Robust adaptive control of piezo-actuated positioning stages with an ellipse-based hysteresis model

Piezo-actuated positioning stages are widely applied in many industrial applications for nanometer or sub-nanometer displacement resolution. However, the non-smooth hysteresis nonlinearity inherent to the piezoelectric material usually degrades the tracking performance of the controlled system. The challenge is that there is no general method to design control laws with general hysteresis models. The control algorithms are always developed based on a specific hysteresis model. In this paper, an ellipse-based hysteresis model is used to describe the hysteresis behaviors observed on the piezo-actuated positioning stages. The benefit for such a model lies on the fact that the expressions of the model are completely analytical and can be determined easily by a set of parameters. It is therefore convenient to fuse this model with the available robust control approach to mitigate the effects of hysteresis. To illustrate this advantage, a discontinue-projection-based robust adaptive controller is specifically designed, which guarantees the global stability of the closed control system and achieves excellent tracking performance within a desired precision. Simulation performed on a piezo-actuated positioning stage validates the effectiveness of the developed control approach.