Abstract
This paper considers the stabilization of non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls. To stabilize the system, the authors propose the torque and nonlinear distributed controls applied on the disk and flexible beam respectively. As long as the angular velocity of the disk does not exceed the square root of the first eigenvalue of the related self-adjoint positive definite operator, the authors show that the torque and nonlinear distributed control laws suppress the system vibrations, in the sense that the beam vibrations are forced to decay exponentially to zero and the body rotates with a desired angular velocity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baillieul J and Levi M, Rotational elastic dynamics, Phys. D, 1987, 27(1–2): 43–62.
Do K D and Pan J, Boundary control of transverse motion of marine risers with actuator dynamics. J. Sound Vibration, 2008, 318: 768–791.
Luo Z H and Guo B Z, Shear force feedback control of a single-link flexible robot with a revolute joint, IEEE Trans. Automat. Control, 1997, 42(1): 53–65.
Wang J M, Guo B Z, and Yang K Y, Stability analysis for an Euler-Bernoulli beam under local internal control and boundary observation, J. Control Theory Appl., 2008, 6(4): 341–350.
Chen X, Chentouf B, and Wang J M, Exponential stability of a non-homogeneous rotating diskbeam- mass system, J. Math. Anal. Appl., 2015, 423(2): 1243–1261.
Chen X, Chentouf B, and Wang J M, Nondissipative torque and shear force controls of a rotating flexible structure, SIAM J. Control Optim., 2014, 52(5): 3287–3311.
Xu C Z and Baillieul J, Stabilizability and stabilization of a rotating body-beam system with torque control, IEEE Trans. Automat. Control, 1993, 38(12): 1754–1765.
Chentouf B and Wang J M, Stabilization and optimal decay rate for a non-homogeneous rotating body-beam with dynamic boundary controls, J. Math. Anal. Appl., 2006, 318(2): 667–691.
Chentouf B and Couchouron J M, Nonlinear feedback stabilization of a rotating body-beam without damping, ESAIM Control Optim. Calc. Var., 1999, 4: 515–535.
Chentouf B and Wang J M, On the stabilization of the disk-beam system via torque and direct strain feedback controls, IEEE Trans. Automat. Control, 2015, 60(11): 3006–3011.
Rao B P, Decay estimates of solutions for a hybrid system of flexible structures, European J. Appl. Math., 1993, 4(3): 303–319.
Zeidler A, Nonlinear Functional Analysis and Its Applications, Springer-Verlag, Berlin, 1986.
Lions J L and Magenes E, Non-homogeneous Boundary Value Problems and Applications, Translated from the French by Kenneth P, Springer-Verlag, Berlin, New York, 1972.
Brezis H, Operateurs Maximaux Monotones et Semi-groupes de Contractions Dans les Espaces de Hilbert, North-Holland, Amsterdam, 1973.
Pierre M, Perturbations localement Lipschitziennes et continues d’opérateurs m-accrétifs, Proc. Amer. Math. Soc., 1976, 58: 124–128.
Bénilan P, Solutions intégrales d’équations d’évolution dans un espace de Banach, C. R. Acad. Sci. Paris Sér. A-B, 1972, 274: A47–A50.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the National Natural Science Foundation of China under Grant Nos. 61273130 and 61673061.
This paper was recommended for publication by Editor CHEN Jie.
Rights and permissions
About this article
Cite this article
Guo, Y., Wang, J. Stabilization of a non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls. J Syst Sci Complex 30, 616–626 (2017). https://doi.org/10.1007/s11424-017-5235-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-017-5235-4