In this article we illustrate how the property of differential flatness can be advantageously joined to the sliding mode controller design methodology for the active stabilization of nonlinear mechanical vibration systems. The proposed scheme suitably combines off-line trajectory planning and an on-line “smoothed” sliding mode feedback trajectory tracking scheme for regulating the evolution of the flat output variables toward the desired equilibria. [S0022-0434(00)00404-4]
Issue Section:
Technical Papers
1.
Fliess
, M.
, Le´vine
, J.
, Martı´n
, P.
, and Rouchon
, P.
, 1995
, “Flatness and defect of nonlinear systems: Introductory theory and examples
,” Int. J. Control
, 61
, pp. 1327
–1361
.2.
Fliess
, M.
, Le´vine
, J.
, Martı´n
, P.
, and Rouchon
, P.
, 1999
, “A Lie-Ba¨cklund approach to equivalence and flatness
,” IEEE Trans. Autom. Control
, 44
, No. 5
, pp. 922
–937
.3.
Sira-Ramı´rez
, H.
, 2000
, “Passivity versus flatness in the regulation of an exothermic chemical reactor
,” Eur. J. Control
, 4
, pp. 1
–17
.4.
Utkin, V., 1977, Sliding Modes and Their Applications in Variable Structure Systems, MIR Publishers, Moscow.
5.
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.
6.
Thomson, W. T., 1981, Theory of Vibrations with Applications, George, Allen and Unwin, London.
7.
Inman, D., 1994, Engineering Vibration, Prentice Hall, New York.
8.
Le´vine, J., 1999, “Are there new industrial perspectives in the control of mechanical systems?” Advances in Control, Paul M. Frank, ed., Springer, London.
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by ASME
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