Bifurcation control of a Duffing oscillator using pole placement

Abstract

This paper presents a numerical study on the control of frequency-domain bifurcation in forced Duffing oscillators, through the use of pole placement techniques. First, the bifurcation frequency range of the Duffing oscillator is identified using the system and forcing parameters. A linear state feedback controller is then applied to the system, in order to assign the peak resonance frequency to a prescribed value, such that bifurcation is minimized or eliminated in the closed-loop system. Additional constraints are applied to the pole placement in order to minimize the control effort, such as assigning the closed-loop poles within an elliptical region in the complex domain. Finally, a constraint is placed on the maximum forcing level, such that bifurcation will not occur at relatively small forcing amplitudes. These techniques are demonstrated using several numerical examples.