Effectiveness of a passive-active vibration isolation system with actuator constraints

In the prediction of active vibration isolation performance, control force requirements were ignored in previous work. This may limit the realization of theoretically predicted isolation performance if control force of large magnitude cannot be supplied by actuators. The behavior of a feed-forward active isolation system subjected to actuator output constraints is investigated. Distributed parameter models are developed to analyze the system response, and to produce a transfer matrix for the design of an integrated passive-active isolation system. Cost functions comprising a combination of the vibration transmission energy and the sum of the squared control forces are proposed. The example system considered is a rigid body connected to a simply supported plate via two passive-active isolation mounts. Vertical and transverse forces as well as a rotational moment are applied at the rigid body, and resonances excited in elastic mounts and the supporting plate are analyzed. The overall isolation performance is evaluated by numerical simulation. The simulation results are then compared with those obtained using unconstrained control strategies. In addition, the effects of waves in elastic mounts are analyzed. It is shown that the control strategies which rely on unconstrained actuator outputs may give substantial power transmission reductions over a wide frequency range, but also require large control force amplitudes to control excited vibration modes of the system. Expected power transmission reductions for modified control strategies that incorporate constrained actuator outputs are considerably less than typical reductions with unconstrained actuator outputs. In the frequency range in which rigid body modes are present, the control strategies can only achieve 5–10 dB power transmission reduction, when control forces are constrained to be the same order of the magnitude as the primary vertical force. The resonances of the elastic mounts result in a notable increase of power transmission in high frequency range and cannot be attenuated by active control. The investigation provides a guideline for design and evaluation of active vibration isolation systems.