Flexible piezoelectric structures-approximate motion equations and control algorithms

Continuous-time and discrete-time algorithms are proposed to control a thin piezoelectric structure which can be described by means of approximate linear time-invariant dynamic models. Generalized coordinates are introduced to approximately represent the kinematics of the structure in a polynomial form; the approximate motion equations are determined by the application of the integral Hamilton principle in the Lagrangian form. The proposed control laws are designed on the basis of the obtained continuous-time and discrete-time approximate dynamic models; they guarantee the gravity force compensation, the noninteracting control of the generalized coordinates, and the asymptotic tracking of reference signals. Simulation results confirming the theoretical effectiveness of the algorithms are reported in the paper.