SEARCH

SEARCH BY CITATION

Keywords:

  • input constraints;
  • model predictive control;
  • Lyapunov-based bounded control;
  • state estimation;
  • controller switching;
  • closed-loop stability region;
  • process control

Abstract

The operation of chemical processes often requires respecting constraints on manipulated inputs and process states. Input constraints typically reflect limits on the capacity of control actuators, such as valves or pumps, whereas state constraints represent desirable ranges of operation for process variables, such as temperatures or concentrations. Constraints, however, limit the set of initial conditions, starting from where a process can be stabilized at a possibly open-loop unstable steady state. Therefore, in control of constrained processes, it is important to obtain an explicit characterization of the region of closed-loop stability. Model predictive control (MPC) provides a suitable framework for implementing control that respects manipulated input and process variable constraints while meeting prescribed performance objectives. Unfortunately, the implicit nature of the feedback law in MPC (the control action is computed by solving on-line a constrained optimization problem at each sampling time) makes the a priori computation of the closed-loop stability region a very difficult task. Such a computation, however, is possible when Lyapunov-based bounded control techniques are used to design controllers for the stabilization of systems with manipulated input constraints. Motivated by this, the present work proposes a hybrid predictive control structure, which seamlessly unites MPC and bounded control, for output feedback stabilization of linear systems with input constraints. The design of the proposed structure is based on the idea of using a bounded controller, with its associated region of stability, as a “fallback” controller for the output feedback implementation of MPC. Switching laws are derived to orchestrate the transition between the two controllers in a way that reconciles their respective stability and optimality properties. The switched closed-loop system is shown to possess a region of guaranteed stability, achieved by appropriately switching between the two controllers. The proposed hybrid control structure is shown to provide a safety net for the practical implementation of MPC by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. Finally, two simulation studies are presented to demonstrate the implementation and evaluate the effectiveness of the proposed hybrid predictive control scheme, as well as test its robustness with respect to modeling errors and measurement noise. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1242–1259, 2004