Delay-induced novel dynamics in a hexagonal centrifugal governor system

Abstract

Inherent time delays are often neglected in the modeling and dynamic analysis of centrifugal governor systems for the sake of simplicity, yet they can have a significant effect on the dynamic behavior of the governor systems. This paper investigates the effect of time-delay on the dynamics of a hexagonal centrifugal governor system through a comparative study on the stability and bifurcation of the equilibrium for the system with and without delay considered. It is found that the presence of time-delay can decrease the stability region of the equilibrium and generate many fine structures on the stability boundaries. New dynamic phenomena can be induced by the time-delay, including the 1:4 resonant and non-resonant double Hopf bifurcations. In addition, generic Hopf and Bautin bifurcations can be observed in the system for both the non-delay and delay cases. The unfolding of bifurcations which exhibits all possible behavior at the points of such complicated bifurcations is given by studying the normal form of the response amplitude obtained using the method of multiple scales. Numerical simulations are performed to validate the proposed theoretical analyses.