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Erschienen in: Journal of Dynamical and Control Systems 1/2016

13.11.2014

Sliding Mode Control to Stabilization of a Tip-Force Destabilized Shear Beam Subject to Boundary Control Matched Disturbance

verfasst von: Jun-Jun Liu, Xin Chen, Jun-Min Wang

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 1/2016

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Abstract

In this paper, we are concerned with the boundary stabilization of a one-dimensional tip-force destabilized shear beam equation subject to boundary control matched disturbance. We use the sliding mode control (SMC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop system is proved and the “reaching condition” is obtained.

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Literatur
1.
Zurück zum Zitat Han SM, Benaroya H, Wei T. Dynamics of transversely vibrating beams using four engineering theories. J Sound Vib 1999;225:935–C988.CrossRefMATH Han SM, Benaroya H, Wei T. Dynamics of transversely vibrating beams using four engineering theories. J Sound Vib 1999;225:935–C988.CrossRefMATH
2.
Zurück zum Zitat Guo BZ, Jin FF. The active disturbance rejection and sliding mode control approach to the stabilization of Euler-Bernoulli beam equation with boundary input disturbance. Automatica 2013;49:2911–2918.CrossRefMathSciNet Guo BZ, Jin FF. The active disturbance rejection and sliding mode control approach to the stabilization of Euler-Bernoulli beam equation with boundary input disturbance. Automatica 2013;49:2911–2918.CrossRefMathSciNet
3.
Zurück zum Zitat Vazquez R, Rubio-Sierra FJ, Stark RW. Multimodal analysis of force spectroscopy based on a transfer function study of micro-cantilevers. Nanotechnology 2007;18:185–504.CrossRef Vazquez R, Rubio-Sierra FJ, Stark RW. Multimodal analysis of force spectroscopy based on a transfer function study of micro-cantilevers. Nanotechnology 2007;18:185–504.CrossRef
4.
Zurück zum Zitat de Queiroz MS, Dawson DM, Agarwal M, Zhang F. Adaptive nonlinear boundary control of a flexible link robot arm. IEEE Trans Robot Autom 1999;15:779–787.CrossRef de Queiroz MS, Dawson DM, Agarwal M, Zhang F. Adaptive nonlinear boundary control of a flexible link robot arm. IEEE Trans Robot Autom 1999;15:779–787.CrossRef
5.
Zurück zum Zitat de Queiroz MS, Dawson DM, Nagarkatti SP, Zhang F. Lyapunov-based control of mechanical systems. Boston: Birkhauser; 2000.CrossRefMATH de Queiroz MS, Dawson DM, Nagarkatti SP, Zhang F. Lyapunov-based control of mechanical systems. Boston: Birkhauser; 2000.CrossRefMATH
7.
Zurück zum Zitat Luo ZH, Guo BZ, Morgul O. Stability and stabilization of infinite dimensional systems with applications. Berlin: Springer-Verlag; 1999.CrossRefMATH Luo ZH, Guo BZ, Morgul O. Stability and stabilization of infinite dimensional systems with applications. Berlin: Springer-Verlag; 1999.CrossRefMATH
9.
Zurück zum Zitat Krstic M, Guo BZ, Balogh A, Smyshlyaev A. Control of a tip-force destabilized shear beam by observer-based boundary feedback. SIAM J Control Optim 2008;47:553–574.CrossRefMathSciNetMATH Krstic M, Guo BZ, Balogh A, Smyshlyaev A. Control of a tip-force destabilized shear beam by observer-based boundary feedback. SIAM J Control Optim 2008;47:553–574.CrossRefMathSciNetMATH
10.
Zurück zum Zitat Luo ZH, Guo BZ. Shear force feedback control of a single link flexible robot with revolute joint. IEEE Trans Automat Control 1997;42:53–65.CrossRefMathSciNetMATH Luo ZH, Guo BZ. Shear force feedback control of a single link flexible robot with revolute joint. IEEE Trans Automat Control 1997;42:53–65.CrossRefMathSciNetMATH
11.
Zurück zum Zitat Cheng MB, Radisavljevic V, Su WC. Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties. Automatica 2011;47:381–387.CrossRefMathSciNetMATH Cheng MB, Radisavljevic V, Su WC. Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties. Automatica 2011;47:381–387.CrossRefMathSciNetMATH
12.
Zurück zum Zitat Guo BZ, Jin FF. Sliding mode and active disturbance rejection control to the stabilization of anti-stable one-dimensional wave equation subject to boundary input disturbance. IEEE Trans Automat Control 2013;58:1269–1274.CrossRefMathSciNet Guo BZ, Jin FF. Sliding mode and active disturbance rejection control to the stabilization of anti-stable one-dimensional wave equation subject to boundary input disturbance. IEEE Trans Automat Control 2013;58:1269–1274.CrossRefMathSciNet
13.
Zurück zum Zitat Guo BZ, Jin FF. The active disturbance rejection and sliding mode control approach to the stabilization of Euler-Bernoulli beam equation with boundary input disturbance. Automatica 2013;49:2911–2918.CrossRefMathSciNet Guo BZ, Jin FF. The active disturbance rejection and sliding mode control approach to the stabilization of Euler-Bernoulli beam equation with boundary input disturbance. Automatica 2013;49:2911–2918.CrossRefMathSciNet
14.
Zurück zum Zitat Guo BZ, Liu JJ. Sliding mode and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance. Int J Robust Nonlinear Control 2014;24:2194–2212.CrossRefMATH Guo BZ, Liu JJ. Sliding mode and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance. Int J Robust Nonlinear Control 2014;24:2194–2212.CrossRefMATH
15.
Zurück zum Zitat Han JQ. From PID to active disturbance rejection control. IEEE Trans Ind Electron 2009;56:900–906.CrossRef Han JQ. From PID to active disturbance rejection control. IEEE Trans Ind Electron 2009;56:900–906.CrossRef
16.
Zurück zum Zitat Vincent J, Morris D, Usher N, Gao Z, Zhao S, Nicoletti A, Zheng Q. On active disturbance rejection based control design for superconducting RF cavities. Nucl Inst Methods Phys Res A 2011;643:11–16.CrossRef Vincent J, Morris D, Usher N, Gao Z, Zhao S, Nicoletti A, Zheng Q. On active disturbance rejection based control design for superconducting RF cavities. Nucl Inst Methods Phys Res A 2011;643:11–16.CrossRef
17.
Zurück zum Zitat Guo BZ, Zhao ZL. On the convergence of extended state observer for nonlinear systems with uncertainty. Syst Control Lett 2011;60:420–430.CrossRefMathSciNetMATH Guo BZ, Zhao ZL. On the convergence of extended state observer for nonlinear systems with uncertainty. Syst Control Lett 2011;60:420–430.CrossRefMathSciNetMATH
18.
Zurück zum Zitat Guo BZ, Kang W. The Lyapunov approach to boundary stabilization of an anti-stable one-dimensional wave equation with boundary disturbance. Int J Robust Nonlinear Control 2014;24:54–69.CrossRefMathSciNetMATH Guo BZ, Kang W. The Lyapunov approach to boundary stabilization of an anti-stable one-dimensional wave equation with boundary disturbance. Int J Robust Nonlinear Control 2014;24:54–69.CrossRefMathSciNetMATH
19.
Zurück zum Zitat Pisano A, Orlov Y, Usai E. Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J Control Optim 2011;49:363–382.CrossRefMathSciNetMATH Pisano A, Orlov Y, Usai E. Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J Control Optim 2011;49:363–382.CrossRefMathSciNetMATH
20.
Zurück zum Zitat Smyshlyaev A, Krist M. Closed form boundary state feedbacks for a class of 1-D partial integro-differential equations. IEEE Trans Automat Control 2004;49:2185–2202.CrossRefMathSciNet Smyshlyaev A, Krist M. Closed form boundary state feedbacks for a class of 1-D partial integro-differential equations. IEEE Trans Automat Control 2004;49:2185–2202.CrossRefMathSciNet
21.
Zurück zum Zitat Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer-Verlag; 1983.CrossRefMATH Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer-Verlag; 1983.CrossRefMATH
22.
Zurück zum Zitat Polyanin AD, Zaltsev VF. Handbook of exact solutions for ordinary differential equation. Boca Raton, FL: CRC Press; 1995. Polyanin AD, Zaltsev VF. Handbook of exact solutions for ordinary differential equation. Boca Raton, FL: CRC Press; 1995.
23.
Zurück zum Zitat Tucsnak M, Weiss G. Observation and control for operator semigroups. Birkhauser: Basel; 2000. Tucsnak M, Weiss G. Observation and control for operator semigroups. Birkhauser: Basel; 2000.
24.
Zurück zum Zitat Weiss G. Admissibility of unbounded control operators, SIAM. J Control Optim 1989;27:527–545.CrossRefMATH Weiss G. Admissibility of unbounded control operators, SIAM. J Control Optim 1989;27:527–545.CrossRefMATH
Metadaten
Titel
Sliding Mode Control to Stabilization of a Tip-Force Destabilized Shear Beam Subject to Boundary Control Matched Disturbance
verfasst von
Jun-Jun Liu
Xin Chen
Jun-Min Wang
Publikationsdatum
13.11.2014
Verlag
Springer US
Erschienen in
Journal of Dynamical and Control Systems / Ausgabe 1/2016
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-014-9262-3

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