Acceleration Control in Nonlinear Vibrating Systems based on Damped Least Squares

Details Acceleration Control in Nonlinear Vibrating Systems based on Damped Least Squares Acceleration Control in Nonlinear Vibrating Systems based on Damped Least Squares

2011-10-12

arxiv.org/abs/1110.2811v2

Mathematics

Optimization and Control

11 pages, 5 figures

Scientific paper

A discrete time control algorithm using the damped least squares is introduced for acceleration and energy exchange controls in nonlinear vibrating systems. It is shown that the damping constant of least squares and sampling time step of the controller must be inversely related to insure that vanishing the time step has little effect on the results. The algorithm is illustrated on two linearly coupled Duffing oscillators near the 1:1 internal resonance. In particular, it is shown that varying the dissipation ratio of one of the two oscillators can significantly suppress the nonlinear beat phenomenon.

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