Finite element modelling and LQG control of piezoelectric composite structure with distributed sensors and actuators

A 4-node quadrilateral piezoelectric element with thin piezoelectric layers embedded on top and bottom surfaces is derived based on the first-order shear deformation theory, and the dynamic equation of a composite beam with distributed sensors and actuators is established by Hamilton's principle. Considering the influence of plant noise and measurement noise, linear quadratic Gauss (LQG) control algorithm is obtained by using Kalman filter for state estimation. The active vibration control of a piezoelectric composite beam subjected to the pulse, harmonic and random excitation is achieved by LQR and LQG control algorithm, respectively. The results indicate that, if the effect of the noise is taken into consideration and the entire states cannot be fully observed, the LQG algorithm demands a lower actuation voltage than LQR does.