Multiplier theory for stability analysis of anti-windup control systems

Kothare, Mayuresh V. and Morari, Manfred (1996) Multiplier theory for stability analysis of anti-windup control systems. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechCDSTR:1996.012]

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Abstract

We apply the passivity theorem with appropriate choice of multipliers to develop sufficient conditions for stability of the general anti-windup bumpless transfer (AWBT) framework presented in [24]. For appropriate choices of the multipliers, we show that these tests can be performed using convex optimization over linear matrix inequalities (LMIs). We show that a number of previously reported attempts to analyze stability of AWBT control systems, using such well-known and seemingly diverse techniques as the Popov, Circle and Off-Axis Circle criteria, the optimally scaled small-gain theorem (generalized μ upper bound) and describing functions, are all special cases of the general conditions developed in this paper. The sufficient conditions are complemented by necessary conditions for internal stability of the AWBT compensated system. Using an example, we show how these tests can be used to analyze the stability properties of a typical anti-windup control scheme.

EPrint Type:	Monograph (Technical Report)
Additional Information:	Submitted to Automatica. Also presented at the 34th IEEE Conference on Decision and Control, New Orleans, LA, December 1995. Partial financial support from the U.S. National Science Foundation and the Swiss Federal Institute of Technology (ETH), Zürich, Switzerland, is gratefully acknowledged. We would like to thank Prof. B. D. O. Anderson for several helpful comments.
Uncontrolled Keywords:	Control input nonlinearity, constrained system, nonlinear system, stability analysis, anti-windup, bumpless transfer, passivity theorem, linear matrix inequality, multiplier theory, absolute stability.
Subjects:	All Records
ID Code:	150
Deposited By:	Kristin Buxton
Deposited On:	14 December 2007
Unique Identifier:	CaltechCDSTR:1996.012
Official Persistent URL:	http://resolver.caltech.edu/CaltechCDSTR:1996.012
Usage Policy:	You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.

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