Enhanced stability regions for model predictive control of nonlinear process systems

Abstract The problem of predictive control of nonlinear process systems subject to input constraints is considered. The key idea in the proposed approach is to use control‐law independent characterization of the process dynamics subject to constraints via model predicative controllers to expand on the set of initial conditions for which closed–loop stability can be achieved. An application of this idea is presented to the case of linear process systems for which characterizations of the null controllable region (the set of initial conditions from where closed–loop stability can be achieved subject to input constraints) are available, but not practically implementable control laws that achieve stability from the entire null controllable region. A predictive controller is designed that achieves closed–loop stability for every initial condition in the null controllable region. For nonlinear process systems, while the characterization of the null controllable region remains an open problem, the set of initial conditions for which a (given) Lyapunov function can be made to decay is analytically computed. Constraints are formulated requiring the process to evolve within the region from where continued decay of the Lyapunov function value is achievable and incorporated in the predictive control design, thereby expanding on the set of initial conditions from where closed–loop stability can be achieved. The proposed method is illustrated using a chemical reactor example, and the robustness with respect to parametric uncertainty and disturbances demonstrated via application to a styrene polymerization process. © 2008 American Institute of Chemical Engineers AIChE J, 2008