Control of Neimark-Sacker bifurcation in a type of weak impulse excited centrifugal governor system

Centrifugal governors play an important role in rotating machinery such as diesel engines and steam engines. This paper considers two impulse excitations of the freewheel. The feedback control issue of the Neimark-Sacker bifurcation design of the centrifugal governor system is studied. A feedback control method is addressed to realize the control objectives of the existence, stability and the mean radius of cross section of the torus solution. An explicit criterion, without the use of eigenvalue calculations, including eigenvalue assignments and transversality conditions, is used to push the linear gain responsible for controlling the existence of bifurcation. Using the central manifold theory and the normal form reduction method, the nonlinear gain of the control torus stability is obtained. The expression of mean radius of cross section of the limit torus is developed to derive the linear gains, which are responsible for controls of torus. Numerical simulations of the centrifugal governor system show that the Neimark-Sacker torus with the desired characteristics can be produced at any of the pre-set parameter points.