Chaos and chaos control for a two-degree-of-freedom heavy symmetric gyroscope

Abstract

A two-degree-of-freedom heavy symmetric gyroscope is studied in this paper. This system is forced by harmonically periodic vertical vibration to enrich dynamic behaviors. Because of the nonlinear terms of the system, the system exhibits chaotic motion. By applying various numerical results, such as phase portraits, Poincare maps, time history and power spectrum analysis, the behaviors of the periodic and chaotic motion are presented. The effects of the change of parameters in the system can be found in the bifurcation diagrams and parametric diagrams. The method of Lyapunov exponents is used to identify the chaos or regular motions of the systems. Next, nine controlling methods are applied into the systems, in which the modified open-plus-closed-loop control is firstly proposed. Open and feedback loops of controls are both studied. It is found that each controller can effectively control the chaotic orbits to the regular ones.