0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Atassi, A. N. , and Khalil, H. K. , 1999, “ A Separation Principle for the Stabilization of a Class of Nonlinear Systems,” IEEE Trans. Autom. Control, 44(9), pp. 1672–1687. [CrossRef]
Freidovish, L. B. , and Khalil, H. K. , 2008, “ Performance Recovery of Feedback-Linearization Based Designs,” IEEE Trans. Autom. Control, 53(10), pp. 2324–2334. [CrossRef]
Qian, C. , and Lin, W. , 2002, “ Output Feedback Control of a Class of Nonlinear Systems: A Nonseparation Principle Paradigm,” IEEE Trans. Autom. Control, 47(10), pp. 1710–1715. [CrossRef]
Yang, J. , Chen, W.-H. , and Li, S. , 2011, “ Non-Linear Disturbance Observer-Based Control for Systems With Mismatched Disturbances/Uncertainties,” IET Control Theory Appl., 5(18), pp. 2053–2062. [CrossRef]
Guo, B.-Z. , and Zhao, Z.-L. , 2013, “ On Convergence of the Nonlinear Active Disturbance Rejection Control for MIMO Systems,” SIAM J. Control Optim., 51(2), pp. 1727–1757. [CrossRef]
Li, S. , Yang, J. , Chen, W.-H. , and Chen, X. , 2014, Disturbance Observer-Based Control: Methods and Applications, CRC Press, Boca Raton.
Chen, H. , 2014, “ Robust Stabilization for a Class of Dynamic Feedback Uncertain Nonholonomic Mobile Robots With Input Saturation,” Int. J. Control Autom. Syst., 12(6), pp. 1216–1224. [CrossRef]
Chen, H. , Wang, C. , Liang, Z. , Zhang, D. , and Zhang, H. , 2014, “ Robust Practical Stabilization of Nonholonomic Mobile Robots Based on Visual Servoing Feedback With Inputs Saturation,” Asian J. Control, 16(3), pp. 692–702. [CrossRef]
Xu, B. , Shi, Z. , and Yang, C. , 2015, “ Composite Fuzzy Control of a Class of Uncertain Nonlinear Systems With Disturbance Observer,” Nonlinear Dyn., 80(1), pp. 341–351. [CrossRef]
Chen, W.-H. , Ballance, D. J. , Gawthrop, P. J. , and O'Reilly, J. , 2000, “ A Nonlinear Disturbance Observer for Robotic Manipulators,” IEEE Trans. Ind. Electron., 47(4), pp. 932–938. [CrossRef]
Chen, W. H. , 2003, “ Harmonic Disturbance Observer for Nonlinear Systems,” ASME J. Dyn. Syst., Meas., Control, 125(1), pp. 114–117. [CrossRef]
Chen, W.-H. , 2004, “ Disturbance Observer Based Control for Nonlinear Systems,” IEEE/ASME Trans. Mechatron., 9(4), pp. 706–710. [CrossRef]
Chen, W.-H. , Yang, J. , Guo, L. , and Li, S. , 2016, “ Disturbance Observer-Based Control and Related Methods: An Overview,” IEEE Trans. Ind. Electron., 63(2), pp. 1083–1095. [CrossRef]
Chen, W.-H. , 2003, “ Nonlinear Disturbance Observer-Enhanced Dynamic Inversion Control of Missiles,” J. Guid. Control Dyn., 26(1), pp. 161–166. [CrossRef]
Yao, J. , Jiao, Z. , and Ma, D. , 2015, “ Output Feedback Robust Control of Direct Current Motors With Nonlinear Friction Compensation and Disturbance Rejection,” ASME J. Dyn. Syst., Meas., Control, 137(4), p. 041004. [CrossRef]
Errouissi, R. , Ouhrouche, M. , Chen, W.-H. , and Trzynadlowski, A. M. , 2012, “ Robust Cascaded Nonlinear Predictive Control of a Permanent Magnet Synchronous Motor With Antiwindup Compensator,” IEEE Trans. Ind. Electron., 59(8), pp. 3078–3088. [CrossRef]
Liu, C. J. , Chen, W.-H. , and Andrews, J. , 2012, “ Tracking Control of Small-Scale Helicopters Using Explicit Nonlinear MPC Augmented With Disturbance Observers,” Control Eng. Pract., 20(3), pp. 258–268. [CrossRef]
Wang, C. , Li, X. , Guo, L. , and Li, Y. , 2014, “ A Nonlinear-Disturbance-Observer-Based DC-Bus Voltage Control for a Hybrid AC/DC Microgrid,” IEEE Trans. Power Electron., 29(11), pp. 6162–6177. [CrossRef]
Gupta, A. , and OMalley, M. K. , 2011, “ Disturbance-Observer-Based Force Estimation for Haptic Feedback,” ASME J. Dyn. Syst., Meas., Control, 133(1), p. 014505. [CrossRef]
Xue, W. , and Huang, Y. , 2014, “ On Performance Analysis of ADRC for a Class of MIMO Lower-Triangular Nonlinear Uncertain Systems,” ISA Trans., 53(4), pp. 955–962. [CrossRef] [PubMed]
Yin, C. , Cheng, Y. , Chen, Y. , Stark, B. , and Zhong, S. , 2015, “ Adaptive Fractional-Order Switching-Type Control Method Design for 3D Fractional-Order Nonlinear Systems,” Nonlinear Dyn., 82(1), pp. 39–52. [CrossRef]
Khalil, H. K. , 2002, Nonlinear Systems, 3rd ed., Prentice Hall, Upper Saddle River, NJ.
Nesline, F. W. , Wells, H. B. , and Zarchan, P. , 1981, “ Combined Optimal/Classical Approach to Robust Missile Autopilot Design,” AIAA J. Guid. Control, 4(3), pp. 316–322. [CrossRef]
Misawa, E. A. , 1997, “ Discrete-Time Sliding Mode Control for Nonlinear Systems With Unmatched Uncertainties and Uncertain Control Vector,” ASME J. Dyn. Syst., Meas., Control, 119(3), pp. 503–512. [CrossRef]
Chen, W.-H. , Ballance, D. J. , Gawthrop, P. J. , and O'Reilly, J. , 1999, “ Nonlinear PID Predictive Controller,” IEE Proc. Control Theory Appl., 146(6), pp. 603–611. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Block diagram of nonlinear DOBC

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 4

Mass spring system

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In