This paper addresses nonlinearity in reset elements and their effects. Reset elements are known for having less phase lag compared to their linear counterparts; however, they are nonlinear elements and produce higher-order harmonics. This paper investigates the higher-order harmonics for reset elements with one resetting state and proposes an architecture and a method of design which allows for band-passing the nonlinearity and its effects, namely, higher-order harmonics and phase advantage. The nonlinearity of reset elements is not entirely useful for all frequencies, e.g., they are useful for reducing phase lag at cross-over frequency region; however, higher-order harmonics can compromise tracking and disturbance rejection performance at lower frequencies. Using proposed "phase shaping" method, one can selectively suppress nonlinearity of a single-state reset element in a desired range of frequencies and allow the nonlinearity to provide its phase benefit in a different desired range of frequencies. This can be especially useful for the reset elements in the framework of "Constant in gain, Lead in phase" (CgLp) filter, which is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation -- the waterbed effect.

中文翻译：

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复位元件中的带通非线性

本文讨论了复位元件中的非线性及其影响。众所周知，复位元件与线性元件相比相位滞后更小；然而，它们是非线性元件，会产生高次谐波。本文研究了具有一个复位状态的复位元件的高次谐波，并提出了一种允许带通非线性及其影响的架构和设计方法，即高次谐波和相位优势。复位元件的非线性并非对所有频率都完全有用，例如，它们可用于减少交叉频率区域的相位滞后；然而，高次谐波可能会影响较低频率下的跟踪和干扰抑制性能。使用建议的“相位整形”方法，可以选择性地抑制单态复位元件在所需频率范围内的非线性，并允许非线性在不同的所需频率范围内提供其相位优势。这对于“增益恒定，相位超前”(CgLp) 滤波器框架中的重置元素特别有用，这是一种新引入的非线性滤波器，必将规避众所周知的线性控制限制——水床效应.