Limit-cycle taming by nonlinear control with applications to flutter

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.