(329b) Mixed H2/H∞ Model Predictive Control for Unstable and Non-Minimum Constrained Processes

In the present work, we introduce the use of Mixed H₂/H_∞ control design in the regime of model predictive control (MPC) for unstable and non-minimum phase constrained process. Although the use of mixed H₂/H_∞ control design in feedback control system design is a decade old idea, it remains relatively unexplored in the paradigm of model predictive control [5].

Mixed H₂/H_∞ control design [1-3] is of interest to control engineers because it combines the merits of both the H₂ and H_∞ robust control design. The mixed H₂/H_∞ control design problem evolves as a cross-coupled Riccati equation [2], for which no effective numerical solving algorithm exists. However, linear matrix inequality (LMI) techniques could be employed to solve such problems [3].

Although lots of such handicaps in numerical and/or analytical methods of solving such mixed H₂/H_∞ control problems exist, solution of such problems could still be extended for robust MPC design for both linear and nonlinear systems with the applicability of LMIs. Orukpe et al. [5] have introduced mixed H₂/H_∞ model predictive control using LMIs, however the possibility of solving the problem of handling both uncertain systems and process disturbances simultaneously is unexplored. In the present work, we highlight the use of mixed H₂/H_∞ model predictive control design of such systems, exploring for both unstable and non-minimum processes, which are quite common in chemical engineering processes. To keep the complexity of problem within the bounds of the available numerical tractability, only a state-feedback case is considered in the present work, but for both unstable and non-minimum phase linear processes. Moreover, the study is also extended for state as well as input constraint case [4], which is more common in process industries due to the actuator saturations.

The case studies addressed in the present work involves treatment of unstable and non-minimum phase processes which are affected by model uncertainty and/or process disturbance. The results are compared against that of the reported literature on robust MPC technique i.e., H_∞ robust MPC.

References

[1] Bernstein, D. S. And Haddad, W. H. LQG control with an H_∞ performance bound: A Riccati equation approach. IEEE Trans. Automat. Contr. Vol. 34, No. 3, pp. 293-305, 1989.

[2] Chen, B-S., Tseng, C-S., and Uang, H-J. Mixed H₂/H_∞ fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach. IEEE Trans. Automat. Contr. Vol. 8, No. 3, pp. 249-265, 2000.

[3] Doyle, J., Zhou, K., Glover, K., and Bodenheimer, B. Mixed H₂/H_∞ performance objectives II: Optimal control. IEEE Automat. Contr. Vol. 39, No. 8, pp. 1575-1587, 1994.

[4] Kothare, M. V., Balakrishnan, V. and Morari, M. Robust constrained model predictive control using linear matrix inequalities. Automatica, Vol. 32, No. 10, pp. 1361-1379, 1996.

[5] Orukpe, P. E., Jaimoukha, I. M. And El-Zobaidi, H. M. H. Model predictive control based on mixed H₂/H_∞ control approach. Proc. American Contr. Conf., pp. 6147-6150, 2007.