Non-linear dynamics and control of chaos for a rotational machine with a hexagonal centrifugal governor with a spring

The dynamic behaviors of the rotational machine with a hexagonal centrifugal governor which is subjected to external disturbance are studied in the paper. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of system. By applying numerical results, phase diagrams, power spectrum, Poincaré maps, and Lyapunov exponents are presented to observe periodic and chaotic motions. The effect of the parameter changes in the system can be found in the bifurcation and parametric diagrams. Finally, eight methods are used to control chaos effectively.