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Augmented nonlinear differentiator design and application to nonlinear uncertain systems

机译：增强非线性微分器设计及应用于非线性不确定系统

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In this paper, an augmented nonlinear differentiator (AND) based on sigmoid function is developed to calculate the noise-less time derivative under noisy measurement condition. The essential philosophy of proposed AND in achieving high attenuation of noise effect is established by expanding the signal dynamics with extra state variable representing the integrated noisy measurement, then with the integral of measurement as input, the augmented differentiator is formulated to improve the estimation quality. The prominent advantages of the present differentiation technique are: (i) better noise suppression ability can be achieved without appreciable delay; (ii) the improved methodology can be readily extended to construct augmented high-order differentiator to obtain multiple derivatives. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, the robust control problems of nonlinear uncertain systems, including a numerical example and a mass spring system, are addressed to demonstrate the effectiveness of AND in precisely estimating the disturbance and providing the unavailable differential estimate to implement output feedback based controller. (C) 2016 ISA. Published by Elsevier Ltd. All rights reserved.
机译：在本文中，开发了一种基于SIGMOID函数的增强非线性微分器（和）来计算噪声测量条件下的噪声时间衍生物。通过将信号动态扩展到具有额外的状态变量的信号动态来建立提出和实现高衰减的基本哲学，即表示集成嘈杂测量，然后用作为输入的测量的积分，制定了增强的微分器以提高估计质量。本分化技术的突出优点是：（i）可以实现更好的噪声抑制能力，而无明显延迟; （ii）可以容易地扩展改进的方法，以构建增强的高阶微分器以获得多种衍生物。此外，通过奇异的扰动理论研究了对噪声的收敛性和鲁棒性能分别描述了功能方法。而且，给出了与若干经典差分差的比较来说明噪声抑制的优越性。最后，解决了非线性不确定系统的鲁棒控制问题，包括数值例子和质量弹簧系统，以证明衡量干扰和提供基于输出反馈的控制的不可用的差异估计的效果和精确估计的有效性。 （c）2016 ISA。 elsevier有限公司出版。保留所有权利。

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