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.

研究了使用三项二次规划的DMC算法，与使用两项二次规划的DMC之间的关系，并基于这种关系得出了闭环响应曲线。根据分析，开发了两种调节控制器的方法，分别用于闭环阶跃响应和干扰减少，并证明了三项DMC比两项DMC具有更高的性能和鲁棒性。使用模拟研究证明了这些发现和调节方法。

三项DMC的分析和调整