Robust model predictive control of stable and integrating linear systems

Model Predictive Control (MPC) has become one of the dominant methods of chemical process control in terms of successful industrial applications. A rich theory has been developed to study the closed loop stability of MPC algorithms when the plant model is perfect, referred to as the nominal stability problem. In practical applications, however, the process model is never perfect and nominal stability results are not strictly applicable. The primary disadvantage of the current MPC design techniques is their inability to deal explicitly with the plant model uncertainty. In this thesis we develop a new framework for robust MPC synthesis that allows explicit incorporation of the plant uncertainty description in the problem formulation. The robust stability results are developed for general uncertainty descriptions. Hard input and soft output constraints can be easily added to the algorithms without affecting closed loop stability. Robust stability is achieved through the addition of constraints that prevent the sequence of the optimal controller costs from increasing for the true plant. These cost function constraints can be solved analytically for the special case of bounded input matrix uncertainty. The closed loop system also remains stable in the face of asymptotically decaying disturbances. The framework developed for bounded input matrix uncertainty for stable plants can also be used for integrating plants. Two formulations are developed; a single stage optimization method that minimizes the state error at the end of the horizon, and a two stage optimization method which minimizes the state error at the end of the horizon in the first stage but uses the remaining degrees in a second stage to minimize state deviations over the full prediction horizon. Hard input and soft output constraints can be easily added to the algorithms without affecting the closed loop stability