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Volume 13
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10.3390/app13158797
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Article

Convergence Analysis of the Phase-Scheduled-Command FXLMS Algorithm with Phase Error

by
Yushuai Wang
1,*,
Feng Liu
2,
Zhenrong Fu
1,
Lianxin Yang
1 and
Pengfei Wang
1
1
College of Mechatronic Engineering, North University of China, Taiyuan 030051, China
2
China Orient Institute of Noise and Vibration, Beijing 100085, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(15), 8797; https://doi.org/10.3390/app13158797
Submission received: 5 June 2023 / Revised: 23 July 2023 / Accepted: 28 July 2023 / Published: 30 July 2023
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Abstract

In this paper, a phase-scheduled-command filtered-x least mean square (FXLMS) algorithm with a phase error between the disturbance and command signal is analyzed in detail. The influence of the phase error on the control effort, convergence time constant and performance of convergence is explained for both stationary and nonstationary disturbance signal cases. An estimation ratio, in both stationary and nonstationary disturbance cases, of the pseudo-error MSE convergence performance is also developed and discussed. Simulation results were collected to verify the analysis. The results show that, for both stationary and nonstationary disturbance, the phase error may heavily increase the distance of the optimum vector from the initial value, leading to a large control effort, a large convergence time constant and poor convergence performance. The estimation ratio also has a satisfactory performance for estimating the influence of the phase error.
Keywords: active noise control; phase-scheduled-command FXLMS; active sound profiling; phase error active noise control; phase-scheduled-command FXLMS; active sound profiling; phase error

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MDPI and ACS Style

Wang, Y.; Liu, F.; Fu, Z.; Yang, L.; Wang, P. Convergence Analysis of the Phase-Scheduled-Command FXLMS Algorithm with Phase Error. Appl. Sci. 2023, 13, 8797. https://doi.org/10.3390/app13158797

AMA Style

Wang Y, Liu F, Fu Z, Yang L, Wang P. Convergence Analysis of the Phase-Scheduled-Command FXLMS Algorithm with Phase Error. Applied Sciences. 2023; 13(15):8797. https://doi.org/10.3390/app13158797

Chicago/Turabian Style

Wang, Yushuai, Feng Liu, Zhenrong Fu, Lianxin Yang, and Pengfei Wang. 2023. "Convergence Analysis of the Phase-Scheduled-Command FXLMS Algorithm with Phase Error" Applied Sciences 13, no. 15: 8797. https://doi.org/10.3390/app13158797

APA Style

Wang, Y., Liu, F., Fu, Z., Yang, L., & Wang, P. (2023). Convergence Analysis of the Phase-Scheduled-Command FXLMS Algorithm with Phase Error. Applied Sciences, 13(15), 8797. https://doi.org/10.3390/app13158797

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