一类动态矩阵控制系统的内稳定性

The internal stability of a kind of DMC control system

由于预测控制采用了多步预测和有限时域的滚动优化 ,使得预测控制系统的稳定性分析非常困难 .Xi Y在文献 [1]中针对一类阶跃响应单调递增的控制对象 ,当建模时域等于预测时域且控制时域为1时 ,证明了动态矩阵控制 ( DMC)系统的稳定性 .在文献 [1]的基础上 ,对于一类阶跃响应单调递增且为凸的控制对象 ,当取 DMC控制器的优化时域、控制时域和建模时域相同时 ,采用内模控制原理证明了控制系统的内稳定性 .

Predictive control is based on multi\|step prediction and finite horizon optimization. So it is very difficult to prove the stability of predictive control system. In reference\, Xi Y. proves the stability of a kind of dynamic matrix control(DMC) system with the same horizon of optimization and modeling and the control horizon equaling to 1 when the control object's step responses are monotone increasing. Basing on Internal Model Control Principle, we have shown the internal stability of a class of DMC control systems with the same horizon of optimization, control and modeling when the control object's step responses are monotone increasing and convex. The result expands the conclusion of reference\.