PID controller design based on optimal servo and v-gap metric

This paper presents a new design method of a PID (proportional-integral-derivative) controller that provides sufficient stability margins and good time responses. It is possible to design an optimal PID controller with properties of a linear quadratic regulator or LQR by taking advantage of the fact that the integral-type optimal servo, which is a kind of the LQR, designed for a second order system is equivalent to an I-PD (proportional and derivative preceded integral) controller, However, the plant order is generally higher than the second. In such a case, the plant-order is reduced to the second based on the criterion of the í-gap metric. Even if open-loop properties of the reduced-order plant are very different from those of the original plant, as long as the í-gap is sufficiently small, a desirable I-PD or PID controller is obtained using the second-order plant model. Several design examples illustrate the effectiveness and usefulness of the method as a practical design tool of a PID controller.