(654c) 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.