Rate-dependent Asymmetric Hysteresis Modeling and Robust Adaptive Trajectory Tracking for Piezoelectric Micropositioning Stages

Hysteresis is an inherent characteristic of piezoelectric materials that can be determined by not only the historical input but also the input signal frequency. Hysteresis severely degrades the positioning precision of piezoelectric micropositioning stages. In this study, the hysteresis characteristics and the excitation frequency effects on the hysteresis behaviors of the piezoelectric micropositioning stage are investigated. Accordingly, a rate-dependent asymmetric hysteresis Prandtl-Ishlinskii (RDAPI) model is developed by introducing a dynamic envelope function into the play operators of the Prandtl-Ishlinskii (PI) model. The RDAPI model uses a relatively simple analytical structure with fewer parameters then other modified PI model to characterize the rate-dependent and asymmetric hysteresis behavior in piezoelectric micropositioning stages. Considering practical situations with the uncertainties and external disturbances associated with the piezoelectric micropositioning stages, the system dynamics are described using a second-order differential equation. On this basis, a corresponding adaptive robust control method that does not involve the construction of a complex hysteretic inverse model is developed. The Lyapunov analysis method proves the stability of the entire closed-loop control system. Experiments confirm that the proposed RDAPI model achieves a significantly improved accuracy compared with the PI model. Furthermore, compared with the inverse RDAPI model-based feedforward compensation and the inverse RDAPI model-based proportional-integral-derivative control methods, the proposed robust adaptive control strategy exhibits improved tracking performance.

Design and Analysis of a Novel Flexure-Based XY Micropositioning Stage

Flexure-based micropositioning stages with high positioning precision are really attractive. This paper reports the design and analysis processes of a two-degree-of-freedom (2-DOF) flexure-based XY micropositioning stage driven by piezoelectric actuators to improve the positioning accuracy and motion performance. First, the structure of the stage was proposed, which was based on rectangular flexure hinges and piezoelectric actuators (PZT) that were arranged symmetrically to realize XY motion. Then, analytical models describing the output stiffness in the XY directions of the stage were established using the compliance matrix method. The finite element analysis method (FEA) was used to validate the analytical models and analyze the static characteristics and the natural frequency of the stage simultaneously. Furthermore, a prototype of the micropositioning stage was fabricated for the performance tests. The output response performance of the stage without an end load was tested using different input signals. The results indicated that the stage had a single direction amplification capability, low hysteresis, and a wide positioning space. The conclusion was that the proposed stage possessed an ideal positioning property and could be well applied to the positioning system.