Supervisory Robust Model Predictive Control for Linear Systems Subject to Parametric Uncertainty and Application to Level Control Process

Abstract

This paper presents supervisory robust model predictive control (RMPC) for linear systems in the presence of parametric uncertainty. The control structure is cascade control where the outer loop controller is RMPC and the inner loop controller as proportional-integral (PI) controller. The parametric uncertainty appears in the dynamic matrix and input matrix and satisfies norm-bounded condition. First, we derive inner closed-loop model and use this model to design RMPC. The design of RMPC involves a min-max optimization problem which aims to find the optimal solution minimizing the worst case performance. We derive an upper bound of the worst case performance and apply Linear Matrix Inequality to determine the control input. We conduct the step tests on the level control loop and obtain 4 dynamic models. Numerical results reveal that supervisory RMPC can ensure reference tracking regardless of uncertain dynamics.