A non-contact vibration measurement and control system for a piezoelectric-patched flexible cantilever plate is presented, using laser displacement sensors. Two laser displacement sensors are utilized to detect the deflection information of the two corners of the end of the flexible board, due to its high measurement accuracy for the small amplitude residual vibration. The vibrations of the first bending and torsional mode of the flexible plate can be extracted from the combined information. To achieve a desirable performance for the active vibration control, a kind of sliding mode predictive control strategy is developed to damp the vibration quickly. Simulation of the controller on bending and torsional vibration is conducted, based on the model built with finite element method. Furthermore, a piezoelectric flexible cantilever plate experimental setup is constructed. Experiments are conducted. The results of simulation and experiment both demonstrate the effectiveness of presented control scheme, compared with proportional and derivative control; the sliding mode predictive control can attenuate the vibration more quickly, particularly for the small amplitude residual vibration.

中文翻译：

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压电柔性板的滑模预测振动控制

提出了一种使用激光位移传感器的压电贴片柔性悬臂板的非接触式振动测量和控制系统。由于其对小幅残余振动的测量精度高，因此利用两个激光位移传感器来检测柔性板端部两个角的挠度信息。可以从组合信息中提取柔性板的第一弯曲和扭转模式的振动。为了获得理想的主动振动控制性能，开发了一种滑模预测控制策略来快速阻尼振动。基于有限元方法建立的模型，对控制器的弯曲和扭转振动进行了仿真。此外，搭建了压电柔性悬臂板实验装置。进行实验。与比例和微分控制相比，仿真和实验结果都证明了所提出的控制方案的有效性；滑模预测控制可以更快地衰减振动，特别是对于小振幅残余振动。