Search

The effect of time delays occurring in the feedback control loop on the linear stability of a simple magnetic bearing system is investigated by analyzing the associated characteristic transcendental equation. It is found that a Hopf bifurcation can take place when time delays pass certain values. The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method. It is also found that a codimension two bifurcation can occur through a Hopf and a steady state bifurcation interaction. Finally, numerical simulations are performed to verify the analytical predictions. [Copyright &y& Elsevier]

The primary, superharmonic, and subharmonic resonances of a harmonically excited non-linear s.d.o.f. system with two distinct time-delays in the linear state feeback are studied. The two different time-delays are presented in the proportional feedback and the derivative feedback respectively. The method of multiple scales is utilized to obtain the first order approximation of response. The effect of the feedback gains and time-delays on the steady state responses of three types of resonances is investigated. It is found that a proper selection of the feedback gains and time-delays can enhance the control performance. [Copyright &y& Elsevier]