(359b) Stochastic-Tube MPC for Offset-Free Tracking in the Presence of Plant-Model Mismatch

Model predictive control (MPC) has been successfully applied for high-performance control of a wide range of multivariable constrained systems [1]. Receding-horizon implementation of MPC provides some degree of robustness to system uncertainties, which generally stem from structural plant/model mismatch, exogenous disturbances, and measurement noise. However, marginal robust performance may not be adequate in practice to prevent, for example, unstable process operation or violation of quality constraints for products with stringent quality requirements.

Tube-based MPC has emerged as a popular approach for MPC of linear systems with bounded uncertainty. The key advantage of tube-based MPC is that it can provide guaranteed constraint satisfaction through an offline tightening of the constraints, while its complexity is comparable to that of a nominal MPC problem. The concept of tubes, originally developed for set-based uncertainty descriptions [2], has also been extended to stochastic systems [3][4]. This work aims to address an open challenge in stochastic-tube MPC related to systematically handling mismatch between the process model and the true plant, which is particularly important in process systems applications. The key notion of this work is to separate the system uncertainty into two distinct sources of additive bounded state error [5][6]. The first source is a non-random uncertainty that represents mismatch between the linear model and the true plant (or other types of persistent disturbances that cannot be modeled with a probability distribution). The second source represents random variations due to either intrinsic stochastic variability in the system or exogenous disturbances. Recursive feasibility and stability of the proposed stochastic-tube MPC strategy is guaranteed by defining a straightforwardly constructible terminal invariant set that includes changes in the steady-state operating conditions/setpoints. This is an extension of the terminal invariant set for tracking, proposed in [7], to stochastic-tube MPC. Offset-free tracking is achieved with a disturbance estimator that can be tuned completely independently of the proposed controller. A new filter model for the deterministic disturbance that is based on a bound on the variation in the plant-model mismatch is also proposed, which allows for further reduction in the conservatism of the control performance.

The proposed stochastic-tube MPC is demonstrated on two simulation case studies to highlight its advantages over alternative tube-based MPC methods. First, a benchmark DC-DC converter problem is used to illustrate how chance constraints can be guaranteed in the presence of plant-model mismatch as well as persistent and random disturbances. In this case study, we also observe that the controller has a significantly enlarged domain of attraction since the terminal set is formulated in terms of a more general tracking problem (as opposed to regulation). The second case study is based on an industrial fluidized-bed catalytic cracking (FCC) unit wherein we demonstrate that setpoints, which are unreachable by standard tube-based MPC, can be tracked without offset using the proposed approach.

References

[1] M. Morari, J. H. Lee. Model predictive control: Past, present and future, Computers & Chemical Engineering, 23, 667–682, 1999.

[2] D. Q. Mayne, M. M. Seron, S. V. Rakovic, Robust MPC of constrained linear systems with bounded disturbances, Automatica, 41, 219–224, 2005.

[3] B. Kouvaritakis, M. Cannon, Model predictive control: Classical, robust and stochastic, Springer, 2015.

[4] M. Lorenzen, F. Dabbene, R. Tempo, F. Allgower, Constraint-tightening and stability in stochastic model predictive control, IEEE Transactions on Automatic Control, 62, 3165–3177, 2017.

[5] J. A. Paulson, L. Xie, A. Mesbah, Offset-free robust MPC of systems with mixed stochastic and deterministic uncertainty, IFAC-PapersOnline, 50, 3530—3535, 2017.

[6] J. A. Paulson, T. L. M. Santos, A. Mesbah, Mixed stochastic-deterministic tube MPC for offset-free tracking in the presence of plant-model mismatch, Journal of Process Control, Submitted, 2018.

[7] D. Limon, I. Alvarado, T. Alamo, E. F. Camacho, MPC for tracking piecewise constant references for constrained linear systems, Automatica, 44, 2382–2387, 2008.