Plate with piezoelectric actuators/sensors

This paper investigates the robust control of low-frequency modes of a thin all-clamped plate with piezoelectric actuators and sensors. Locations of the actuators and sensors are important in reducing the spillover effects of uncontrolled modes. Locations good for controlling the low-frequency modes are evaluated by using the modal shapes. The uncertainties at the high-frequency region and the low-frequency region around the frequency zero should be considered for the stability of the control system. These two uncertainties can limit the gain of the vibration controller. Low-pass filters and high-pass filters are introduced to alleviate the high-frequency and the low-frequency uncertainty, respectively. The linear quadratic Gaussian (LQG) control with the low-pass filters and high-pass filters is demonstrated to suppress the first three modes of an all-clamped plate and gives 10~20-dB reduction of vibration in the experiment. Also, the highest gains of the controller for the plant, which consists of the nominal model and several uncontrolled modes, are evaluated to vindicate the usefulness of high-pass filters