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Research Papers

Robust Control of Uncertain Nonlinear Systems: A Nonlinear DOBC Approach

[+] Author and Article Information
Wen-Hua Chen

Department of Aeronautical and Automotive Engineering,
Loughborough University,
Leicestershire LE11 3TU, UK
e-mail: w.chen@lboro.ac.uk

Jun Yang

School of Automation,
Southeast University,
Nanjing 210096, China
e-mail: j.yang84@seu.edu.cn

Zhenhua Zhao

School of Automation,
Southeast University,
Nanjing 210096, China
e-mail: hndcdfzzh@163.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 26, 2014; final manuscript received February 29, 2016; published online May 3, 2016. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 138(7), 071002 (May 03, 2016) (9 pages) Paper No: DS-14-1436; doi: 10.1115/1.4033018 History: Received October 26, 2014; Revised February 29, 2016

This paper advocates disturbance observer-based control (DOBC) for uncertain nonlinear systems. Within this framework, a nonlinear controller is designed based on the nominal model in the absence of disturbance and uncertainty where the main design specifications are to stabilize the system and achieve good tracking performance. Then, a nonlinear disturbance observer is designed to not only estimate external disturbance but also system uncertainty/unmodeled dynamics. With described uncertainty, rigorous stability analysis of the closed-loop system under the composite controller is established in this paper. Finally, the robust control problems of a missile roll stabilization and a mass spring system are addressed to illustrative the distinct features of the nonlinear DOBC approach.

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References

Figures

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Fig. 1

Block diagram of nonlinear DOBC

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Fig. 2

Response curves of the roll stabilization system (25) under DOBC (28) with γ = 10 in the presence of various cases of uncertainties δf (case I): (a) roll angle, (b) roll rate, and (c) fin deflection

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Fig. 3

Response curves of the roll stabilization system (25) under DOBC (28) with various observer scalar γ in the presence of uncertainties δf=0.9 (case II): (a) roll angle, (b) roll rate, and (c) fin deflection

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Fig. 4

Mass spring system

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Fig. 5

Response curves of the mass spring system (29) under DOBC (33) with γ = 6 in the presence of various cases of uncertainties δf1 (case I): (a) displacement, (b) velocity, and (c) control force

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Fig. 6

Response curves of the mass spring system (29) under DOBC (33) with γ = 6 in the presence of various cases of uncertainties δf3 (case II): (a) displacement, (b) velocity, and (c) control force

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Fig. 7

Response curves of the mass spring system (29) under DOBC (33) with various observer scalar γ in the presence of uncertainties δf1=−50% (case III): (a) displacement, (b) velocity, and (c) control force

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Fig. 8

Response curves of the mass spring system (29) under DOBC (33) with various observer scalar γ in the presence of uncertainties δf3=−30% (case IV): (a) displacement, (b) velocity, and (c) control force

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