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Dynamics of a Jeffcott rotor-magnetic bearing system with time delays. (English) Zbl 1348.93031

Summary: A Jeffcott rotor with an additional magnetic bearing locating at the disc is employed to investigate the effect of time delays on the non-linear dynamical behavior of the system. The time delays are presented in the proportional and derivative feedback, respectively. For the corresponding autonomous system, a linear stability analysis is performed for the system with two identical time delays in the control loop. The nature of a single Hopf bifurcation is determined by constructing a center manifold. For the non-autonomous system, the primary resonance response is studied for its small non-linear motions using the method of averaging. The effects of time delays and control gains, as well as excitation amplitude, on the amplitude of the steady-state response are investigated. Finally, experiments are carried out to validate the theoretical predictions.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
93C20 Control/observation systems governed by partial differential equations
70Q05 Control of mechanical systems
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