An improved identification and control of 3 × 3 multi-input multi-output system using relay and subspace method

Abstract

ABSTRACTIn this work, a simple closed-loop identification method for Multi-Input Multi-Output (MIMO) system has been proposed. Subspace closed-loop identification method is employed for identification of MIMO system, while relay is used as a replacement to pre-design PID controllers. The transfer function matrix of the dynamic system is identified in the form of state-space model using N4SID algorithm from system identification toolbox of MATLAB. The proposed method neither requires pre-designed controller nor involves extensive calculation. Due to the use of ideal relay as a replacement, the proposed method fails to identify systems containing unstable transfer functions while retaining the other advantages of subspace identification method. The identified model is further controlled by the designed tuning of controller parameters. Firstly, decoupler is designed to eliminate the interaction in MIMO system. The estimated transfer function, derived by Relative Normalised Gain Array – Relative Gain Array (RNGA-RGA) method, is further used to calculate ideal, stable, causal and proper decoupler. Introduction of decoupler into the system decomposes 3 × 3 MIMO system into ‘3’ SISO systems which are further controlled by basic controller tuning methods such as Zeigler–Nichol’s PID tuning method and Skogested’s IMC tuning method.