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TECHNICAL BRIEFS

An Alternate Geometric Perspective on MIMO Systems

[+] Author and Article Information
M. L. Nagurka, T. R. Kurfess

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

J. Dyn. Sys., Meas., Control 115(3), 538-543 (Sep 01, 1993) (6 pages) doi:10.1115/1.2899134 History: Received April 02, 1991; Revised November 02, 1992; Online March 17, 2008

Abstract

An alternate graphical representation of linear, time-invariant, multi-input, multi-output (MIMO) system dynamics is proposed that is highly suited for exploring the influence of closed-loop system parameters. The development is based on the adjustment of a scalar forward gain multiplying a cascaded multivariable controller/plant embedded in an output feedback configuration. By tracking the closed-loop eigenvalues as explicit functions of gain, it is possible to visualize the multivariable root loci in a set of “gain plots” consisting of two graphs: (i) magnitude of system eigenvalues versus gain and (ii) argument (angle) of system eigenvalues versus gain. The gain plots offer an alternative perspective of the standard MIMO root locus plot by depicting unambiguously the polar coordinates of each eigenvalue in the complex plane. Two example problems demonstrate the utility of gain plots for interpreting closed-loop multivariable system behavior.

Copyright © 1993 by The American Society of Mechanical Engineers
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