Active vibration control of a polyvinylidene fluoride laminated membrane plate mirror

Lightweight optical mirrors usually play key roles in aerospace and optical structural systems applied to space telescopes, radars, solar collectors, communication antennas, etc. Due to their high flexibility and low damping properties, external excitations such as orbital maneuver may induce unexpected oscillations and thus reduce their working performance. Active vibration control is therefore essential for the lightweight optical mirror systems. In this spirit, a lightweight mirror structronic system with a linear quadratic optimal controller is presented. The mirror is modeled as a membrane plate with pretension and distributed polyvinylidene fluoride sensors and actuators. The sensing sensitivity of the piezoelectric (PVDF) sensors and the modal actuation factor of the PVDF actuators are derived. The state-space equations are established and the feedback control gains between sensing and control signals are obtained. Sensor and actuator of different shape, size, and position are employed to actively control the first four natural modes of the mirror. The influences of mode order, pretension, and the two weighting factors Q and R on the control performance are also investigated. Analytical results in this paper could guide the design and layout of the PZT sensor and actuator on lightweight membrane plate mirrors.