IMC-PID controller design based on loop shaping via LMI approach

Abstract

This paper presents a new approach to designing a PID controller based on internal model control (IMC). For this purpose, the parameters of PID controller in the standard structure of IMC are calculated such that the gain crossover frequency, phase margin, and phase and amplitude of the open-loop system at various frequencies are separately adjusted to the desired values. This loop shaping procedure is wholly formulated as a linear matrix inequality (LMI) generalized eigenvalue problem (GEVP). Hence, using this approach, one can combine the advantages of PID, IMC, and LMI. Unlike the traditional methods, here the LMIs are derived directly in the frequency domain without using state-space models. The proposed method was applied to various widely used process models to verify its efficiency, and the results were compared with competing methods.