Controller Design for MIMO Processes Based on Simple Decoupled Equivalent Transfer Functions and Simplified Decoupler

Abstract

A method for the independent design of proportional-integral/proportional-integral derivative (PI/PID) controllers is proposed based on the equivalent transfer function (ETF) model of the individual loops and the simplified decoupler matrix. It is shown that the conventional effective open-loop transfer function (EOTF, derived from the dynamic relative gain array (DRGA)) is equivalent to the ETF (derived from the relative normalized gain array (RNGA) and relative average residence time array (RARTA)). This relation is used to approximate the decoupled process models as ETF models. The simplified decoupler is shown to decompose the multiloop systems into independent loops (multi-single loop systems) with the ETFs as the resulting decoupled process model. The concept of the ETF (perfect control approximation) is validated by introducing the decoupler. Based on the corresponding ETFs, the decentralized PI controllers are designed using the simplified internal model control (SIMC) method. Three simulation examples of multi-input multi-output (MIMO) process models are considered to demonstrate the simplicity and effectiveness of the proposed method. The performance of the proposed control system is compared with the ideal, normalized, inverted decoupling, and centralized control systems.