Robust Proportional–Integral–Derivative (PID) Design for Parameter Uncertain Second-Order Plus Time Delay (SOPTD) Processes Based on Reference Model Approximation

Abstract

To design robust proportional–integral–derivative (PID) controllers for second-order plus time delay (SOPTD) processes with parameter uncertainty, a reference model approximation method is proposed in this article. The central idea is to allow the frequency response of the PID controller to approximate that of a user-specified reference model. A convex hull is used to approximate the frequency template of the process with parameter uncertainty, and the maximum approximation error of the reference model among all candidate processes is bounded. To guarantee that the set-point response trajectory of each possible candidate model can well approach that of the reference model, a convex optimization problem is formulated to calculate the PID parameters by minimizing the upper bound for the approximation error. Constraints on the closed-loop maximum sensitivity peak are imposed on the reference-model approximation problem for loop robustness. The proposed method is able to ensure balanced tracking performance a...