Adaptive Control of Semiactive Variable Stiffness Devices for Narrow-Band Disturbance Rejection

The present study examines the potential of using a semiactive controllable stiffness device, whose spring coefficient can be modulated in real-time, for tonal disturbance rejection applications. A frequency-domain control algorithm is developed for determining the spring coefficient variation (at twice the disturbance frequency) that minimizes the force transmitted to the support at the disturbance frequency. The effectiveness of open loop, closed loop, and adaptive controllers in rejecting the transmitted disturbances are evaluated. The results of the study indicate that when limits in stiffness coefficient variation are considered, the support force could be reduced by about an additional 30%, beyond the levels due to the passive isolation characteristics (no cyclic stiffness modulation). When the disturbance phase changes during operation, the effectiveness of the open loop controller is rapidly degraded. While the closed loop controller (with inputs based on current levels of force transmitted to the support) performed better, there was still some degradation in performance, and transmitted support forces were not reduced to levels prior to change in disturbance phase. The results show that for the semiactive system to retain its effectiveness in rejecting disturbances, a closed loop, adaptive controller (with on-line system identification) is required; even when there is only a change in disturbance, and no change in basic system properties. An explanation for this phenomenon, related to the bilinear nature of the semiactive system, is provided.