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Limit-cycle taming by nonlinear control with applications to flutter

Published online by Cambridge University Press:  04 July 2016

F. Mastroddi  and
L. Morino
F. Mastroddi
Affiliation:
University of Rome La Sapienza, Rome, Italy
L. Morino
Affiliation:
University of Rome III, Rome, Italy
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Abstract

This paper addresses the problem of limit-cycle taming, which is defined in this paper as the use of nonlinear control laws to ensure that the limit-cycle behaviour of the system beyond the stability boundary is of a benign rather than a destructive nature. Specifically, we consider a one-parameter (denoted by λ) autonomous dynamic system having algebraic nonlinearities. We assume that the system has a stable solution, x = 0, for λ < λ0, and experiences a Hopf bifurcation at λ = λ0. Using a singular perturbation analysis about the stability boundary, it is shown that, using a simple nonlinear control law, limit-cycle taming is always possible in the neighbourhood of a Hopf bifurcation. The control system proposed for limit-cycle taming is fully nonlinear, and therefore does not affect the linear behaviour of the system (in particular its stability characteristics). Hence, limit-cycle taming may be used in conjunction with a standard linear active control (e.g. use of linear active control to increase the stability boundary). Applications of the theory to the problem of flutter are presented.

Type
Research Article
Information
The Aeronautical Journal , Volume 100 , Issue 999 , November 1996 , pp. 389 - 396
Copyright
Copyright © Royal Aeronautical Society 1996 

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Footnotes

†

Assistant Professor, Dipartimento Aerospaziale, via Eudossiana 16, 00184 Roma

‡

Professor, Dipartimento di Meccanica e Automatica, via C. Segre 60, 00146 Roma

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