(214d) Model Predictive Control of Nonlinear Singularly Perturbed Systems: Application to a Large-Scale Process Network

Authors: 
Chen, X., Univ. of California, Los Angeles
Heidarinejad, M., University of California, Los Angeles
Liu, J., University of California, Los Angeles
Muñoz de la Peña, D., University of California, Los Angeles


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.

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