Proposition of dynamic vibration absorbing with linearizing feedback control 2018-36-0330
It is proposed a dynamic vibration absorber (DVA) where the variation of the dynamic stiffness is a consequence of the displacement of the secondary mass. Such a mass has its position determined by a control input, by linearization feedback, allowing attenuation of the vibration modes actively. Such an approach allows specifying the self-structure of the system under the DVA action through a feedback gain of linear state feedback. Therefore, the mechanical rigidity of the overall structure can be easily reduced by a suitable choice of a linear matrix gain. In addition, unlike literature approaches aimed at attenuating specific frequencies, the proposed strategy alleviates a much wider spectrum of interest. The proposed DVA consists of a fixed mass to a threaded rod coupled to a stepper motor; the rotation is transformed into translation, producing a vertical displacement of the secondary mass that changes the effective length of the force application and, consequently, the mechanical stiffness. Thus, a simple and low cost maintenance device is proposed that can be easily adapted for applications in the automotive industry, robotic actuators, compressors, etc. The modal analysis of a 1 degree freedom structure was performed to determine the mechanical stiffness, resonance frequency and mass. Then, with the insertion of the proposed device, this procedure was repeated and the new resonance frequency of 10Hz corresponding to the seventh vibration mode was calculated. The dynamic model of the structure does not consider damping and was expressed nonlinearly in the state space with 4 states and a control input (secondary mass position). The nonlinear control law used allows to mitigate the nonlinearities of the structure model with DVA in all frequencies and operating conditions. Thus, on the linearized model there is a linear control law designed through standard self-structure allocation techniques.