| Abstract: | Dynamic Matrix Control (DMC) is the advanced control strategy preferred by industry in the presence of process input/output constraints. The presence of such constraints causes the closed-loop DMC system to behave nonlinearly even if the plant dynamics axe linear. Consequently, well known linear control theory is not sufficient to analyze the stability properties of such a system. The analysis is even further complicated by the facts that no analytic expression is available for the DMC controller and uncertainty always exists in the process model. Present design techniques of DMC controllers rely on experience or ad hoc solutions, without closed-loop stability guarantees. Widespread usage of DMC controllers in industry makes the development of a controller design theory a formidable problem whose solution is of great practical importance. In this work, we provide a theory which utilizes the basic dynamic programming principles to analyze and design DMC controllers in the presence of disturbances, process input/output constraints, and modeling error. The key point of the theory is the modification of the classical DMC formulation by including an extra constraint which we called end-condition. Simulation results verify the theory's predictions. |
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