Unified PID design method based on a maximum peak resonance specification

The paper presents a unified approach for the design of PID controllers, based on the contours of the Nichols chart. Using a maximum peak resonance specification, the controller parameters are adjusted such that the open-loop frequency response curve follows the corresponding contour. This approach gives the possibility of handling (at the same time) the maximum peak overshoot, the minimum phase and amplitude margins and the bandwidth of the closed-loop system. The method can be applied to a wide range of processes and it provides useful a priori information concerning the behaviour of the closed-loop system. Different ways are proposed for the calculations of the controller parameters. An optimisation procedure is first proposed to illustrate the basic idea of the method, but the aim of the paper is to provide simple tuning expressions for low-order models. These expressions are given for stable, integrating and unstable processes