2-DOF Observer Based Controller for First Order with Dead Time Systems

Authors: Ashu Ahuja, Shiv Narayan, Jagdish Kumar

Abstract:

This paper realized the 2-DOF controller structure for first order with time delay systems. The co-prime factorization is used to design observer based controller K(s), representing one degree of freedom. The problem is based on H∞ norm of mixed sensitivity and aims to achieve stability, robustness and disturbance rejection. Then, the other degree of freedom, prefilter F(s), is formulated as fixed structure polynomial controller to meet open loop processing of reference model. This model matching problem is solved by minimizing integral square error between reference model and proposed model. The feedback controller and prefilter designs are posed as optimization problem and solved using Particle Swarm Optimization (PSO). To show the efficiency of the designed approach different variety of processes are taken and compared for analysis.

Keywords: 2-DOF, integral square error, mixed sensitivity function, observer based controller, particle swarm optimization, prefilter.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1090554

References:

[1] S. Skogestad, "Simple analytical rules for model reduction and PID controllers tuning”, Journal of Process Control, vol. 13, pp. 291-309, 2003.
[2] M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: The MIT Press, 1985.
[3] D. C. Youla and J. J. Bongiorno, "A feedback theory of two-degree-of-freedom optimal Wiener-Hopf design”, IEEE Transaction on Automatic Control, vol. 30, no. 7, pp. 652-665, July 1985.
[4] R. Vilanova, C. Pedret, I. Serra and F. Tadeo, "Observer controller configuration approach to controller robustification”, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona, USA, pp. 74-75, 1999.
[5] C. Pedret, R. Vilanova, R. Moreno and I. Serra, "A new architecture for robust model reference control”, Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference 2005, Seville, Spain, pp. 7876-7881, 2005.
[6] S. Alcantra, C. Pedret, R. Vilanova, A. Ibeas and P. Balaguer, "A 2DOF H∞ robust tracking design for a special type of observer state feedback controllers”, Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, pp. 2238-2243, 2008.
[7] Leonid Mirkin and Qing-Chang Zhong, "2DOF controller parameterization for systems with a single I/O delay”, IEEE Transaction on Automatic Control, vol. 48, no. 11, Oct. 2003.
[8] S. Alcantra, C. Pedret, A. Ibeas and R. Vilanova’ "General Smith Predictors from an observer-controller perspective”, 18th IEEE International Conference on Control Applications, pp. 1203-1208, July 2009.
[9] Qing-Chang Zhong, Robust Control of Time-delay Systems, Springer-Verlag London Limited, 2006.
[10] W. D. Zhang, Y. X. Sun and X. Xu, "Two degree-of-freedom Smith predictor for processes with time delay”, Automatica, vol. 34 pp. 1279-1282, 1998.
[11] M R Matausek and A. D. Micic, "On the modified Smith predictor for controlling a process with an integrator and long dead time”, IEEE Transaction on Automatic Control, vol. 44, no. 8, pp. 1603-1606, Aug. 1999.
[12] S. Majhi and D. P. Atherton, "Modified Smith predictor and controller for processes with time delay”, IEE Proc. Control Theory Application, vol. 146, no. 5, pp. 359-366, Sep. 1999.
[13] K. J. Astrom, C. C. Hang and B. C. Lim, "A new Smith predictor for controlling a process with an integrator and long dead-time”, IEEE Transaction on Automatic Control, vol. 39, no. 2, pp. 343-345, 1994.
[14] J. E. Normey Rico and E. F. Camacho, "A unified approach to design dead-time compensators for stable and integrative processes with dead-time”, IEEE Transaction on Automatic Control, vol. 47, no. 2, pp. 299-305, Feb. 2002.
[15] Hosein Nemati and Peyman Bagheri, "A new approach to tune the two-degree-of-freedom (2DOF)”, 2010 IEEE International Symposium on Computer – Aided Control System Design, Part of 2010 IEEE Multi – Conference on Systems and Control, Yokohama, Japan, pp. 1819-1824, 2010.
[16] J. E. Normey Rico, C. Bordons and E. F. Camacho, "Improving the robustness os dead time compensating PI controllers”, Control Engineering Practice, vol. 5, no. 6, pp. 801-810, 1997.
[17] W. D. Zhang and Y. X. Sun, "Modified Smith predictor for controlling integrator/time delay processes”, Industrial and Engineering Chemistry Research, vol. 35, pp. 2769-2772, 1996.