LQR vibration control of piezoelectric composite plates

LQR vibration control of piezoelectric composite plates is investigated via the finite element method. Laminated composite plates with bounded or embedded piezoelectric sensors (PVDFs) and actuators (PZTs) are discretized by an isoparametric element and the governing equations of motion are derived by using the Hamilton's principle. The optimal LQR method is used to couple the discrete distributed actuation and sensing. The Algebraic Riccati Equation (ARE) is solved by MATLAB. To avoid possible numerical difficulty, in the present study only Potter's method rather than MATLAB's control toolbox functions is used. More emphasis is put on appropriate selection of the weighting matrices of the optimal quadratic objective functions. The present study tried to relate the quadratic functions with some physical meanings to avoid the usual trial and error procedure. The quadratic functions are assumed to consist of independent strain energy, kinetic energy and actuators' input energy. The frequency matrix and the identity matrix are used as the relative weight of the strain energy and the kinetic energy and the actuators' input energy with an adjustable coefficient for each actuator is used as the relative weight of the actuators' input energy. Numerical results show that this method works fairly well for either the output constraint control (OCC) or input constraint control (ICC) and the active damping effect is more sensitive when approaching the breakdown voltages of the actuators.