Model Predictive Control of Nonlinear Singularly Perturbed Systems: Application to a Large-Scale Process Network

Chemical processes and plants are characterized by nonlinear behavior and strong coupling of physico-chemical phenomena occurring at disparate time-scales. Examples 
include fluidized catalytic crackers, distillation columns, biochemical reactors as well as chemical process networks in which the individual processes evolve in a fast timescale
and the network dynamics evolve in a slow time-scale. Two-time-scale processes can be conveniently described using nonlinear singularly perturbed systems. Model predictive control (MPC) is a practically-important control framework which can be used to design and coordinate control systems and can explicitly handle input and state constraints. MPC utilizes a model to predict the future evolution of the plant at each sampling time according to the current state over a given prediction horizon. In the context of MPC of
singularly perturbed systems, most of the efforts have been dedicated to linear systems or to MPC of specific classes of two-time-scale processes, and general stability results are not available.

This work focuses on model predictive control of nonlinear singularly perturbed systems. A composite control system using multirate sampling (i.e., fast sampling of the fast
state variables and slow sampling of the slow state variables) and consisting of a “fast” feedback controller that stabilizes the fast dynamics and a model predictive controller that stabilizes the slow dynamics and enforces desired performance objectives in the slow subsystem is designed. Using stability results for nonlinear singularly perturbed systems, the closed-loop system is analyzed and sufficient conditions for stability are derived. A large-scale nonlinear reactor-separator process network which exhibits two-time-scale behavior is used to demonstrate the controller design including a distributed implementation of the predictive controller.