Some Bond Graph Structural Properties: Eigen Spectra and Stability

[+] Author and Article Information
A. Zeid

Mechanical Engineering Department, Wayne State University, Detroit, MI 48202

J. Dyn. Sys., Meas., Control 111(3), 382-388 (Sep 01, 1989) (7 pages) doi:10.1115/1.3153065 History: Received February 01, 1988; Revised September 06, 1988; Online July 21, 2009


What does the structure of the bond graph reveal about the eigenvalues of linear systems and about the stability of the linear and nonlinear systems they represent? In an earlier work, estimates of the eigen spectra of systems were given based on the structural classification of a canonical form of the bond graph. This work provides stability criteria based on the structure of the bond graph canonical form for linear and nonlinear time invariant dynamic systems. Tighter bounds on the eigen spectrum are also provided for the class of systems with uniform tree simple full graphs. It is shown that if a system is modeled by a standard bond graph whose canonical form is of the simple full or simple partial class, then estimates of the system stability, asymptotic stability, or instability can be obtained directly from the properties of the resistance field. The stability estimates can be automated and are obtained prior to the derivation of the dynamic equations. The stability properties can be used also as a design tool to suggest stabilizing feedback at the graphical modeling stage of the design process.

Copyright © 1989 by ASME
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