Abstract
The static bifurcation characteristic and the stability of a nonlinear electromechanical coupling system with time delay are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamic equation of electromechanical coupling transmission system is deduced by using the dissipation Lagrange equation. The equivalent low-dimensional bifurcation equation is obtained by using the method of Lyapunov–Schmidt reduction. And the bifurcation characteristic is analyzed by the method of the singularity theory. In order to control the dynamic behavior of the system, a time delay feedback is introduced and the distribution of the roots is studied. The analytical conditions that determine the feedback gain and time delay are given based on the delay differential equation stability theory. Under certain conditions, it is shown that the zero solution is locally asymptotically stable when the time delay is suitably small, while the change of stability of zero solution will cause a bifurcating periodic solution as the time delay passes through a certain critical value. Numerical simulations are also performed, which confirm the analytical results.
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