Optimal tuning of PID-type controllers

Abstract

Direct methods for optimal tuning of the parameters of a PID-type controller are developed using the theory of LQR when the order of the plant model equation is known. This is achieved through two fundamental results. The first one defines a link between the weighting matrix of the LQR performance index with the desired temporal specifications of the closed-loop controlled response, expressed through a desired overshoot and settling time, as well as the tracking of a constant reference input with zero steady-state error. The second result establishes the connection between the state feedback solution of the LQR problem and the parameters of the PID-type controller. The design method is validated through simulation studies on a heat flow experiment, a coupled tank system, and a radar antenna.