Coupled Stability of Multiport Systems—Theory and Experiments

[+] Author and Article Information
J. E. Colgate

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208

J. Dyn. Sys., Meas., Control 116(3), 419-428 (Sep 01, 1994) (10 pages) doi:10.1115/1.2899237 History: Received July 01, 1991; Revised July 01, 1993; Online March 17, 2008


This paper presents both theoretical and experimental studies of the stability of dynamic interaction between a feedback controlled manipulator and a passive environment. Necessary and sufficient conditions for “coupled stability”—the stability of a linear, time-invariant n-port (e.g., a robot, linearized about an operating point) coupled to a passive, but otherwise arbitrary, environment—are presented. The problem of assessing coupled stability for a physical system (continuous time) with a discrete time controller is then addressed. It is demonstrated that such a system may exhibit the coupled stability property; however, analytical, or even inexpensive numerical conditions are difficult to obtain. Therefore, an approximate condition, based on easily computed multivariable Nyquist plots, is developed. This condition is used to analyze two controllers implemented on a two-link, direct drive robot. An impedance controller demonstrates that a feedback controlled manipulator may satisfy the coupled stability property. A LQG/LTR controller illustrates specific consequences of failure to meet the coupled stability criterion; it also illustrates how coupled instability may arise in the absence of force feedback. Two experimental procedures—measurement of endpoint admittance and interaction with springs and masses—are introduced and used to evaluate the above controllers. Theoretical and experimental results are compared.

Copyright © 1994 by The American Society of Mechanical Engineers
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