Centralized PI controller design method for MIMO processes based on frequency response approximation

Abstract

A simple method of controller design for multi-input multi-output (MIMO) processes have been proposed in frequency domain. The intensive calculation for the inverse of the process transfer function matrix is simplified to a great extent by evaluating the process transfer function matrix at a low frequency point. The desired closed loop transfer functions are derived for the process using a single tuning parameter for each diagonal element of the process transfer function matrix which represents the desired closed loop time constant. Centralized PI controllers are then designed using a model matching technique by evaluating the transfer functions at a low frequency point. The PI controllers provide acceptable performances for lag dominated as well as time-delay dominated processes and is also applicable to high-dimensional processes. The proposed method is extended for the non-square MIMO processes using two approaches one of which squares up the process transfer function matrix to apply the proposed technique while the other is based on pseudo-inverse evaluation of the process transfer function matrix at a low frequency point.