Active control of a piezo-composite rotating beam using coupled plant dynamics

Optimal control of a thin-walled rotating beam is considered using a higher-order shear deformation theory (HSDT). The beam is pretwisted, doubly tapered, and carries a tip rotor. It comprises an orthotropic host with surface-embedded transversely isotropic piezoelectric sensor-actuator pairs. Spanwise and thicknesswise variation of the electric field applied to actuators is considered. This yields a coupled electro-mechanical system, wherein all displacement variables are coupled via the electric field. Hence, coupling between bending-transverse shear and extension-twist occurs even when the ply angle configuration has circumferentially uniform stiffness. Optimal LQR control with state feedback is used to obtain the control input, i.e., charge density (hence voltage) applied to actuators. Parametric studies involving ply-angle, rotation speeds of beam and rotor, pretwist, taper, rotor mass, and saturation constraint on actuator voltage, are performed. The HSDT yields lowest coupled natural frequencies (as compared to unshearable and first-order shear models) thus providing conservative data, useful for passive and active control designs. The present plant model, with spanwise varying electric field, yields an order-of-magnitude reduction in settling time and control voltage, and lower response, vis-a-vis the decoupled approach.