Robust model predictive control

The success of the single-model model predictive control (SMPC) method depends on the accuracy of the process model. Modeling errors cause sub-optimal control performance and may cause the system to become closed-loop unstable. The goal of this research project is to design a new robust model predictive control (RMPC) method that guarantees closed-loop stability and offset-free set point tracking in the presence of model uncertainty.; The first RMPC method I considered is a SMPC controller with zone regions instead of set points as the control objective for the controlled outputs. The addition of the zone regions relaxes the control objectives so that control actions are taken only when the controlled outputs are outside the zone limits. Even though this method apprears attractive in theory, it is unsuccessful in practice. The method remains closed-loop stable in the presence of model uncertainty if the controlled outputs remain inside the zone limits. As soon as control actions are needed to move the controlled outputs into the zone region, SMPC with zones behave the same as SMPC with set points. In other words, if SMPC with set points is closed-loop unstable when model uncertainty is present, then SMPC with zone regions is closed-loop unstable as well.; Next, I proposed a new RMPC method that explicitly accounts for model uncertainty in the controller design procedure. A min-max optimization problem is used to determine the optimal control action subject to input and output constraints. The robust regulator uses a tree trajectory to forecast the time-varying model uncertainty. The controller design procedure uses integrators to reject non-zero disturbances and maintain the system at the set points. I developed a closed-loop stability condition that determines if there exist a feedback law u = Kx and disturbance filters L_i's that satisfy the stability condition, then the new RMPC method can achieve offset-free non-zero set point tracking for a constrained system with time-varying model uncertainty described by an uncertainty set.; Table 7.1 summarizes the examples studies in this research project. The examples include model uncertainty sets with: (1) process dynamic uncertainty, (2) process gain uncertainty, (3) stable and unstable models, (4) time-delay uncertainty, (5) ill-conditioned models, (6) integrating models, and systems with constraint saturation. The new RMPC method successfully controlled all of the above examples for offset-free non-zero set point tracking. The new RMPC controller increases the tolerance of the controller to model uncertainty, but the decrease in nominal performance is relatively small. Indeed, in most cases, the RMPC control performance is almost as good as the nominal SMPC performance.