 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.
[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] 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.
[5] 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.
[6] S. Mukherjee, Satakshi and R. C. Mittal, "Model order reduction using
response-matching technique", Journal of Franklin Inst., Vol. 342 , pp.
503-519, 2005.
[7] J. G. Ziegler, N. B. Nichols, "Optimum settings for automatic
controllers", Transaction of the AMSE, Vol. 64, pp. 759-768, 1942.
[8] C. C. Hang, K. J. Astrom and W. K. Ho "Refinements of the Ziegler-
Nichols tuning formula", IEEE Proceedings of Control Theory and
Applications, Vol. 138, No. 2, pp. 111-118, 1991.
[9] 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.
[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] K. Rattan, "Digitalization of existing continuous control system", IEEE
Trans. Auto. Control, Vol. 29, pp. 282- 285, 1984.
[12] J. Tschauner, "A General Formulation of the Stability Constraints for
Sampled Data Control System", IEEE Proceedings, Vol. 51, pp. 613-
621, 1963.
[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] R. C Eberhart and Y. Shi, "Particle Swarm Optimization: Developments
applications and resourses", Proceedings Congress on Evolutionary
Computation IEEE service, NJ, Korea, 2001.
[20] 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. 125-130,2011V.
[21] Krishnamurthy and V. Seshadri, "Model reduction using Routh stability
criterion", IEEE Trans. Auto. Control, Vol. 23, pp. 729 731, Aug.1978.
@article{"International Journal of Information, Control and Computer Sciences:51240", author = "S. N. Deepa and G. Sugumaran", title = "Design of PID Controller for Higher Order Continuous Systems using MPSO based Model Formulation Technique", abstract = "This paper proposes a new algebraic scheme to design a PID controller for higher order linear time invariant continuous systems. Modified PSO (MPSO) based model order formulation techniques have applied to obtain the effective formulated second order system. A controller is tuned to meet the desired performance specification by using pole-zero cancellation method. Proposed PID controller is attached with both higher order system and formulated second order system. The closed loop response is observed for stabilization process and compared with general PSO based formulated second order system. The proposed method is illustrated through numerical example from literature.
", keywords = "Higher order systems, model order formulation, modified particle swarm optimization, PID controller, pole-zero cancellation.", volume = "5", number = "8", pages = "834-7", }
