由于开闭环迭代学习控制方法能在加快收敛速度的情况下降低跟踪误差, 本文利用该控制方法来提高压电驱动器(PZT)的高频轨迹跟踪精度。首先, 提出了离散时间下的开环P型结合闭环PI型的迭代学习律, 并且给出了基于该学习律的收敛性条件。然后, 设计了用于PZT系统的离散开闭环迭代学习控制器。最后, 针对50 Hz单频和25 Hz+50 Hz复频三角波轨迹进行了跟踪控制实验。实验结果表明: 所提出的迭代学习控制器对上述2种轨迹的最大跟踪误差分别为10.6 nm和12.5 nm, 相对于PID控制器, 分别降低了96.25%和95.62%。结果显示: 提出的控制方法易于实现, 无需准确的PZT迟滞和系统模型就可以获得很高的跟踪精度, 能有效地满足高频和复频轨迹跟踪的精度要求。

As open-closed loop iterative learning control scheme can up the convergence and reduce the tracking error, this paper uses the scheme to improve high frequency trajectory tracking accuracy of a piezoelectric actuator(PZT). First, a discrete-time open-loop P-type with closed-loop PI-type iterative learning law was proposed and its convergence condition was given. Then, a discrete-time open-closed loop iterative learning controller was designed for the PZT system. Finally, as to 50 Hz and 25Hz+50Hz triangular desired trajectories with single and compound frequencies, the tracking control experiment was performed. Experimental results indicate that the proposed iterative learning controller can achieve 10.6 nm and 12.5 nm maximum tracking errors for the 2 kinds of trajectories, which are 96.25% and 95.62% less than that of the PID controller. It concludes that the proposed control scheme can be easily implemented and can obtain the high accuracy of trajectory tracking without precise hysteresis and PZT system models. It meets both the requirements of single and compound frequency trajectory tracking for high tracking accuracy.