Synthesis of PID-type controllers without parametric models: A graphical approach

Abstract

This paper considers the problem of determining the set of all stabilizing proportional–integral–derivative (PID) type controllers without parametric models for any given linear time-invariant (LTI) plants. It is shown that the only information for designing is the frequency response data and the number of right-half-plane (RHP) poles of the plant, and all stabilizing domains in the parameter space of PID-type controllers are determined by the boundaries which are analytically described based on the technique of D-decomposition. The method can handle arbitrary order minimum phase, non-minimum phase, stable or unstable plants and particularly, plants that have zeros or poles on the imaginary axis. It is shown that the approach presented does not require any parametric models of plants and can be applied to a wide range of industrial applications, especially where plants parametric models (transfer function and state space) are not available or identification is difficult. Several examples illustrate the proposed method.