Ming Chi University of Technology/No. 84, Gungjuan Road, Taishan, Taipei, 243, Taiwan.
Sensors (Basel). 2010;10(12):10545-59. doi: 10.3390/s101210545. Epub 2010 Nov 24.
Since the piezoelectrically actuated system has nonlinear and time-varying behavior, it is difficult to establish an accurate dynamic model for a model-based sensing and control design. Here, a model-free adaptive sliding controller is proposed to improve the small travel and hysteresis defects of piezoelectrically actuated systems. This sensing and control strategy employs the functional approximation technique (FAT) to establish the unknown function for eliminating the model-based requirement of the sliding-mode control. The piezoelectrically actuated system's nonlinear functions can be approximated by using the combination of a finite number of weighted Fourier series basis functions. The unknown weighted vector can be estimated by an updating rule. The important advantage of this approach is to achieve the sliding-mode controller design without the system dynamic model requirement. The update laws for the coefficients of the Fourier series functions are derived from a Lyapunov function to guarantee the control system stability. This proposed controller is implemented on a piezoelectrically actuated X-Y table. The dynamic experimental result of this proposed FAT controller is compared with that of a traditional model-based sliding-mode controller to show the performance improvement for the motion tracking performance.
由于压电致动系统具有非线性和时变行为，因此很难为基于模型的传感和控制设计建立准确的动态模型。在这里，提出了一种无模型自适应滑模控制器，以改善压电致动系统的小行程和滞后缺陷。这种传感和控制策略采用函数逼近技术 (FAT) 来建立未知函数，以消除滑模控制的基于模型的要求。可以使用有限数量的加权傅里叶级数基函数的组合来逼近压电致动系统的非线性函数。可以通过更新规则来估计未知加权向量。这种方法的一个重要优点是可以在不要求系统动态模型的情况下实现滑模控制器设计。傅里叶级数函数的系数的更新定律是从 Lyapunov 函数推导出来的，以保证控制系统的稳定性。该控制器在压电致动的 X-Y 台上进行了实现。将所提出的 FAT 控制器的动态实验结果与传统的基于模型的滑模控制器的结果进行了比较，以显示在运动跟踪性能方面的性能改善。
