Analysis and tuning of a three-term DMC

Most MPC (Model Predictive Control) algorithms used in industries and studied in the control academia use a two-term QP (quadratic programming), where the first term is the weighted norm of the output errors, and the second term is that of the input increments. In this work, a DMC (Dynamic Matrix Control) algorithm that uses three-term QP is studied, where the third term is the weighted norm of the output increments. In the analysis, a relationship between the three-term DMC and the two-term DMC is established; based on that, the closed-loop response curves are derived. Based on the analysis, two controller tuning procedures are developed for the three-term DMC, one for closed-loop step response and one for disturbance reduction. Finally, it will be proven that the three-term DMC can achieve a higher performance and robustness than the two-term DMC can. Simulation studies are used to demonstrate the findings and the tuning methods.