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

Johannes Schrock, Thomas Meurer, Andreas Kugi
2013 IEEE Transactions on Control Systems Technology  
Motion planning and feedforward control is considered 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
more » ... is, 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 parametrizations 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 non-trivial domain and non-isotropic material behavior. In addition, the convergence of the system parametrization 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. Index Terms-Motion planning, feedforward control, flatness, smart structure, flexible structure, piezoelectric actuation, Kirchhoff plate, experimental validation, in-domain control. J. Schröck, T. Meurer, A. Kugi are with the Automation and Control Institute (ACIN),
doi:10.1109/tcst.2012.2196043 fatcat:cxp4vvrmmneebbrjmdqm6rkahm