Trajectory tracking of piezoelectric positioning stages using a dynamic sliding-mode control

Area of Science:

• Control Systems Engineering
• Mechatronics
• Nanotechnology

Background:

• Piezoelectric positioning stages are crucial for high-precision applications like scanning microscopy.
• Hysteresis nonlinearity significantly degrades the trajectory tracking performance of these stages.
• Effective compensation of hysteresis is essential for reliable operation.

Purpose of the Study:

• To propose a novel dynamic sliding-mode control (DSMC) with backstepping for piezoelectric positioning stages.
• To develop an equivalent model that incorporates hysteresis nonlinearity for accurate system representation.
• To enhance the trajectory tracking accuracy of piezoelectric stages in microscopy.

Main Methods:

• Development of an equivalent model combining linear dynamics with hysteresis and strain-dependent nonlinearities.
• Design of a DSMC with an asymptotical sliding surface based on the equivalent model.
• Mathematical stability analysis and experimental validation using a computer-based controller and capacitive displacement sensor.

Main Results:

• The proposed DSMC effectively compensates for the inherent hysteresis phenomenon in piezoelectric stages.
• Stability analysis confirms the system's robustness.
• Experimental results demonstrate the feasibility and effectiveness of the DSMC for precise trajectory tracking.

Conclusions:

• The DSMC with backstepping offers a robust solution for trajectory tracking control of piezoelectric positioning stages.
• The proposed method significantly improves positioning accuracy, making stages more suitable for demanding microscopy applications.
• This control strategy enhances the practical applicability of piezoelectric stages requiring diverse trajectory tracking.