The variations of the basins of attraction are also discussed in the plane of initial history conditions to demonstrate the multistability phenomena and chaotic transitions.Ĭentrifugal dampers are used to reduce the vibrations and irregularities of motion of rotating parts subjected to torque perturbations. For example, the commonly exhibited period-one orbit may have two or more intersection points on the Poincaré section rather than one point. An interesting phenomenon that the number of intersection points of some periodic responses on the specified Poincaré section differs from the actual period characteristics is found in classifying the dynamic behavior. The path-following calculation scheme and time domain collocation method are used to explore the detailed bifurcation mechanisms. By identifying different responses in the two-parameter plane, the effect of time delay on the complexity of the evolutionary process is fully revealed. By combining the GPU parallel computing technique with two determinate indicators, namely the Lyapunov exponents and Poincaré section, this paper presents a detailed study on the two-parameter dynamics of a mechanical governor system with different time delays. A numerical simulation is given to show the robustness and effectiveness of the proposed finite-time controller and to verify the theoretical results of the paper.Ī deep understanding of the dynamical behavior in the parameter-state space plays a vital role in both the optimal design and motion control of mechanical systems. The finite-time stability and convergence of the closed-loop system are analytically proved. Using the adaptation laws and finite-time control theory, a robust adaptive controller is derived to stabilize the non-autonomous uncertain centrifugal flywheel governor system with nonlinear control inputs in a given finite time. Appropriate adaptation laws are designed to undertake the system’s unknown parameters. In this paper, the problem of finite-time stabilization of non-autonomous chaotic centrifugal flywheel governor systems in the presence of model uncertainties, external disturbances, fully unknown parameters and input nonlinearities is studied. Recent research has discovered that this system exhibits very rich and complex dynamics such as chaos. The centrifugal flywheel governor is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by an abrupt change of load torque.