This paper proposes a fractional-order reset element whose architecture allows for the suppression of nonlinear effects for a range of frequencies. Suppressing the nonlinear effects of a reset element for the desired frequency range while maintaining it for the rest is beneficial, especially when it is used in the framework of a "Constant in gain, Lead in phase" (CgLp) filter. CgLp is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation -- the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies. However, CgLp's ideal behaviour is based on the describing function, which is a first-order approximation that neglects the effects of the higher-order harmonics in the output of the filter. Although CgLp is fundamentally a nonlinear filter, its nonlinearity is not required for all frequencies. Thus, it is shown in this paper that using the proposed reset element architecture, CgLp gets closer to its ideal behaviour for a range of frequencies, and its performance will be improved accordingly.

中文翻译：

---

分数阶单态复位元件

本文提出了一种分数阶复位元件，其架构允许抑制一定频率范围内的非线性效应。在所需频率范围内抑制复位元件的非线性效应，同时在其余频率范围内保持它是有益的，尤其是在“增益恒定、相位超前”(CgLp) 滤波器的框架中使用时。CgLp 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。这种滤波器在频域中的理想行为是单位增益，同时为广泛的频率范围提供相位超前。然而，CgLp 的理想行为基于描述函数，它是一阶近似值，忽略了滤波器输出中高次谐波的影响。尽管 CgLp 基本上是一个非线性滤波器，但并非所有频率都需要非线性。因此，本文表明，使用所提出的复位元件架构，CgLp 在一定频率范围内更接近其理想行为，其性能将相应提高。