Vibration Absorption With Linear Active Resonators: Continuous and Discrete Time Design and Analysis

Abstract

The concept of the linear active resonator (LAR) as a vibration absorber is presented. It is formed of a classical passive absorber with a simple dynamic linear feedback. The LAR is, on one hand, a well-known passive absorber but has, on the other hand, an additional actuator that produces a force (lateral system) or a torque (rotational system). This additional actuator is controlled by a feedback signal that is processed in a linear compensator and the reference value for the actuator is produced. The parameters in the compensator are set to produce a designated resonance frequency in the LAR, that is, the damping of the passive absorber is "removed." As a result, the LAR becomes an ideal resonator that theoretically absorbs vibrations from the point of attachment completely. The resonant frequency of the LAR is variable in real time. It is also shown that with this concept the absorber can have more than one resonant frequency, though it is a single- degree-of-freedom system. This active absorber does not need information from the primary system that it is attached to; it is autonomous in online operation. The signal used for the absorber feedback is either the position, velocity, or acceleration of the absorber mass. Depending on the application and convenience, this signal can be an absolute one, or a signal relative to the point of attachment. The global system characteristics are used only in the off-line analysis, such as for stability and robustness analysis. In this paper, the general concept of the LAR is derived in the continuous and the discrete time domain; the stability analysis of the system with LAR is presented using parameter space analysis.