Design and Implementation of an Efficient Tracking Differentiator

Xie, Ying; Zhang, Hehong; Long-hua, She; Xiao, Gaoxi; Zhai, Chao; Pan, Tso–Chien

doi:10.1109/access.2019.2930963

Cited by 12 publications

(9 citation statements)

References 26 publications

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“…A and Γ θ (see (12)), where θ = 0.25 can be driven to the region Ω 2 (see Fig. 1) when u = r(1 − 2θ).…”

Section: Convergence Analysis With Disturbancesmentioning

confidence: 99%

“…+ 1]h 2 r and the parameter θ ∈ [0, 1] has the same meaning as that in (12). Substituting (25) to (20), we have…”

Section: Convergence Analysis With Disturbancesmentioning

confidence: 99%

“…The point of intersection between Γ θ (see (12)), where θ = 0.25 and the line y = x 1 + hx 2 = h 2 r (see Fig. 1) can be determined as follows:…”

Section: Convergence Analysis With Disturbancesmentioning

confidence: 99%

“…To obatin better differentiational signals, the Fast algorithm was adopted to construct the control signal sequences when the state is at certain region around the origin (11) . Also the convergence of the Fast algorithm without consideration of any disturbances was presented (12) . In the reference (13) , to lessen the recline on the sampling time in the f han algorithm, the control strategy via the time criterion was proposed to construct the TD.…”

Section: Introductionmentioning

confidence: 99%

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Discrete-Time Optimal Control of Double Integrators and its Application in Maglev Train

Zhang

Xie

et al. 2022

IEEJ Journal IA

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Non-member Zhiqiang Long * 5 Non-member As an alternative to bang-bang control, a time optimal control (TOC) algorithm for discrete-time systems was first reported by Han (1) . This algorithm not only acts as a noise-tolerant tracking differentiator (TD) to avoid setpoint jumps in control processes, but also has wide applications in the design of controllers and observers. However, determination of the real-time state position on the phase plane involves complex boundary transformations, which renders this algorithm impractical for some engineering applications. This paper proposes a methodology for discrete-time optimal control (DTOC) of double integrators with disturbances. The closed-form solution with lower computational burden can be easily extended to general second-order systems. Further, in consideration of the inevitable disturbances in the systems, a rigorous and full-convergence proof is presented for the proposed algorithm. The results show finite-time and fast convergence as well as provide the ultimate stable attraction regions for the system states. Examples and experiments are also presented to demonstrate the effectiveness of the proposed algorithm for solving a signal processing problem in a maglev train.

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“…A and Γ θ (see (12)), where θ = 0.25 can be driven to the region Ω 2 (see Fig. 1) when u = r(1 − 2θ).…”

Section: Convergence Analysis With Disturbancesmentioning

confidence: 99%

“…+ 1]h 2 r and the parameter θ ∈ [0, 1] has the same meaning as that in (12). Substituting (25) to (20), we have…”

Section: Convergence Analysis With Disturbancesmentioning

confidence: 99%

“…The point of intersection between Γ θ (see (12)), where θ = 0.25 and the line y = x 1 + hx 2 = h 2 r (see Fig. 1) can be determined as follows:…”

Section: Convergence Analysis With Disturbancesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Discrete-Time Optimal Control of Double Integrators and its Application in Maglev Train

Zhang

Xie

et al. 2022

IEEJ Journal IA

Self Cite

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“…In [19], a fuzzy variable parameter is proposed to adjust the parameter of tracking differentiator. In [20], the impact of the algorithm parameter setting on filtering is analyzed in the frequency domain. However, these design processes are too complicated for practical engineering implementations.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Self-tuning Tracking Differentiator for Motion Measurement Sensors and Application in Wide-Bandwidth High-accuracy Servo Control

Gao

Tian

Wang

2020

Sensors

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Sensor differential signals are widely used in many systems. The tracking differentiator (TD) is an effective method to obtain signal differentials. Differential calculation is noise-sensitive. There is the characteristics of low-pass filter (LPF) in the TD to suppress the noise, but phase lag is introduced. For LPF, fixed filtering parameters cannot achieve both noise suppression and phase compensation lag compensation. We propose a fuzzy self-tuning tracking differentiator (FSTD) capable of adaptively adjusting parameters, which uses the frequency information of the signal to achieve a trade-off between the phase lag and noise suppression capabilities. Based on the frequency information, the parameters of TD are self-tuning by a fuzzy method, which makes self-tuning designs more flexible. Simulations and experiments using motion measurement sensors show that the proposed method has good filtering performance for low-frequency signals and improves tracking ability for high-frequency signals compared to fixed-parameter differentiator.

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