Relay feedback tuning of robust PID controllers with iso-damping property

Abstract

A new tuning method for PID controller design is proposed for a class of unknown, stable, and minimum phase plants. We are able to design a PID controller to ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the is zero, at a given called the frequency so that the closed-loop system is robust to gain variations and the step responses exhibit an iso-damping property. At the frequency, the Nyquist curve tangentially touches the sensitivity circle. Several relay feedback tests are used to identify the plant gain and phase at the tangent in an iterative way. The identified plant gain and phase at the desired tangent are used to estimate the derivatives of amplitude and phase of the plant with respect to at the same point by Bode's integral relationship. Then, these derivatives are used to design a PID controller for slope adjustment of the Nyquist plot to achieve the robustness of the system to gain variations. No plant model is assumed during the PID controller design. Only- several relay tests are needed. Simulation examples illustrate the effectiveness and the simplicity of the proposed method for robust PID controller design with an iso-damping property.