An improved time-delay saturation controller for suppression of nonlinear beam vibration

In this paper, a nonlinear saturation controller is improved by using quadratic velocity coupling term with time delay instead of the original quadratic position coupling term in the controller and adding a negative time-delay velocity feedback to the primary system. The improved controller is utilized to control the high-amplitude vibration of a flexible, geometrically nonlinear beam-like structure when the primary resonance and the 1:2 internal resonance occur simultaneously. To explain analytically mechanism of the saturation controlled system, an integral iterative method is presented to obtain the second-order approximations and the amplitude equations. It is shown that the quadratic velocity coupling term can enlarge the effective frequency bandwidth and enhance the performance of the vibration suppression by comparison with the quadratic position coupling term, and the linear velocity feedback can suppress the transient vibrations. The effects of different control parameters on saturation control are investigated. We found that time delays can be used as control parameters to change the effective frequency bandwidth and avoid the controller overload risk. The analyses show that numerical simulations are in good agreement with the analytical solutions.