Abstract
An on-line identification and control algorithm is developed based on the properties of collocated sensing and actuation. The feedback control law consists of second-order compensators that achieve equivalent damping in both the filter dynamics and resonant structural dynamics, thus maximizing the damping in the structure and controller. Optimal design of the feedback compensator is obtained using a pole placement algorithm applied to a single, undamped resonant mode. Numerical analysis indicates that multiple modes and structural damping do not appreciably change the damping achieved using the optimal parameters. The pole placement analysis demonstrates that only the pole-zero spacing and DC gain of the collocated transfer function are required to choose the optimal parameters. An on-line identification procedure is developed that sequentially determines the DC gain and pole-zero spacing and automatically designs the feedback compensator. This forms the basis for the autonomous control algorithm. Experimental results on a flexible beam demonstrate that the procedure can accurately identify the pole-zero spacing and automatically design the feedback compensator. A fivefold increase in damping is achieved in the first mode and a twofold increase in damping is achieved in the second mode. Discrepancies between predicted and measured damping are attributed to phase lags due to signal conditioning and low-pass filtering of the sensor signal.
