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27 April 2000 Active vibration control of an oscillating rigid bar using nonlinear output regulation techniques
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The work describes the attenuation problem of vibrations affecting a nonlinear oscillatory mechanical system using passive and active vibration control methods based on nonlinear techniques. The mechanical system consists of an oscillating rigid bar coupled to a passive absorber. The undesirable vibration is a harmonic torque, with variable frequency, applied to the bar. The main goal consists of the design of feedback and feedforward control laws, employing information of the open-loop frequency response parameterized in terms of a new coordinate in order to tune appropriately the system. Physically, this coordinate stand for the position the passive absorber along the bar, implying the addition of a degree of freedom and enabling the horizontal motion of the absorber. With the measurement of the excitation frequency it can be computed the optimal attenuation position (minimal disturbance-output gain). Then, the application of a control law that asymptotically reach such position yields indirectly reduction of the angular motion of the bar to the minimum. The control scheme is designed using partial feedback linearization and output regulation techniques. Both cases lead to a fourth order zero dynamics (passive absorber), which is globally asymptotically stable. Some numerical simulations illustrate the resulting dynamic behavior and performance.
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Benjamin Vazquez, Gerardo Silva, and Jaime Alvarez-Gallegos "Active vibration control of an oscillating rigid bar using nonlinear output regulation techniques", Proc. SPIE 3989, Smart Structures and Materials 2000: Damping and Isolation, (27 April 2000);

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