Shieh Hsin-Jang, Huang Po-Kai
Department of Electrical Engineering, National Dong Hwa University, Shoufong, Hualien 97401, Taiwan.
IEEE Trans Ultrason Ferroelectr Freq Control. 2006 Oct;53(10):1872-82. doi: 10.1109/tuffc.2006.119.
Trajectory tracking performance of a piezoelectric positioning stage almost depends on whether the tracking controller can effectively compensate the inherent hysteresis phenomenon. In this paper, a dynamic sliding-mode control (DSMC) with backstepping is proposed for the trajectory tracking of the piezoelectric positioning stage, which is suitable for a component of scanning microscopes. An equivalent model developed from a linear motion dynamics with addition of the hysteresis nonlinearity and strain-dependent function first is proposed to approximately represent the dynamics of motion of a one-dimensional piezoelectric positioning stage. Then, based on the equivalent model, the DSMC with an asymptotical sliding surface is proposed for the trajectory tracking control of the piezoelectric positioning stage. Moreover, the analysis of stability can be completed by mathematics, and the convergence rate of the tracking error can be governed by the choice of the control parameter values. Using the DSMC to trajectory tracking control, the piezoelectric positioning stage becomes more suitable for practical applications, especially with the need of various trajectories tracking in microscopy. To validate the proposed control scheme, a computer-based controller and a piezoelectric positioning stage with a capacitive displacement sensor are implemented. Experimental results illustrate the feasibility of the proposed controller for trajectory tracking applications.
压电定位平台的轨迹跟踪性能几乎取决于跟踪控制器能否有效补偿固有的滞后现象。本文针对适用于扫描显微镜部件的压电定位平台的轨迹跟踪，提出了一种带有反步法的动态滑模控制（DSMC）。首先提出一个从线性运动动力学发展而来的等效模型，该模型加入了滞后非线性和应变相关函数，以近似表示一维压电定位平台的运动动力学。然后，基于该等效模型，提出了一种具有渐近滑模面的DSMC用于压电定位平台的轨迹跟踪控制。此外，可以通过数学方法完成稳定性分析，跟踪误差的收敛速度可以通过控制参数值的选择来控制。将DSMC用于轨迹跟踪控制，使压电定位平台更适合实际应用，特别是在显微镜中需要进行各种轨迹跟踪的情况下。为了验证所提出的控制方案，实现了基于计算机的控制器和带有电容式位移传感器的压电定位平台。实验结果说明了所提出的控制器在轨迹跟踪应用中的可行性。
