Classical proportional–integral–derivative (PID) control is exploited widely in industrial motion systems with dry friction motivated by the intuitive and easy-to-use design and tuning tools available. However, classical PID control suffers from severe performance limitations. In particular, friction-induced limit cycling (i.e., hunting) is observed when integral control is employed on frictional systems that suffer from the Stribeck effect, thereby compromising setpoint stability. In addition, the resulting time-domain behavior, such as rise time, overshoot, settling time, and positioning accuracy, highly depends on the particular frictional characteristic, which is typically unknown or uncertain. On the other hand, omitting integral control can lead to constant nonzero setpoint errors (i.e., stick). To achieve superior setpoint performance for frictional motion systems in a repetitive motion setting, we propose a PID-based feedback controller with a time-varying integrator gain design. To ensure optimal setpoint positioning accuracy, a data-based sampled-data extremum-seeking architecture is employed to obtain the optimal time-varying integrator gain design. The proposed approach does not rely on knowledge on the friction characteristic. Finally, the effectiveness of the proposed approach is evidenced experimentally by application to an industrial nanopositioning motion stage setup of a high-end electron microscope.

中文翻译：

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摩擦运动系统高精度重复定位的比例-积分-微分学习控制

经典的比例-积分-微分 (PID) 控制在工业运动系统中得到广泛应用，其干摩擦由直观且易于使用的设计和可用的调整工具驱动。然而，经典的 PID 控制受到严重的性能限制。特别是，当对受 Stribeck 效应影响的摩擦系统采用积分控制时，会观察到摩擦引起的极限循环（即，振荡），从而危及设定点稳定性。此外，由此产生的时域行为，例如上升时间、过冲、稳定时间和定位精度，在很大程度上取决于特定的摩擦特性，而这些特性通常是未知的或不确定的。另一方面，忽略积分控制会导致恒定的非零设定点误差（即粘滞）。为了在重复运动设置中为摩擦运动系统实现卓越的设定点性能，我们提出了一种具有时变积分器增益设计的基于 PID 的反馈控制器。为确保最佳设定点定位精度，采用基于数据的采样数据极值搜索架构来获得最佳时变积分器增益设计。所提出的方法不依赖于关于摩擦特性的知识。最后，通过应用于高端电子显微镜的工业纳米定位运动台设置，实验证明了所提出方法的有效性。采用基于数据的采样数据极值搜索架构来获得最佳的时变积分器增益设计。所提出的方法不依赖于关于摩擦特性的知识。最后，通过应用于高端电子显微镜的工业纳米定位运动台设置，实验证明了所提出方法的有效性。采用基于数据的采样数据极值搜索架构来获得最佳的时变积分器增益设计。所提出的方法不依赖于关于摩擦特性的知识。最后，通过应用于高端电子显微镜的工业纳米定位运动台设置，实验证明了所提出方法的有效性。