Dynamics of a Nonlinear Oscillator With Feedback Control I: Local Analysis

Abstract

We study stability and bifurcations of solutions of a single degree of freedom structural system with nonlinear stiffness, subject to linear feedback control. The controller dynamics is modelled by a first order differential equation, so that the full system is of third order. In this paper we consider local bifurcations: solutions branching from equilibria as various parameters (damping, gain, etc.) are varied. Using two different nonlinear stiffness functions, we show that interactions between steady and periodic modes of instability leads to complicated dynamical behavior near the boundaries of the “stable” region of parameter space.