Tuning method of PID controller for desired damping coefficient

In the previous paper, we proposed the tuning method of PI controller for a plant model described by a first-order lag plus deadtime system based on a desired damping, and demonstrated its effectiveness and limitation by simulation studies. The PI parameters have been adjusted so that their influence on the damping was transparent. It is well known that the derivative action is effective in obtaining the desired damping. In this paper, of particular interest to us is how to tune PID controller to suppress overshoot. In tuning controllers it is often convenient to specify a damping coefficient of the closed system. For PID control, the integral time T_d and the derivative time Td are kept fixed to degenerate the order of the closed-loop transfer function. This can be easily led to pole-zero cancellation. Thus, the only one parameter of PID controller to be adjusted now becomes the proportional gain k_p. It can be concluded that the PID controller provides a much better response than the PI controller presented last year. The resultant graphical comparisons document how to give a guide line for tuning of PID controller.