A New Stabilizing GPC for Nonminimum Phase LTI Systems Using Time Varying Weighting

In this paper, we show that the stability can not be achieved with current stabilizing MPC methods for some unstable processes. Hence we present a new method for stabilizing these processes. The main idea is to use a new time varying weighted cost function for traditional GPC. This stabilizes the closed loop system without adding soft or hard constraint in optimization problem. By studying different examples it is shown that using the proposed method, the closed-loop stability of unstable nonminimum phase process is achieved.

Authors:

• Mahdi Yaghobi
• Mohammad Haeri

Keywords:

• GPC
• Stability
• Varying Weighting Coefficients.

References:

[1] B. Kouvaritakis, J.A. Rossiter, A.O.T. Chang, "Stable generalized
predictive control: an algorithm with guaranteed stability", IEE
Proceedings-D, Vol. 139, No.4, July 1992.
[2] J.R. Gossner, B. Kouvaritakis, J.A. Rossiter, "Constrained Multivariable
cautious Stable Predictive Control", IEE Proceedings-D, Vol. 145, No.
5, September 1998.
[3] J.A. Rossiter, J.R. Gossner, B. Kouvaritakis, "Constrained cautious
stable predictive control", IEE Proceedings-D, Vol. 144, No. 4, July
1997.
[4] Y.I. Lee, W.H. Kwon, Y.H. Kim, "'Weighted Receding Horizon
Predictive Control and its Related GPC with Guaranteed Stability",
Proceedings of the 32nd Conference on Decision and Control, Texas,
December, 1993.
[5] H.W. Gomma, D.H. Owens, "Time Varying Weighting Generalized
Predictive Control (TGPC) with prediction to performance, stability and
robustness", Proceedings of the 38th Conference on Decision and
Control, Phoenix, Arizona USA, December 1999.
[6] S. Weiland, A.A. Stoorvogel, A.A. Tiagounov, "End-Point
Parameterization and Guaranteed Stability for a Model Predictive
Control Scheme", Proceedings of the 40th IEEE Conference Decision
and Control, Orlando, Florida USA, December 2001.
[7] J.A. Rossiter, J.R. Gossner, B. Kouvaritakis, "Infinite Horizon Predictive
Control", IEEE Transactions On Automatic Control, Vol. 41, No. 10,
October 1996.
[8] Li-F. Zhou, "The Mixed-Weights Least -Square Stable Predictive
Control for Constrained Multi-Object Multivariable System",
Proceedings of the Second International Conference on Machine
Learning and Cybernetic, Xian, November 2003.