On the Use of the Smith-McMillan Form in Decoupling System Dynamics

TL;DR

This paper explores how the Smith-McMillan form can be used to decouple MIMO system dynamics, ensuring stability and performance, demonstrated through a simulation of a mechanical system.

Contribution

It presents conditions for achieving stable and performant decoupled systems using the Smith-McMillan form, with practical guidelines and a simulation example.

Findings

Decoupling preserves original system poles and zeros.

Full decoupling achievable at all frequencies.

Simulation confirms improved control performance.

Abstract

In this paper, the use of the Smith-McMillan form in decoupling multiple-input multiple-output system dynamics is analyzed. In short, from a transfer matrix plant model one can obtain a decoupling compensator which leads to a decoupled plant that contains the same transmission poles and zeros of the transfer matrix of the original system. As a result, full decoupling of the plant transfer matrix is obtained for all frequencies, which can be individually addressed by single-input single-output control. The aim of this paper is to present conditions for the decoupled system that guarantee internal stability and performance requirements for the overall control system. Performance specifications are defined in terms of magnitude limits for the maximum singular value of the closed-loop transfer matrices. The potential of the decoupling procedure is shown in a simulation study of a mechanical system.