Integral back-stepping active disturbance rejection control for piezoelectric stick-slip drive nanopositioning stage

Abstract

Piezoelectric stick-slip driven nanopositioning stage (PSSNS) with nanometer resolution has been widely used in the field of micro-operation. However, it is difficult to achieve nanopositioning over large travel, and its positioning accuracy is affected by the hysteresis characteristics of the piezoelectric elements, external uncertain disturbances, and other nonlinear factors. To overcome the above-mentioned problems, a composite control strategy combining stepping mode and scanning mode is proposed in this paper, and an integral back-stepping linear active disturbance rejection control (IB-LADRC) strategy is proposed in the scanning mode control phase. First, the transfer function model of the system in the micromotion part was established, and then the unmodeled part of the system and the external disturbance were treated as the total disturbance and extended to a new system state variable. Second, a linear extended state observer was used as the core of the active disturbance rejection technique to estimate displacement, velocity, and total disturbance in real time. In addition, by introducing virtual control variables, a new control law was designed to replace the original linear control law and improve the positioning accuracy and robustness of the system. Furthermore, the effectiveness of the IB-LADRC algorithm was verified by simulation comparison experiments and experimentally validated on a PSSNS. Finally, experimental results show that the IB-LADRC is a practical solution for a controller capable of handling disturbances during the positioning of a PSSNS with a positioning accuracy of less than 20 nm, which essentially remains constant under load.