On a Synthesis of Multivariable PID Controllers for a Class of Linear Systems

This paper is concerned with a synthesis problem of multivariable PID controllers for a class of linear systems. First, mathematical model is given. The closed-loop system is described in the descriptor form and investigated comparing with conventional ones. The comparison reveals that the proposed method loosens up the constraints on signal dimensions, and enables us to deal with the synthesis problem of multivariable PID controller with fixed structure. The synthesis problem of multivariable PID controller is reduced to that of static output feedback controller. Secondly, the controller is synthesized under H_infin criterion by using an iterative linear matrix inequality (LMI) algorithm. Finally, numerical examples are given to illustrate the effectiveness of the proposed method