On the Feedforward Control of Hysteresis for a Piezoelectric Plate

This paper discusses the modeling and feedforward control of hysteresis in a Cantor-like piezoelectric plate. The generalized play operator is analyzed in connection with the plate equations. Results show that hysteresis can be reduced to less than 40% when applying the feedforward control. The subject of the paper belongs to the field of dynamics, characterization and control at the micro/nanoscale. The choose of the Cantor-like piezoelectric plate is motivated by its special property to generate the subharmonic waves due to the anharmonic coupling between the extended-vibration (phonon) and the localized-mode (fracton) regimes. This behavior is a benefit for several applications to the mechanics of grippers and manipulators at the micro/nano scale. In spite of this, the nonlinearities make the piezoelectric plates lose their accuracy if not controlled. For that, the generalized play operator is connected in this paper to the plate equations and the control is focused on feedforward or compensation technique with no sensor requirement. Such advantage is appreciated in the micro/nano-scale because existing sensors that have the required performances are hardly embeddable. The results have confirmed that feedforward control can give general performances such as accuracy and speed required for this particular application. Such control is of great interest because the costs, sizes, and performances of existing sensors limit their use in this domain.