Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate

Some flexible appendages of spacecraft are cantilever plate structures, such as sun plate and satellite antenna. Thus, vibration problem will be caused by parameter uncertainties and environmental disturbances. In this paper, piezoelectric ceramics patches are used as sensors and actuators to suppress the vibration of the smart flexible clamped plate. Firstly, modal equations and piezoelectric control equations of cantilever plate are derived. Secondly, an optimal placement method for the locations of piezoelectric actuators and sensors is developed based on the degree of observability and controllability indices for cantilever plate. The bending and torsional modes are decoupled by the proposed method using bandwidth Butterworth filter. Thirdly, an efficient control method by combining positive position feedback and proportional-derivative control is proposed for vibration reduction. The analytical results for modal frequencies, transient responses and control responses are carried out. Finally, an experimental setup of piezoelectric smart plate is designed and built up. The modal frequencies and damping ratios of the plate setup are obtained by identification method. Also, the experimental studies on vibration control of the cantilever plate including bending modes and torsional modes are conducted. The analytical and experimental results demonstrate that the presented control method is feasible, and the optimal placement method is effective.