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Benefiting from Linear Behaviour of a Nonlinear Reset-based Element at Certain Frequencies
arXiv - CS - Systems and Control Pub Date : 2020-04-07 , DOI: arxiv-2004.03529
Nima Karbasizadeh, Ali Ahmadi Dastjerdi, Niranjan Saikumar, Duarte Valerio, S. Hassan HosseinNia

This paper addresses a phenomenon caused by resetting only one of the two states of a so-called second order "Constant in gain Lead in phase" (CgLp) element. CgLp is a recently introduced reset-based nonlinear element, 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, which clearly violates the linear Bode's gain phase relationship. However, CgLp's ideal behaviour is based on a describing function, which is a first order approximation that neglects the effects of higher order harmonics in the output of the filter. Consequently, achieving the ideal behaviour is challenging when higher order harmonics are relatively large. It is shown in this paper that by resetting only one of the two states of a second order CgLp, the nonlinear filter will act as a linear one at a certain frequency, provided that some conditions are met. This phenomenon can be used to the benefit of reducing higher order harmonics of CgLp's output and achieving the ideal behaviour and thus better performance in terms of precision.

中文翻译:

受益于某些频率下基于非线性复位的元件的线性行为

本文解决了由仅重置所谓的二阶“增益常数先导相位”(CgLp) 元件的两种状态中的一种而引起的现象。CgLp 是最近引入的基于复位的非线性元件,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,同时为宽范围的频率提供相位超前,这显然违反了线性波德增益相位关系。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。因此,当高次谐波相对较大时,实现理想行为具有挑战性。本文表明,通过仅重置二阶 CgLp 的两个状态之一,非线性滤波器将在特定频率下充当线性滤波器,前提是满足某些条件。这种现象可用于减少 CgLp 输出的高次谐波并实现理想行为,从而在精度方面获得更好的性能。
更新日期:2020-04-08
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