The ever-growing demands on speed and precision from the precision motion industry have pushed control requirements to reach the limitations of linear control theory. Nonlinear controllers like reset provide a viable alternative since they can be easily integrated into the existing linear controller structure and designed using industry-preferred loop-shaping techniques. However, currently, loop-shaping is achieved using the describing function (DF) and performance analysed using linear control sensitivity functions not applicable for reset control systems, resulting in a significant deviation between expected and practical results. This major bottleneck to the wider adaptation of reset control is overcome in this paper with two important contributions. First, an extension of frequency-domain tools for reset controllers in the form of higher-order sinusoidal-input describing functions (HOSIDFs) is presented, providing greater insight into their behaviour. Second, a novel method that uses the DF and HOSIDFs of the open-loop reset control system for the estimation of the closed-loop sensitivity functions is proposed, establishing for the first time — the relation between open-loop and closed-loop behaviour of reset control systems in the frequency domain. The accuracy of the proposed solution is verified in both simulation and practice on a precision positioning stage and these results are further analysed to obtain insights into the tuning considerations for reset controllers.

精密运动行业对速度和精度的日益增长的要求推动了控制要求达到线性控制理论的局限性。诸如复位之类的非线性控制器提供了一种可行的选择，因为它们可以轻松地集成到现有的线性控制器结构中，并使用行业首选的环路整形技术进行设计。但是，目前，使用描述函数（DF）实现了环路成形，并使用了不适用于复位控制系统的线性控制敏感度函数对性能进行了分析，从而导致预期结果与实际结果之间存在重大偏差。本文克服了更大范围的复位控制适应性的主要瓶颈，有两个重要的贡献。第一的，本文以高阶正弦输入描述函数（HOSIDF）的形式介绍了用于复位控制器的频域工具扩展，以提供对其行为的更深入了解。其次，提出了一种使用开环复位控制系统的DF和HOSIDF来估计闭环灵敏度函数的新方法，首次建立了-开环和闭环行为之间的关系。在频域中重置控制系统。在精确定位阶段的仿真和实践中均验证了所提出解决方案的准确性，并对这些结果进行了进一步分析，以了解复位控制器的调整注意事项。提出了一种利用开环复位控制系统的DF和HOSIDF估计闭环灵敏度函数的新方法，首次建立了复位控制的开环与闭环行为之间的关系。频域中的系统。在精确定位阶段的仿真和实践中均验证了所提出解决方案的准确性，并对这些结果进行了进一步分析，以了解复位控制器的调整注意事项。提出了一种利用开环复位控制系统的DF和HOSIDF估计闭环灵敏度函数的新方法，首次建立了复位控制的开环与闭环行为之间的关系。频域中的系统。在精确定位阶段的仿真和实践中均验证了所提出解决方案的准确性，并对这些结果进行了进一步分析，以了解复位控制器的调整注意事项。