Controller design for highly interacting multivariable systems

Abstract

Controller design for multivariable systems is a challenging task due to interactions. For highly interacting systems, controller design is even more challenging. In this paper controller design for system having significant interactions, as quantified by relative gain value larger than 2, is considered. It is an extremely challenging task to obtain PI controller gains for higher dimensional multivariable processes due to the existence of high interaction effects (RG > 2) among the process input-output (i-o) variables. The aim is to propose scalable methodology that can be applied to higher dimensional system without much computational effort. For multivariable systems, detuning based controller design is very popular due to simplicity. Contribution in this manuscript is a new controller design method, i.e. relative gain (RG) detuning-based multi-loop internal model control (IMC) for highly interacting and higher dimensional multivariable processes. The PI controller parameters are first evaluated for the process of each main loop (diagonal elements) independently by employing IMC-PI tuning rules. In highly interacting systems, the off-diagonal (interactive elements) transfer functions have higher time delays than the diagonal transfer functions. When each loop RG value is used as the detuning factor, superior controller performance is obtained. The proposed control algorithm is applicable for highly interacting and higher dimensional multivariable processes. Various simulation studies for a wide range of $2\times 2$, 3 $\times 3$, and 4 $\times 4$ multivariable processes were carried out to demonstrate the effectiveness of the proposed method.