title: Augmented nonlinear differentiator design and application to nonlinear uncertain systems.
abstract: 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.
authors.affiliation: Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China. Electronic address: huanying3557913@sina.com.
authors.forename: Xingling
authors.initials: X
authors.lastname: Shao
authors.affiliation: Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China.
authors.forename: Jun
authors.initials: J
authors.lastname: Liu
authors.affiliation: Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China.
authors.forename: Jie
authors.initials: J
authors.lastname: Li
authors.affiliation: Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China.
authors.forename: Huiliang
authors.initials: H
authors.lastname: Cao
authors.affiliation: Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China.
authors.forename: Chong
authors.initials: C
authors.lastname: Shen
authors.affiliation: Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China.
authors.forename: Xiaoming
authors.initials: X
authors.lastname: Zhang
keywords: Augmented nonlinear differentiator (AND); Describing function; Noise suppression ability; Noisy measurement; Nonlinear uncertain systems; Output feedback based controller