Vibration Suppression of a Principal Parametric Resonance

In this paper, a control method that combines linear and nonlinear-velocity feedback control is proposed to suppress the principal parametric resonance in a flexible cantilever beam structure. Linear-velocity feedback is employed for bifurcation control, and cubic-velocity feedback is employed to suppress high-amplitude vibration. A unified bifurcation parameter gamma that includes both the excitation frequency and amplitude is defined for the stability analysis, so that bifurcations under quasi-stationary frequency-response and quasi-stationary force-response can be treated uniformly when gamma is quasi-statically varied. This unified bifurcation parameter simplifies the system stability analysis as well as the controller design procedure. Numerical simulation and experimental results show that the combined bifurcation control and nonlinear feedback control strategy performs better than linear-velocity or cubic-velocity feedback control alone, and is less susceptible to actuator saturation.