engleski

Active vibration control of a two degree of freedom system using blended velocity feedback

In this paper a theoretical study of active vibration control of a two degree of freedom system is presented. The study is motivated by the stability properties of feedback loops with reactive actuators used for the active control of sound transmission through a smart double panel [1]. The system consists of two lumped masses connected by a coupling spring. Either mass is also attached to a firm reference base by a mounting spring. The vibrations of the primary mass are excited by a point force and transmitted to the secondary mass via the coupling spring. A reactive control force actuator is used between the two masses in parallel with the coupling spring. Each mass is equipped with an absolute velocity sensor. The two sensors and the actuator are used to close a velocity feedback control loop which aims to reduce the vibrations transmitted from the primary to the secondary mass. The error velocity signal is obtained by blending the velocities measured by the two velocity sensors. The blending of the two velocities is obtained by subtracting weighted velocity signals of the two sensors. The primary mass velocity is weighted with by the weighting factor (1-a), whereas the secondary mass velocity is weighted by the weighting factor a. In such a way it is possible to generate error signals proportional to either the primary mass absolute velocity (a=1), or the secondary mass absolute velocity (a=0). Also, it is possible to smoothly change between these two extremes by using the a factors between zero and one. In particular it is possible to use the relative velocity of the two masses (a=0.5). Finally, after the blending, the error signal is amplified and fed back to the actuator. The system is studied in the frequency domain. The point and transfer mobilities of the two degree of freedom system are obtained using the modal decomposition method for the passive system and the system under control [2]. A light modal damping is assumed. The stability of the feedback control is assessed using the Nyquist criterion, and the performance of the control is assessed by analysing broadband reductions of the vibration velocity of the secondary mass. It is shown that the stability and the performance of the active control depend upon the velocity weighting factor used. In fact, for given lumped parameters of the passive system, there is a critical velocity weighting factor where the active control system changes from unconditional stability to conditional stability. The value of the critical velocity weighting factor depends on the parameters of the passive system before the control.

Active Control; Velocity Feedback; Vibration Transmission

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