An adaptive integral sliding mode control approach for piezoelectric nano-manipulation with optimal transient performance

This paper presents a control framework supporting high precision tracking of a piezoelectric nano-manipulating system with guaranteed transient performance, where a modified dynamic model describing the hysteresis behavior is also proposed. To achieve the desired optimal transient performance, a dynamic hysteresis compensation based control approach is developed by employing robust adaptive integral sliding mode control technique to accommodate both hysteresis nonlinearities and model uncertainties. An adaptive law is designed to estimate the gain of the integral sliding mode controller such that the chattering behavior is alleviated and the upper bound of uncertainties is no longer required a priori. In particular, it can be proved that the tracking error converges to zero in a finite time. The proposed control architecture is applied to a PZT actuated nano-manipulating stage, where real time implementations demonstrate excellent tracking performance with tracking error around 4.6‰for multi-frequency trajectory tracking experiments. Comparisons with existing results are also given, where significant improvements are achieved in various tracking scenarios.