Bifurcation Analysis of Flywheel Governor Subject to Stochastic Excitation Under Time-Delay Feedback

Abstract

The stability and Hopf bifurcation of a class of flywheel governor systems subject to stochastic excitation under time-delay feedback are studied. The model is simplified using center manifold reduction to obtain a paradigm for a two-dimensional central subsystem. The system converges asymptotically to an It[Formula: see text] stochastic differential equation based on polar transformations and stochastic averaging method. The stochastic stability of the system is analyzed by applying the maximum Lyapunov exponent and the singular boundary theory, and its probability density function is calculated. In addition, it is found through Monte Carlo numerical simulations that the effects of noise intensity and time-delay on the stochastic P-bifurcation of the system are opposite, and proper noise intensity makes the flywheel governor system converge to the equilibrium position, while a large time-delay leads to stochastic bifurcation and makes the flywheel governor system unstable. Finally, the two-parameter bifurcation diagram is used to further analyze the impact of time-delay and noise intensity on the bifurcation of the system under variable load torque. It is found that the influence of noise intensity and time-delay on the periodic oscillation state is the same, and the stability of the flywheel governor system will decrease with both of their increases. This also further demonstrates the duality of the impact of noise intensity on the same system under different conditions. The above research provides better theoretical references for the design and safe operation of speed control systems.