An extended state observer with adjustable bandwidth for measurement noise

doi:10.23919/JSEE.2023.000166

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (1): 233-241.doi: 10.23919/JSEE.2023.000166

• CONTROL THEORY AND APPLICATION • Previous Articles

An extended state observer with adjustable bandwidth for measurement noise

Shihua ZHANG(), Xiaohui QI(), Sen YANG()

¹ Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang 050053, China

Received:2022-10-20 Online:2024-02-18 Published:2024-03-05
Contact: Shihua ZHANG E-mail:zsh3991171@126.com;qi-xh@163.com;sanmu_oec@163.com
About author:
ZHANG Shihua was born in1981. She received her B.E. and M.E. degrees from Hebei Normal University, Shijiazhuang, China, in 2003 and 2006, respectively, and Ph.D. degree from the Army Engineering University of PLA, Shijiazhuang, China, in 2023. Her research interests include theory and application of active disturbance rejection control and flight control of unmanned aerial vehicle. E-mail: zsh3991171@126.com

QI Xiaohui was born in1963. She received her B.E., M.E., and Ph.D. degrees from Nanjing University of Science and Technology, Nanjing, China, in 1983, 1988, 2010, respectively. She is a professor at the Department of Unmanned Aerial Vehicle Engineering, Army Engineering University of PLA. Her research interests include flight control theory and application or unmanned aerial vehicle, and adaptive control. E-mail: qi-xh@163.com

YANG Sen was born in1984. He received his B.E. degree from Guilin University of Electronic Technology Guilin, China, in 2007, M.E. and Ph.D. degrees from the Department of Mechanical Engineering College, Shijiazhuang, China, in 2009 and 2013, respectively. He is a lecturer and the director at the Department of Unmanned Aerial Vehicle Engineering, Army Engineering University of PLA. His research interests include system parameter and identification and adaptive control. E-mail: sanmu_oec@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (61873126).

Abstract

Abstract:

In this paper, a bandwidth-adjustable extended state observer (ABESO) is proposed for the systems with measurement noise. It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise, which conflicts with observation accuracy. Therefore, we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system. The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error. When the tracking error decreases, the bandwidth decreases to suppress the noise, otherwise the bandwidth does not change. It is proven that the error dynamics are bounded and converge in finite time. The relationship between the upper bound of the estimation error and the scaling factor is given. When the scaling factor is less than 1, the ABESO has higher estimation accuracy than the linear extended state observer (LESO). Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments. The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.

Key words: extended state observer (ESO), boundedness and convergence, adjustable bandwidth, measurement noise

Shihua ZHANG, Xiaohui QI, Sen YANG. An extended state observer with adjustable bandwidth for measurement noise[J]. Journal of Systems Engineering and Electronics, 2024, 35(1): 233-241.

Figures/Tables 12

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References 16

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Index	Expression
$ {J_{{e_x}}} $	$ \dfrac{1}{t}\displaystyle\int_0^t \| x(s) - \hat x(s)\|{\mathrm{d}}s $
$ {J_{{e_{\dot x}}}} $	$ \dfrac{1}{t}\displaystyle\int_0^t \| \dot x(s) - \dot {\hat x}(s)\|{\mathrm{d}}s $
$ {J_{{e_d}}} $	$ \dfrac{1}{t}\displaystyle\int_0^t \| d(s) - \hat d(s)\|{\mathrm{d}}s $

Index	w_o
Index	4	5	6	7	8	9	10
$ {J_{{e_x}}} $	1.76	1.68	1.65	1.66	1.72	1.74	1.77
$ {J_{{e_{\dot x}}}} $	10.79	10.73	11.53	12.75	14.85	16.83	17.21
$ {J_{{e_d}}} $	26.03	26.32	28.73	33.48	40.43	48.91	59.03

Index	$ {w_o} $
Index	5			6			7
$ {e_i} $	$ {e_x} $	$ {e_{\dot x}} $	$ {e_d} $	$ {e_x} $	$ {e_{\dot x}} $	$ {e_d} $	$ {e_x} $	$ {e_{\dot x}} $	$ {e_d} $
$ {t_r} $	0.7	0.64	2.09	0.62	0.52	1.56	0.5	0.46	1.34
$ \|{e_{{\text{max}}}}\| $	0.04	0.39	0.53	0.04	0.43	0.62	0.05	0.51	0.73

Index	$ {w_o} $
Index	4	5	6	7	8	9	10
$ {J_{{e_x}}} $	2.84	2.76	2.68	2.59	2.78	2.66	2.77
$ {J_{{e_{\dot x}}}} $	19.91	23.34	25.85	27.97	34.49	35.36	39.93
$ {J_{{e_d}}} $	39.10	53.34	70.59	89.23	119.52	142.82	171.19

Index	$ {w_o} $
Index	5			6			7
$ {e_i} $	$ {e_x} $	$ {e_{\dot x}} $	$ {e_d} $	$ {e_x} $	$ {e_{\dot x}} $	$ {e_d} $	$ {e_x} $	$ {e_{\dot x}} $	$ {e_d} $
$ {t_r} $	0.64	0.57	2.22	0.51	0.47	2.22	0.47	0.39	2.22
$ \|{e_{{\text{max}}}}\| $	0.06	0.61	0.94	0.06	0.71	1.26	0.06	0.97	1.64

An extended state observer with adjustable bandwidth for measurement noise

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Algorithm	Index
Algorithm	$ {J_{{e_x}}} $	$ {J_{{e_{\dot x}}}} $	$ {J_{{e_d}}} $	$ {t_r} $($ {e_x} $)	$ {t_r} $($ {e_{\dot x}} $)	$ {t_r} $($ {e_d} $)
LESO	1.66	12.75	33.48	0.5	0.46	1.34
BESO	2.59	27.97	89.23	0.47	0.39	2.22
ABESO	1.57	11.03	28.37	0.48	0.41	1.33
Reduction¹/%	4.89	13.46	15.28	4	10.87	0.75
Reduction²/%	39.26	60.56	68.21	-2.13	-5.13	40.09

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Index	$ {w_o} $
Index	4	5	6	7	8	9	10
$ {J_{{e_x}}} $	1.57	1.50	1.54	1.57	1.67	1.72	1.87
$ {J_{{e_{\dot x}}}} $	8.97	8.81	10.10	11.03	14.13	15.63	21.54
$ {J_{{e_d}}} $	23.26	22.67	25.05	28.37	38.32	46.61	63.23