Motion Planning for Piezo-Actuated Flexible Structures: Modeling, Design, and Experiment

We consider motion planning and feedforward control for a cantilevered flexible plate-like structure actuated by a finite number of surface-mounted piezoelectric patches to realize prescribed highly dynamic trajectories for the deflection profile in open loop. For this, a distributed-parameter mathematical model including damping and localized effects originating from the spatially distributed patch actuators is derived by means of the extended Hamilton's principle. With this, a flatness-based design methodology is proposed for motion planning and feedforward control, which directly exploits the distributed-parameter system description. In particular, differential state, input, and output parameterizations are systematically constructed in terms of a basic output to achieve a one-to-one correspondence between system trajectories. Finite element methods are incorporated into the design to account for structures with nontrivial domain and nonisotropic material behavior. In addition, the convergence of the system parameterization is analyzed analytically and by means of numerical results. Finally, measurement results demonstrate the applicability of this approach for the realization of highly dynamic rest-to-rest transitions of the deflection profile of an orthotropic plate structure with macro-fiber composite patch actuators.