Plant-model reduction for PID controller design

A plant-order reduction method has been developed for PID controller design based on the integral-type optimal servo, which is a kind of the linear quadratic regulator (LQR). The order-reduction consists of two steps: The first step is to apply the balanced truncation to reduce the plant order to the second order. The second step is to adjust the plant parameters by the homotopy method to reduce the v-gap between the original plant and the reduced-order plant. The method can be applied to a plant that is not stable but stabilizable by static output feedback by replacing the plant with the stabilized plant. If the v-gap becomes sufficiently small, then the PID controller designed with the reduced-order plant model provides good control performance and desirable stability margins as the LQR provides.