Bifurcation control of a flexible beam under principal parametric excitation
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A new approach is proposed in this paper for the nonlinear control of a flexible cantilever beam which is excited under a principal parametric vibration. The approach is based on a bifurcation control principle that combines linear and nonlinear feedback control strategies. A simplified nonlinear vibration model, that accounts for the beam's flexibility and the control feedback, is first derived by using the method of multiple scales. The analysis of stability based on Krasovskii's theorem is then applied to the above system. Simulation results show that the proposed approach is effective for use in the case of parametric vibration control.