Closed-Loop Tuning of Set-Point-Weighted Proportional–Integral–Derivative Controllers for Stable, Integrating, and Unstable Processes: A Unified Data-Based Method

Abstract

This paper presents a unified method for closed-loop tuning of set-point-weighted proportional–integral–derivative (PID) controllers for stable, integrating, and unstable time-delayed processes. The controller tuning directly exploits a set of closed-loop plant data collected during set-point change, without resorting to a process model. In the proposed method, the parameters of a conventional PID controller are first derived such that the resulting control system behaves as closely as possible to the prescribed reference model for disturbance rejection. A simple one-dimensional optimization problem is formulated to determine an appropriate reference model for the controlled process. The set-point-weighted PID controller is subsequently designed to improve the set-point response. The set-point weighting parameters for the proportional and derivative modes are obtained so that the set-point response follows a prescribed reference trajectory. The proposed PID tuning method allows the user to manage the performance/robustness trade-off on the basis of the specification of maximum sensitivity. Simulation examples covering a wide variety of process dynamics show the superiority of the proposed method over existing tuning methods.