Nonlinear dynamic analysis and control of chaos for a suspended track with moving load

Abstract

This paper presents detailed dynamic analysis of a suspended track with a moving load. By subjecting the system to a harmonic torque and external periodic force chaotic behaviors of the system are investigated. By using the Lyapunov direct method the stability of the relative equilibrium position can be determined. The instability of the system is studied by using Chetaev's theorem. By applying various numerical results such as phase plane, Poincare map, time history and power spectrum analysis, a variety of periodic solutions and phenomena of chaotic motion can be predicted. The effects of changes of parameters in the system can be found in the bifurcation diagrams. Further, chaotic behavior can be predicted by using Lyapunov exponents and Lyapunov dimensions. The modified interpolated cell mapping method (MICM) is used to study the basins of attraction of periodic attractors and fractal structure. Furthermore addition of a constant torque, addition of a periodic torque, delayed feedback control, adaptive control and band-bang control are used to control the chaos phenomena effectively.