Adaptive parameter estimation with nonswitching reaching law for variable structure control of a nanopositioning stage

In this paper, an innovative motion controller is proposed to compensate for both the nonlinear hysteresis and the vibration dynamics effects of a nanopositioning stage driven by piezoelectric actuators. With the increasing of operating bandwidth and motion range, large positioning errors are produced because of the hysteresis, vibration, external disturbance and noise, as well as uncompleted modeled dynamic errors. The main contribution of this work is that an adaptive approach is developed to estimate these uncertainties and errors in real-time. Furthermore, a nonswitching type of reaching law for variable structure control of the discrete-time system is applied to regulate the position state, which is effective to compensate for nonrepeating disturbance. In addition, the proposed control algorithm is applied to experimentally validate the effectiveness of enhancing the performance in precise positioning control of the nanopositioning stage.