EFFICIENT IMPLEMENTATION OF CONSTRAINED ROBUST MODEL PREDICTIVE CONTROL USING A STATE SPACE MODEL

Amira Kheriji, Faouzi Bouani, Mekki Ksouri

2010

Abstract

The goal of this paper is to evaluate the closed loop performances of a new approach in constrained state space Robust Model Predictive Control (RMPC) in the presence of parametric uncertainties. The control law is obtained by the resolution of a min-max optimization problem, initially non convex, under input and input deviation constraints, using worst case strategy. The technique used is the Generalized Geometric Programming (GGP) which is a global optimization method for non convex functions constrained in a specific domain. The key idea of the proposed approach is the convexification of the optimization problem allowing to compute the optimal control law using standard optimization technique. The proposed method is efficient since it guarantees set-point tracking different from the origin and non zero disturbances rejection. The efficiency of this approach is illustrated with two examples and compared with a recent state space RMPC algorithm.

References

  1. Alamo, T., Ramirez, D., and Camacho, E. (2004). Efficient implementation of constrained min-max model predictive control with bounded uncertainties: a vertex rejection approach. Journal of Process Control, 15 (2005):149-158.
  2. Bouzouita, B., Bouani, F., and Ksouri, M. (2007). Solving non convex min-max predictive controller. In Conference Proceedings of 2007 Information, Decision and Control, Adelaide.
  3. Camacho, E. and Bordons, C. (2004). Model Predictive Control. Springer, London.
  4. Campo, P. and Morari, M. (1987). Robust model predictive control. In American control conference, pages 1021- 1026.
  5. Chul, C. and Dennis, L. (1996). Effectiveness of a geometric programming algorithm for optimization of machining economics models. Computers and operations research, 23:957-961.
  6. Cordon, P. and Boucher, P. (1994). Multivariable generalized predictive control with new multiple reference model: a robust stability analysis. Mathematics and computers in simulation, 37:207-219.
  7. Fukushima, H., Kim, T., and Sugie, T. (2007). Adaptive model predictive control for a class of constrained linear systems based on comparison model. Automatica, 43 (2):301-308.
  8. Henson, M. and Seborg, D. (1997). Non linear Process Control. Prentice Hall.
  9. Huaizhong, L., Niculescu, S., Dugard, L., and Dion, J. (1998). Robust guaranteed cost control of uncertain linear time-delay systems using dynamic output feedback. Mathematics and computers in simulation, 45:3-4.
  10. Kothare, M., Balakrishnan, V., and Morari, M. (1996). Robust constrained model predictive control using linear matrix inequalities. Automatica, 32 (10):1361-1379.
  11. Lee, Y. and Kouvaritakis, B. (2000). A linear programming approach to constrained robust predictive control. IEEE Trans. Auto. Contr., 45:1765-1770.
  12. Maranas, C. and Floudas, C. (1997). Global optimization in generalized geometric programming. Computers and chemical engineering, 21:351-369.
  13. Mayne, D., Rakovic, S., Findeisen, R., and Allgower, F. (2009). Robust output feedback model predictive control of constrained linear systems: Time varying case. Automatica, 45:2082-2087.
  14. Messaoud, H. and Akoum, Z. (2000). An algorithm for computing parameter bounds using prior information on physical parameter bounds. In 7th conference on Electronics, Circuits and Systems (ICECS), pages 218-221.
  15. Messaoud, H. and Favier, G. (1994). Recursive determination of parameter uncertainty intervals for linear models with unknown but bounded errors. In 10th IFAC Symp. on SYSID, Copenhagen, Denmark, pages 365- 370.
  16. Nand, K. (1995). Geometric programming based robot control design. Computers and industrial engineering, 29:631-635.
  17. Pannochia, G. (2004). Robust model predictive control with guaranteed set point tracking. Journal of process control, 14 (2004):927-937.
  18. Porn, R., Bjork, K., and Westerlund, T. (2007). Global solution of optimization problems with signomial parts. Discrete optimization, 5:108-120.
  19. Qian, W., Liu, J., Sun, Y., and Fei, S. (2010). A less conservative robust stability criteria for uncertain neutral systems with mixed delays. Mathematics and computers in simulation, 80:1007-1017.
  20. Ramirez, D., Alamo, T., , and Camacho, E. (2002). Effecient implementation of constrained min-max model predictive control with bounded uncertainties. In Conference on decision and control.
  21. Rossiter, J. and Kouvaritakis, B. (1998). Youla parameter and robust predictive control with constraints handling. In Workshop on Non linear Predictive Control ,Ascona, Switzerland.
  22. Tsai, J. (2009). Treating free variables in generalized geometric programming problems. Computers and chemical engineering, 33:239-243.
  23. Tsai, J., Lin, M., and Hu, Y. (2007). On generalized geometric programming problems with non positive variables. European journal of operational research, 178:10-19.
  24. Watanabet, K., Ikeda, K., Fukuda, T., and Tzafestas, S. (1991). Adaptive generalized predictive control using a state space approach. In International workshop on intelligent robots and systems IROS, Osaka, Japan.
Download


Paper Citation


in Harvard Style

Kheriji A., Bouani F. and Ksouri M. (2010). EFFICIENT IMPLEMENTATION OF CONSTRAINED ROBUST MODEL PREDICTIVE CONTROL USING A STATE SPACE MODEL . In Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 978-989-8425-02-7, pages 116-121. DOI: 10.5220/0002945101160121


in Bibtex Style

@conference{icinco10,
author={Amira Kheriji and Faouzi Bouani and Mekki Ksouri},
title={EFFICIENT IMPLEMENTATION OF CONSTRAINED ROBUST MODEL PREDICTIVE CONTROL USING A STATE SPACE MODEL},
booktitle={Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2010},
pages={116-121},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002945101160121},
isbn={978-989-8425-02-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - EFFICIENT IMPLEMENTATION OF CONSTRAINED ROBUST MODEL PREDICTIVE CONTROL USING A STATE SPACE MODEL
SN - 978-989-8425-02-7
AU - Kheriji A.
AU - Bouani F.
AU - Ksouri M.
PY - 2010
SP - 116
EP - 121
DO - 10.5220/0002945101160121