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In this paper, a modeling method of XY micropositioning stage with piezoelectric actuators is proposed. In the modeling scheme, a sandwich model consists of both input and output linear submodels, and an embedded neural-network-based hysteresis submodel is used to describe the motion behavior of each axis of the stage. Moreover, a neural-network-based submodel is constructed to describe the nonlinear interactive dynamics caused by the movement of another axis. Then, a tracking control scheme combined with a nonlinear decoupling control is proposed to compensate for the effect of the interactions between axes and track the reference trajectory. Then, the robust design method for the tracking and decoupling control is discussed. Finally, the experimental results on an XY micropositioning stage are presented.