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Anti-disturbance control based on disturbance observer for nonlinear systems with bounded disturbances. (English) Zbl 1395.93264
Summary: A composite anti-disturbance control problem for a class of nonlinear systems is studied in this paper. There are two types of disturbances in the systems, one is the matched disturbance with bounded variation rate, the other is the unmatched time-varying disturbances. A nonlinear disturbance observer is designed to estimate the matched disturbances, which can be presented separately from the controller design. By integrating DOBC with back-stepping method, a composite DOBC and back-stepping controller is proposed, and the disturbance estimations are introduced into the design of virtual control laws to compensate the unmatched disturbances. In addition, it is proved that all the states in the closed-loop system are uniformly ultimate bounded (UUB). Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method.

MSC:
93C10 Nonlinear systems in control theory
93C73 Perturbations in control/observation systems
93B07 Observability
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93B35 Sensitivity (robustness)
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[1] Liu, H.; Li, S., Speed control for PMSM servo system using predictive functional control and extended state observer, IEEE Trans. Ind. Electron., 59, 2, 1171-1183, (2014)
[2] Zhang, Z.; Xie, X. J., Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs, IEEE Trans. Autom. Control, 59, 5, 1336-1341, (2014) · Zbl 1360.93305
[3] Xu, S.; Lam, J., h_∞ model reduction for discrete-time singular systems, Syst. Control Lett., 48, 2, 121-133, (2003) · Zbl 1134.93330
[4] Guo, L.; Cao, S. Y., Anti-disturbance control theory for systems with multiple disturbances: a survey, ISA Trans., 53, 4, 846-849, (2014)
[5] Cao, S. Y.; Yi, Y.; Guo, L., Anti-disturbance fault diagnosis for non-Gaussian stochastic distribution systems with multiple disturbances, Neurocomputing, 136, 315-320, (2014)
[6] Yao, X. M.; Guo, L., Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer, Automatica, 49, 8, 2538-2545, (2013) · Zbl 1364.93102
[7] Song, G.; Chen, F.; Xu, S., Disturbance tolerance and rejection of discrete-time stochastic systems with saturating actuators, J. Frankl. Inst., 350, 6, 1488-1499, (2013) · Zbl 1293.93697
[8] Lam, J.; Zhang, B.; Chen, Y., Reachable set estimation for discrete time linear systems with time delays, Int. J. Robust Nonlinear Control, 25, 2, 269-281, (2015) · Zbl 1305.93034
[9] Zhang, B.; Lam, J.; Xu, S., Reachable set estimation and controller design for distributed delay systems with bounded disturbances, J. Frankl. Inst., 351, 6, 3068-3088, (2014) · Zbl 1290.93020
[10] Wu, Z.; Cui, M.; Shi, P., Backstepping control in vector form for stochastic Hamiltonian systems, Siam J. Control Optim., 50, 2, 925-942, (2012) · Zbl 1247.60087
[11] Chan, S. P., A disturbance observer for robot manipulators with application to electronic components assembly, IEEE Trans. Ind. Electron., 42, 5, 487-493, (1995)
[12] Iwasaki, M.; Shibata, T.; Matsui, N., Disturbance-observer-based nonlinear friction compensation in the table drive systems, IEEE/ASME Trans. Mechatron, 4, 1, 3-8, (1999)
[13] Kemf, C. J.; Kobayashi, S., Disturbance observer and feedforward design for a highspeed direct drive positioning table, IEEE Trans. Control Syst. Technol., 7, 5, 513-526, (1999)
[14] Huang, Y.; Messner, W., A novel disturbance observer design for magnetic hard drive servo system with a rotary actuator, IEEE Trans. Magnet., 34, 4, 1892-1894, (1998)
[15] Li, S. H.; Yang, J.; Chen, W. H.; Chen, X. S., Disturbance observer based control: methods and applications, (2014), CRC Press
[16] Chen, W. H., Disturbance observer based control for nonlinear systems, IEEE/ASME Trans. Mechatron., 9, 706-710, (2004)
[17] Chen, W. H., Harmonic disturbance observer for nonlinear systems, J. Dyn. Syst. Measur. Control, 125, 1, 114-117, (2003)
[18] Chen, W. H.; Ballance, D. J.; Gawthrop, P. J., A nonlinear disturbance observer for robotic manipulators, IEEE Trans. Ind. Electron., 47, 4, 932-938, (2000)
[19] Chen, M.; Chen, W. H., Sliding mode control for a class of uncertain nonlinear system based on disturbance observer, Int. J. Adapt. Control Signal Process., 24, 1, 51-64, (2010) · Zbl 1185.93039
[20] Chen, W. H.; Guo, L., Analysis of disturbance observer based control for nonlinear systems under disturbances with bounded variation, Proceedings of International Conference on Control, ID-048, (2004)
[21] Yang, J.; Li, S.; Yu, X., Sliding-mode control for systems with mismatched uncertainties via a disturbance observer, IEEE Trans. Ind. Electron., 60, 1, 160-169, (2013)
[22] Yang, J.; Zolotas, A.; Chen, W. H., Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach, ISA Trans., 50, 3, 389-396, (2011)
[23] Guo, L.; Cao, S. Y., Anti-disturbance control for systems with multiple disturbances, (2013), CRC Press Inc
[24] Guo, L.; Chen, W. H., Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach, Int. J. Robust Nonlinear Control, 15, 109-125, (2005) · Zbl 1078.93030
[25] Zhang, H. F.; Wei, X. J.; Zhang, L. Y., Disturbance rejection for nonlinear systems with mismatched disturbances based on disturbance observer, J. Frankl. Inst., 354, 11, 4404-4424, (2017) · Zbl 1380.93214
[26] Wei, X. J.; Wu, Z. J.; Karimi, H. R., Disturbance observer-based disturbance attenuation control for a class of stochastic systems, Automatica, 63, 21-25, (2016) · Zbl 1329.93129
[27] Wei, X. J.; Guo, L., Composite disturbance-observer-based control and terminal sliding mode control for nonlinear systems with disturbances, Int. J. Control, 82, 6, 1082-1098, (2009) · Zbl 1168.93322
[28] Wei, X. J.; Guo, L., Composite disturbance-observer-based control and h_∞ control for complex continuous models, Int. J. Robust Nonlinear Control, 20, 1, 106-118, (2010) · Zbl 1191.93014
[29] Wei, X. J.; Chen, N., Composite hierarchical anti-disturbance control for nonlinear systems with DOBC and fuzzy control, Int. J. Robust Nonlinear Control, 24, 362-373, (2014) · Zbl 1279.93029
[30] Wei, X. J.; Chen, N.; Li, W. Q., Composite adaptive disturbance observer-based control for a class of nonlinear systems with multisource disturbance, Int. J. Adapt. Control Signal Process., 27, 3, 199-208, (2013) · Zbl 1273.93099
[31] Guo, L.; Wen, X. Y., Hierarchical anti-disturbance adaptive control for non-linear systems with composite disturbances and applications to missile systems, Trans. Inst. Measur. Control, 33, 8, 942-956, (2011)
[32] Sun, H.; Guo, L., Composite adaptive disturbance observer based control and back-stepping method for nonlinear system with multiple mismatched disturbances, J. Frankl. Inst., 351, 2, 1027-1041, (2014) · Zbl 1293.93120
[33] Chen, W. H., Nonlinear PID predictive control of two-link robotic manipulators, Proceedings of 6th IFAC Symposium on Robot Control, 217-222, (2000)
[34] He, W.; Zhang, S.; Ge, S. S., Boundary output-feedback stabilization of a Timoshenko beam using disturbance observer, IEEE Trans. Ind. Electron., 60, 11, 5186-5194, (2013)
[35] Tee, K. P.; Ge, S. S., Control of fully actuated Ocean surface vessels using a class of feedforward approximators, IEEE Trans. Control Syst. Technol., 14, 4, 750-756, (2006)
[36] Kim, Y. H.; Ha, I. J., Asymptotic state tracking in a class of nonlinear systems via learning-based inversion, IEEE Trans. Autom. Control, 45, 11, 2011-2017, (2000) · Zbl 0991.93096
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