×

Stabilization control and motion control for some mechanical systems by using bifurcation control. (English) Zbl 1224.70028

Summary: In the first half of this presentation, nonlinear control methods are theoretically and experimentally proposed for nonlinear phenomena in mechanical systems, which are the 1/3-order subharmonic resonance in a magnetically levitated body and the hunting motion in a railway vehicle wheelset. In the second half, we consider a positive utilization of a nonlinear phenomenon for the motion control of an underactuated manipulator which has a free link without an actuator.

MSC:

70K20 Stability for nonlinear problems in mechanics
70K50 Bifurcations and instability for nonlinear problems in mechanics

Software:

CONTACT

References:

[1] Arai, H.; Tanie, K.; Shiroma, N., Nonholonomic control of a three-DOF planar underactuated manipulator, IEEE Trans. Robot. Auto., 14, 681-695 (1998)
[2] Kalker, J. J., Three-dimensional Elastic Bodies in Rolling Contact (1990), Kluwer: Kluwer Dordrecht · Zbl 0709.73068
[3] Lorant, G.; Stepan, G., The role of non-linearity in the dynamics of a single railway wheelset, Mach. Vib., 5, 18-26 (1996)
[4] Molle, D.; Gasch, R., Nonlinear bogie hunting, (Wickend, A. H., Nonlinear Bogie Hunting, Proceedings Seventh IAVSD-Symposium (1982), Swets and Aeitlinger B.V.: Swets and Aeitlinger B.V. Lisse), 455-467
[5] Nayfeh, A. H.; Balachandran, B., Modal interactions in dynamical and structural systems, ASME Appl. Mech. Rev., 42, s175-s201 (1989) · Zbl 0755.70023
[6] Whickens, A. H., The dynamics stability of a simplified four-wheel railway vehicle having profiled wheels, Int. J. Solids Struct., 1, 385-406 (1965)
[7] Xu, G.; Troger, H.; Steindl, A., Global analysis of the loss of stability of a special railway body, (Schiehlen, W., Nonlinear Dynamics in Engineering Systems (1990), Springer: Springer Berlin), 345-352
[8] Yabuno, H.; Endo, Y.; Aoshima, N., Stabilization of \(1 / 3\)-order subharmonic resonance using an autoparametric vibration absorber, ASME J. Vib. Acoust., 121, 309-315 (1999)
[9] Yabuno, H.; Goto, K.; Aoshima, N., Swing-up and stabilization of an underactuated manipulator without state feedback of free joint, IEEE Trans. Robot. Auto., 20, 359-365 (2004)
[10] Yabuno, H.; Miura, M.; Aoshima, N., Bifurcation in an inverted pendulum with tilted high-frequency excitation: analytical and experimental investigations on the symmetry-breaking of the bifurcation, J. Sound Vib., 273, 493-513 (2004)
[11] Yabuno, H.; Okamoto, T.; Aoshima, N., Effect of lateral linear stiffness on nonlinear characteristics of hunting motion of a railway wheelset, Meccanica, 37, 555-568 (2002) · Zbl 1015.70500
[12] Zeng, J.; Zhang, W. H.; Dai, H. Y.; Wu, X. J.; Shen, Z. Y., Hunting instability analysis and \(H^\infty\) controlled stabilizer design for high speed railway passenger car, Vehicle System Dynam. Suppl., 28, 655-668 (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.