Ultrahigh precision scanning has emerged as a promising and challenging technology in nanoscale measurement and manipulation. Besides the requirement of dynamical tracking of periodical references, the existence of control saturation, due to the limited stroke of microactuators, poses additional challenges for the control of such systems. To address this problem, we propose a repetitive control structure with predictive antiwindup compensation to support nanoscale repetitive tracking/scanning with a minimized impact of actuator saturation. In particular, the proposed antiwindup compensator is activated by the time-lead control output ahead of saturation due to the time-delay block in the repetitive control structure. According to the input/output (I/O)-based equivalent representation and sector bound criterion, stability conditions for the antiwindup compensator are derived, which are further formulated as an $H_\infty $ optimization problem with the robustness against model uncertainties, where the optimal compensator is developed. The effectiveness of the proposed tracking control architecture is further verified in real-time experiments on a piezoelectric-actuator-driven nanostage, where significant improvements are demonstrated comparing with the existing results.

中文翻译：

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支持纳米扫描的重复控制的预测性抗饱和补偿

超高精度扫描已成为纳米级测量和操作中一项有前途且具有挑战性的技术。除了需要动态跟踪周期性参考之外，由于微执行器行程有限，控制饱和的存在对此类系统的控制提出了额外的挑战。为了解决这个问题，我们提出了一种具有预测性抗饱和补偿的重复控制结构，以支持纳米级重复跟踪/扫描，同时最大限度地减少致动器饱和的影响。特别是，由于重复控制结构中的时间延迟块，所提出的抗饱和补偿器在饱和之前由时间超前控制输出激活。根据基于输入/输出（I/O）的等效表示和扇区边界准则， $H_\infty $ 具有针对模型不确定性的鲁棒性的优化问题，其中开发了最佳补偿器。在压电致动器驱动的纳米级的实时实验中进一步验证了所提出的跟踪控制架构的有效性，与现有结果相比，证明了显着的改进。