Composite Fast-Slow MPC Design for Nonlinear Singularly Perturbed Systems

Time-scale multiplicity arises in numerous chemical processes and industrial plants due to the strong coupling of physico-chemical phenomena, like slow and fast reactions, occurring at different time-scales. Also, the dynamics of control actuation and measurement sensing systems very often induces a fast-dynamics layer in the closed-loop system. Conventionally, the analysis and controller design problems for multiple-time-scale systems are formulated through taking advantage of the mathematical framework of singular perturbations [1]. Model predictive control (MPC) has been widely employed in industrial process control applications due to its ability to satisfy state and input constraints by minimizing a meaningful objective function and taking advantage of system model to predict future evolution of the system over a predefined horizon while applying its solution in a receding horizon manner.

In this work, we focus on MPC of nonlinear singularly perturbed systems in standard form where the separation between the fast and slow state variables is explicit. Specifically, a composite control system comprised of a ``fast" MPC acting to regulate the fast dynamics and a ``slow'' MPC acting to regulate the slow dynamics is designed. The composite MPC system uses multirate sampling of the plant state measurements, i.e., fast sampling of the fast state variables is used in the fast MPC and slow-sampling of the slow state variables is used in the slow MPC as well as in the fast MPC. Both fast and slow MPCs take advantage of their corresponding Lyapunov-based controllers to characterize closed-loop system stability region [2]. Using singular perturbation theory, the stability and optimality of the closed-loop nonlinear singularly perturbed system are analyzed. The proposed control scheme does not require exchange of information between the two MPC layers, and thus, it can be classified as decentralized in nature. The theoretical results are demonstrated through a nonlinear chemical process example.

[1] P. D. Christofides, P. Daoutidis. "Feedback control of two-time-scale nonlinear systems". International Journal of Control. Vol. 63, 965-994, 1996.
[2]P. D. Christofides, J. Liu, and D. Munoz de la Pena. "Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications". Advances in Induatrial Control Series. Springer-Verlag, London, England, 2011.