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TECHNICAL PAPERS

Sliding Mode Control of Nonlinear Mechanical Vibrations

[+] Author and Article Information
Hebertt Sira-Ramı́rez

CINVESTAV-IPN, Dept. Ingenierı́a Eléctica, Av. IPN # 2508, Col. San Pedro Zacatenco, A.P. 14740, 7300 México D.F., Méxicoe-mail: hsira@mail.cinvestav.mx

Orestes Llanes-Santiago

Instituto Superior Politécnico J. A. Echeverrı́a, Departamento de Ingenierı́a Eléctrica, La Habana, Cubae-mail: orestes@electrica.ispjae.edu.cu

J. Dyn. Sys., Meas., Control 122(4), 674-678 (Feb 25, 2000) (5 pages) doi:10.1115/1.1316788 History: Received February 25, 2000
Copyright © 2000 by ASME
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References

Fliess,  M., Lévine,  J., Martı́n,  P., and Rouchon,  P., 1995, “Flatness and defect of nonlinear systems: Introductory theory and examples,” Int. J. Control, 61, pp. 1327–1361.
Fliess,  M., Lévine,  J., Martı́n,  P., and Rouchon,  P., 1999, “A Lie-Bäcklund approach to equivalence and flatness,” IEEE Trans. Autom. Control, 44, No. 5, pp. 922–937.
Sira-Ramı́rez,  H., 2000, “Passivity versus flatness in the regulation of an exothermic chemical reactor,” Eur. J. Control, 4, pp. 1–17.
Utkin, V., 1977, Sliding Modes and Their Applications in Variable Structure Systems, MIR Publishers, Moscow.
Astolfi, A., and Menini, L. 1999, “Further results on decoupling with stability for Hamiltonian systems,” Stability and Stabilization of Nonlinear Systems, D. Aeyels, F. Lamnabhi-Lagarrigue and A. van der Schaft (eds.), Lecture Notes in Control and Information Sciences, Vol. 246, Springer, London.
Thomson, W. T., 1981, Theory of Vibrations with Applications, George, Allen and Unwin, London.
Inman, D., 1994, Engineering Vibration, Prentice Hall, New York.
Lévine, J., 1999, “Are there new industrial perspectives in the control of mechanical systems?” Advances in Control, Paul M. Frank, ed., Springer, London.

Figures

Grahic Jump Location
Nonlinear mechanical vibration system
Grahic Jump Location
A two stage stabilization process, via trajectory tracking with clutched control actions
Grahic Jump Location
Responses of sliding mode controlled mechanical vibration system
Grahic Jump Location
Responses of sliding mode controlled perturbed mechanical vibration system

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