Active disturbance rejection control based on cascade high-order extended state observer for systems with time-varying disturbances and measurement noise

doi:10.23919/JSEE.2025.000094

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (6): 1679-1691.doi: 10.23919/JSEE.2025.000094

• CONTROL THEORY AND APPLICATION • Previous Articles

Active disturbance rejection control based on cascade high-order extended state observer for systems with time-varying disturbances and measurement noise

Bin FENG(), Weihua FAN(), Yang GAO(), Qingwei CHEN()

School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

Received:2024-09-27 Online:2025-12-18 Published:2026-01-07
Contact: Weihua FAN E-mail:fengbin@njust.edu.cn;fanweihua@njust.edu.cn;gaoyang_zdh@njust.edu.cn;cqw1002@sina.com
About author:
FENG Bin was born in 1995. He received his B.E. degree from Nanjing University of Posts and Telecommunications, Nanjing, China, in 2020. He is currently pursuing his Ph.D. degree in control science and engineering with the School of Automation, Nanjing University of Science and Technology, Nanjing. His research interests include high-precision servo control, active disturbance rejection control, and adaptive control. E-mail: fengbin@njust.edu.cn

FAN Weihua was born in 1975. He received his B.E., M.E., and Ph.D. degrees from Nanjing University of Science and Technology, Nanjing, China, in 1998, 2001, 2005, respectively. He is an associate professor at the School of Automation, Nanjing University of Science and Technology. His research interests include intelligent control and intelligent systems, networked control systems, servo systems, and intelligent robots. E-mail: fanweihua@njust.edu.cn

GAO Yang was born in 1994. He received his Ph.D. degree from Nanjing University of Science and Technology in 2021. He is an associate professor at the School of Automation, Nanjing University of Science and Technology. His research interest includes the cooperative control technology of unmanned aircraft swarm systems. E-mail: gaoyang_zdh@njust.edu.cn

CHEN Qingwei was born in 1963. He received his B.S. degree in electric engineering from Jiangsu University, in 1985, and Ph.D. degree from Nanjing University of Science and Technology, in 2005. He was a recipient of the Second Prize of the National Defense Technology Invention and hosts many national projects about servo system control and robot control. He is currently a professor at Nanjing University of Science and Technology. His research interests include servo system control, machine learning, and robot control. E-mail: cqw1002@sina.com
Supported by:
This work was supported by the National Natural Science Foundation of China (62203222), the Science and Technology Major Project of Jiangsu Province (BG2024041), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX24_0676).

Abstract

Abstract:

This paper investigates the high-performance control issues of systems affected by time-varying disturbances and measurement noise. Conventionally, active disturbance rejection control (ADRC) is a favorable control strategy to reject unknown disturbances and uncertainties. However, its control performance is limited because standard extended state observer (ESO) struggles to effectively estimate time-varying disturbances. The emergence of high-order ESO (HESO) alleviates the limitation. Unfortunately, it deteriorates the noise suppression capability when the disturbance rejection is enhanced. To tackle this challenge, an improved ADRC with cascade HESO (CHESO) is proposed. A comprehensive theoretical analysis associated with the performance of HESO is given for the first time. The presented analyses provide an intuitive understanding of the performance of HESO. Then, a novel CHESO is developed. The convergence of CHESO is proved via input-to-state stable theory. Extensive frequency domain analyses indicate that CHESO has stronger disturbance rejection and high-frequency noise attenuation performance than ESO and HESO without increasing the observer bandwidth. Comparative simulations conducted on a servo control system validate the effectiveness and preponderance of the proposed method.

Key words: active disturbance rejection control (ADRC), extended state observer (ESO), time-varying disturbance, noise suppression

Bin FENG, Weihua FAN, Yang GAO, Qingwei CHEN. Active disturbance rejection control based on cascade high-order extended state observer for systems with time-varying disturbances and measurement noise[J]. Journal of Systems Engineering and Electronics, 2025, 36(6): 1679-1691.

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Integral criteria	Observer type
Integral criteria	ESO	HESO	CHESO
$\displaystyle\int_0^{10} {\left\| {r(t) - y(t)} \right\|{\mathrm{d}}t} $	0.00928	0.00181	0.00181
$\displaystyle\int_0^{10} {\left\| {\dot r(t) - \dot y(t)} \right\|} {\mathrm{d}}t$	0.048	0.028	0.014
$\displaystyle\int_0^{10} {\left\| {u(t)} \right\|{\mathrm{d}}t} $	23.45	23.62	23.55
$\displaystyle\int_0^{10} {\left\| {\dot u(t)} \right\|{\mathrm{d}}t} $	289.5	746.0	119.0
$\displaystyle\int_0^{10} {\left\| {{x_3}(t) - {{\hat x}_3}(t)} \right\|{\mathrm{d}}t} $	8.54	12.52	2.71

Index of comparison	ESO	HESO	CHESO
Number of observer state variables	3	4	8
Observer design complexity	Lower	Medium	Higher
Disturbance estimation accuracy	Lower	Medium	Higher
Disturbance rejection ability at low frequency	Lower	Medium	Higher
Noise suppression ability at high frequency	Medium	Lower	Higher

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Active disturbance rejection control based on cascade high-order extended state observer for systems with time-varying disturbances and measurement noise

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