The LQG control of piezoelectric intelligent structure based on the finite element method

Because of the positive and inverse piezoelectric effect, piezoelectric materials can be used in the active control of flexible structures. Based on the first-order shear deformation theory, combined with the electrical and mechanical effects, a 4-node quadrilateral piezoelectric composite element is derived, and the dynamic characteristic equation of a composite beam is established by Hamilton´s principle. Considering the influence of outside noise and measurement noise, using Kalman filter for state estimation, the linear quadratic Gauss (LQG) control algorithm is obtained based on LQR algorithm. The vibration control of a piezoelectric beam in the pulse, harmonic and random excitation is achieved by LQR and LQG control algorithm, respectively. The results indicate that, without considering the entire states and the impact of noise as prerequisites, the LQG algorithm needs a smaller actuation voltage than LQR does.