This paper puts forward contemporary designs of sliding mode differentiator and state observer for evaluation of unknown nonlinear signal derivatives and unknown internal system states, respectively, by the virtue of tangential and inverse sinusoidal hyperbolic functions. The utility of the proposed frameworks is that it bestows smooth and robust estimation without inciting unacceptable oscillations (chattering), unlike high gain discontinuous function-based preliminary observers/differentiators. Moreover, the employed double hyperbolic functions would drive the various deviations in estimations of signals or states to a very close neighborhood of origin in finite time which is substantiated via Lyapunov's energy function. To demonstrate the efficiency of the introduced techniques, two examples for estimating the derivatives of a nonlinear signal and internal states of motor are also illustrated with time varying uncertainties. At last, the attained simulation outcomes of the proposed differentiator are further compared with formerly formulated designs such as higher-order sliding mode differentiator (HOSMD) and uniformly convergent differentiator (UCD).

中文翻译：

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基于双曲函数的鲁棒滑模微分器和非线性动力学观测器的框架

本文提出了现代设计的滑模微分器和状态观测器，分别利用切向和反正弦双曲函数来评估未知的非线性信号导数和未知的内部系统状态。与基于高增益不连续函数的初步观察器/微分器不同，所提出的框架的实用性在于它提供了平滑和稳健的估计，而不会引发不可接受的振荡（颤振）。此外，所采用的双曲线函数将在有限时间内将信号或状态估计中的各种偏差驱动到非常接近的原点邻域，这通过李雅普诺夫的能量函数得到证实。为了证明所介绍技术的效率，还说明了估计非线性信号的导数和电机内部状态的两个示例，其中包含随时间变化的不确定性。最后，将所提出的微分器获得的模拟结果与以前制定的设计，如高阶滑模微分器（HOSMD）和一致收敛微分器（UCD）进行了进一步的比较。