Vibration absorption with linear active resonators: Continuous and discrete time design and analysis

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 dyna mic 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 i s controlled by a feedback signal that is processed in a linear compensator and the reference value for the actuator is produced. The parameters in th e compensator are set to produce a designated resonance frequency in the LA R, that is, the damping of the passive absorber is "removed." As a result, the LAR becomes an ideal resonator that theoretically absorbs vibrations fr om 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 pr imary 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 conv enience, this signal can be an absolute one, or a signal relative to the po int of attachment. The global system characteristics are used only in the o ff-line analysis, such as for stability and robustness analysis. In this pa per, the general concept of the LAR is derived in the continuous and the di screte time domain; the stability analysis of the system with LAR is presen ted using parameter space analysis.