Modeling and control of a membrane mirror strip actuated using single piezoelectric bimorph

This paper presents an improved finite-element model of a membrane strip actuated by a single piezoelectric bimorph. The paper also treats the static shape control problem of the structure under study. The membrane strip is modeled as an Euler—Bernoulli beam under tension, with non-uniform physical properties. The finite-element method allows the development of a model that accounts for the actuator dynamics. The static shape control problem is formulated as a disturbance rejection problem and solved using a proportional-integral (PI) controller. The PI control gains are obtained using the linear quadratic regulator theory. The proposed model is verified experimentally, and the closed loop system is simulated to demonstrate the effectiveness of the control law.