PID controller design with constraints on sensitivity functions using loop slope adjustment

This paper presents a PID controller design method for stable minimum- phase systems. The approach is similar to the one proposed in the so-called modified Ziegler- Nichols method, where only one point on the frequency response of the plant is measured and then moved to the desired position on the unit circle. This technique provides the specified phase margin and crossover frequency to the closed-loop system. However, the ratio between integral and derivative time is not fixed prior to the design in the proposed approach. This ratio is chosen is order to obtain the desired loop slope at the crossover frequency. Constraints on the infinity-norm of sensitivity functions are used to shape the loop transfer function and to determine the corresponding loop slope value. The proposed method, which is based on Bode’s integral relationships for the slope adjustment, does not require any parametric model of the plant and can be applied with only modest effort.