Constant in gain Lead in phase (CgLp) compensators, which are a type of reset elements, have shown high potential to overcome limitations of linear control systems. There are few works which investigate the tuning of these compensators. However, there are some significant drawbacks which make those methods unreliable. First, their analyses are performed in the open-loop configuration which do not guarantee the existence of steady-state response of the closed-loop. If it is guaranteed, unlike linear control systems, open-loop analyses cannot precisely predict the closed-loop steady-state performance. In addition, the stability condition could not be assessed during the tuning process. These significant challenges have been separately solved in our recent works by proposing frequency-domain frameworks for analyzing the closed-loop performance and stability of reset control systems. However, they are not formulated and implemented for tuning CgLp compensators. In this paper, based on the loop-shaping approach, the recent frequency-domain framework and the frequency-domain stability method are utilized to provide a reliable frequency-domain tuning method for CgLp compensators. Finally, different performance metrics of a CgLp compensator, tuned by the proposed method, are compared with those of a PID controller on a precision positioning stage. The results show that this method is effective, and the tuned CgLp can achieve more favorable dynamic performance than the PID controller.

中文翻译：

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薄型高品质直下式 LED 背光系统的直接设计


恒定增益超前相位 (CgLp) 补偿器是一种复位元件，已显示出克服线性控制系统限制的巨大潜力。很少有研究研究这些补偿器的调整。然而，存在一些显着的缺点，使得这些方法不可靠。首先，他们的分析是在开环配置中进行的，这不能保证闭环稳态响应的存在。如果得到保证，与线性控制系统不同，开环分析无法精确预测闭环稳态性能。此外，在调整过程中无法评估稳定性条件。这些重大挑战已在我们最近的工作中通过提出用于分析复位控制系统的闭环性能和稳定性的频域框架来单独解决。然而，它们并不是为了调整 CgLp 补偿器而制定和实现的。本文基于环路整形方法，利用最新的频域框架和频域稳定性方法，为CgLp补偿器提供可靠的频域调谐方法。最后，将通过所提出的方法调整的 CgLp 补偿器的不同性能指标与精密定位级上的 PID 控制器的性能指标进行比较。结果表明，该方法是有效的，整定后的CgLp能够比PID控制器获得更良好的动态性能。