Decentralized PID control for systems with relative degree no more than 2

In this paper, we propose a PID control design method for decentralized control systems by using the structure of controllers obtained by the ILQ(Inverse Linear Quadratic) design method. First, we show an optimal decentralized PID design method for systems with relative degree no more than 2 and block diagonal decoupling matrix. Then, we derive a necessary and sufficient condition for the stability of the closed loop system using our proposed design method of decentralized PID control in the case where the decoupling matrix is not block diagonal. Moreover, we show that a desired transient response with decoupled input/output characteristics can be achieved by our decentralized PID controller.