Centralised Multi-input Multi-output Controllers for Non-minimum Phase Systems

TL;DR: In this paper, a centralised controller for non-minimum-phase quadruple tank systems is designed based on the direct synthesis method, which is further improved by using equivalent transfer functions derived from relative normalised gain array and relative average residence time array as process inverse transfer function matrix.

Abstract: In the present work, the method of designing the centralised controllers for the minimum phase multivariable systems proposed by Vijay Kumar et al. is extended to non-minimum phase systems. The controller is designed based on the direct synthesis method. Inverse of process transfer function matrix in the direct synthesis method is approximated based on relative gain array concept. Maclaurin's series is applied to reduce it to a standard proportional and integral form. The method is further improved by using equivalent transfer function matrix derived from relative normalised gain array and relative average residence time array as process inverse transfer function matrix. Effective transfer function is the equivalent transfer function of gij(s) when all other loops are closed. The desired closed-loop transfer function should contain the process right half plane zero. Quadruple tank process with non-minimum phase behaviour is considered to analyse the performance of the proposed centralised controll...