Sliding mode control of chaotic vibrations of spinning disks with uncertain parameter under bounded disturbance

Abstract

In order to eliminate lateral oscillation of spinning disk with uncertain parameter and dispel their adverse effect on the system performance or the working conditions of the system, supposing that the point force acting on the spinning disk is uncertain and bounded, the chaotic complex dynamic characteristics of the four-dimensional nonlinear equations in lateral oscillations of spinning disk under bounded disturbance were analyzed in view of the ubiquity of disturbance, including the space trajectory, the Lyapunov exponent and the Poincaré map. These characteristics enable us to know them deeply, and indicate that the four-dimensional dynamical system contains chaotic attractor. To ensure the robustness of the system control, the author stabilized the chaotic orbits to arbitrary chosen fixed points and periodic orbits by means of sliding mode method, and MATLAB simulations were presented to confirm the validity of the controller. The results show that using sliding mode method can make the system track target orbit strictly and smoothly with short transition time, and its insensitivity to noise disturbance is shown. It provides reference for relevant chaos control in mechanical system.