Recent tuning guidelines for algebraic differentiators based on the analysis of the Fourier transform of the kernels are reviewed. A region of validity for the previous analyses carried out for high frequencies is proposed and the results are related to those based on the analysis of the ${\mathcal{L}}_2$-norm of the Fourier transform of the differentiators. These results are then used for a systematic comparison with established approaches from the literature (homogeneous, high-gain and sliding mode differentiators) for the estimation of the second derivative of a known signal corrupted by a known disturbance. It is shown that properly tuned and discretized algebraic differentiators outperform the other analyzed approaches in terms of robustness, convergence time, and tuning simplicity. The tuning guidelines are then used in the context of control of a partially known system, thus bridging the gap to the tuning of recent model-free control approaches.

回顾了基于核傅立叶变换分析的代数微分器的最新调整指南。提出了先前针对高频进行的分析的有效性区域，并且结果与基于对高频的分析的结果相关。${\mathcal{升}}_2$-微分器傅里叶变换的范数。然后将这些结果用于与文献中已建立的方法（齐次、高增益和滑模微分器）进行系统比较，以估计已知干扰破坏的已知信号的二阶导数。结果表明，适当调整和离散化的代数微分器在鲁棒性、收敛时间和调整简单性方面优于其他分析方法。然后在部分已知系统的控制上下文中使用调整指南，从而弥合与最近的无模型控制方法的调整之间的差距。