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The centrifugal governor system plays an indispensable role in maintaining the near-constant speed of engines. Although different arrangements have been developed, the governor systems are still applied in many machines for its simple mechanical structure. Therefore, the large-amplitude vibrations of the governor system which can lead to the function failure of the system should be attenuated to guarantee reliable operation. This paper adopts a time-delay control strategy to suppress the undesirable large-amplitude motions in the centrifugal governor system, which can be regarded as the practical application of the delayed feedback controller in this system. The stability region of the trivial equilibrium of the controlled system is determined by investigating the characteristic equation and generic Hopf bifurcations. It is found that the dynamic behavior of multistability can be induced by the Bautin bifurcation, arising on the stability boundary of the trivial equilibrium with a constant delay. More specifically, a coexistence of two desirable stable motions, i.e., an equilibrium or a small-amplitude periodic motion, can be observed in the controlled centrifugal governor system without changing the physical parameters. This is a new feature of the motion control in the centrifugal governor systems, which has not yet been reported in the existing studies. Finally, the results of theoretical analyses are verified by numerical simulations.

Saddle-node or period-doubling bifurcations of the near-grazing impact periodic motions have been extensively studied in the impact oscillators, but the near-grazing Neimark-Sacker bifurcations have not been discussed yet. For the first time, this paper uncovers the novel dynamic behavior of Neimark-Sacker bifurcations, which can appear in a small neighborhood of the degenerate grazing point in a two degree-of-freedom impact oscillator. The higher order discontinuity mapping technique is used to determine the degenerate grazing point. Then, shooting method is applied to obtain the one-parameter continuation of the elementary impact periodic motion near degenerate grazing point and the peculiar phenomena of Neimark-Sacker bifurcations are revealed consequently. A two-parameter continuation is presented to illustrate the relationship between the observed Neimark-Sacker bifurcations and degenerate grazing point. New features that differ from the reported situations in literature can be found. Finally, the observed Neimark-Sacker bifurcation is verified by checking the existence and stability conditions in line with the generic theory of Neimark-Sacker bifurcation. The unstable bifurcating quasi-periodic motion is numerically demonstrated on the Poincaré section.

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