Multistability in a Fractional-Order Centrifugal Flywheel Governor System and Its Adaptive Control

Abstract

In this paper, a 4D fractional-order centrifugal flywheel governor system is proposed. Dynamics including the multistability of the system with the variation of system parameters and the derivative order are investigated by Lyapunov exponents (LEs), bifurcation diagram, phase portrait, entropy measure, and basins of attraction, numerically. It shows that the minimum order for chaos of the fractional-order centrifugal flywheel governor system is q = 0.97, and the system has rich dynamics and produces multiple coexisting attractors. Moreover, the system is controlled by introducing the adaptive controller which is proved by the Lyapunov stability theory. Numerical analysis results verify the effectiveness of the proposed method.