Frequency analysis of a discrete-time fast nonlinear tracking differentiator algorithm based on isochronic region method

Zhizhou Zhang; Yueliang Pan; Weilong Zhao; Jinchu Zhang; Zheng Zi; Yuan Xie; Hehong Zhang; Zhizhou Zhang; Yueliang Pan; Weilong Zhao; Jinchu Zhang; Zheng Zi; Yuan Xie; Hehong Zhang

doi:10.3934/era.2024238

Electronic Research Archive

2024, Volume 32, Issue 9: 5157-5175. doi: 10.3934/era.2024238

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Research article Topical Sections

Frequency analysis of a discrete-time fast nonlinear tracking differentiator algorithm based on isochronic region method

1.
School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China
2.
College of Computer and Data Science, Fuzhou University, Fuzhou 350108, China

Received: 14 July 2024 Revised: 19 August 2024 Accepted: 27 August 2024 Published: 02 September 2024

In fault detection, feedback control, and other fields, real-time differential estimation of a given signal in a complex noise environment is an important but challenging task. In this paper, a discrete-time fast nonlinear tracking differentiator (FNTD) based on hyperbolic tangent functions was proposed. To start, the differential signal acquisition problem was equated to the time-optimal control (TOC) law for constructing a double-integral system using a state feedback approach. Next, the FNTD algorithm based on the hyperbolic tangent function was presented by utilizing the isochronic region (IR) method in the discrete time domain. Then, the frequency-domain characteristics of the FNTD were analyzed and the rule for tuning the parameters was provided by the frequency scan test method. Finally, the simulation results demonstrated that the proposed FNTD had fast and accurate tracking performance, as well as excellent filtering and differential extraction capability compared with other differentiators.
Citation: Zhizhou Zhang, Yueliang Pan, Weilong Zhao, Jinchu Zhang, Zheng Zi, Yuan Xie, Hehong Zhang. Frequency analysis of a discrete-time fast nonlinear tracking differentiator algorithm based on isochronic region method[J]. Electronic Research Archive, 2024, 32(9): 5157-5175. doi: 10.3934/era.2024238

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Abstract

In fault detection, feedback control, and other fields, real-time differential estimation of a given signal in a complex noise environment is an important but challenging task. In this paper, a discrete-time fast nonlinear tracking differentiator (FNTD) based on hyperbolic tangent functions was proposed. To start, the differential signal acquisition problem was equated to the time-optimal control (TOC) law for constructing a double-integral system using a state feedback approach. Next, the FNTD algorithm based on the hyperbolic tangent function was presented by utilizing the isochronic region (IR) method in the discrete time domain. Then, the frequency-domain characteristics of the FNTD were analyzed and the rule for tuning the parameters was provided by the frequency scan test method. Finally, the simulation results demonstrated that the proposed FNTD had fast and accurate tracking performance, as well as excellent filtering and differential extraction capability compared with other differentiators.

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