Robust Stability of SISO Quadratic Dynamic Matrix Control with Hard Output Constraints

Abstract

The inclusion of output constraints in the on-line optimization problem solved by Quadratic Dynamic Matrix Control (QDMC) can result in a closed-loop unstable system, even when the corresponding unconstrained algorithm is stable. The presence of constraints in the optimization problem produces a nonlinear closed-loop system, although the plant and model dynamics are assumed linear. This paper quantifies the effect of output constraints on both nominal and robust stability for single-input single-output (SISO) processes. Stability conditions are provided which can be used to select the QDMC parameters and constraint window. The ability of these conditions to capture the nonlinear effect of the constraint is illustrated through examples that demonstrate that tuning rules developed for the unconstrained case should not be used with output constraints. an example with deat time error is used to illustrate the use of this framework to guarantee the robustness the robustness of constrained QDMC with respect to modeling error.