Weighted sensitivity design of multivariable PID controllers via a new iterative LMI approach. (February 2022) - Feng, Zhi-Yong; Guo, Huiru; She, Jinhua; Xu, Li
Abstract: This paper addresses the weighted sensitivity design of multivariable proportional–integral–derivative (PID) controllers for multi-input multi-output (MIMO) processes. First, the PID reference tracking problem is formulated into an H ∞ PID control problem by using the weighted sensitivity synthesis, and the problem is further casted into an H ∞ SOF control problem. Second, based on the idea of T–K iteration, a new iterative LMI algorithm has been developed to locally solve the optimal H ∞ SOF control problem. Then, a design procedure is presented for weighted sensitivity design of multivariable PID Controllers for MIMO processes. Finally, three application examples are provided to show the effectiveness and good performance of our method for practical industrial processes. Highlights: The weighted sensitivity design of multivariable PID controllers for MIMO processes is formulated into an H ∞ SOF control problem. A new iterative LMI algorithm has been developed to solve the optimal H ∞ SOF control problem. Our method provides a locally optimal solution for the weighted sensitivity design of multivariable PID controllers.