Codimension-two bifurcation analysis and chaos synchronization of a quarter-car vehicle model

Abstract

In this study, codimension-two bifurcation analysis was used in conjunction with a novel control method to mediate chaos in a semi-active suspension system based on a quarter-car model with excitation introduced by the road surface profile. The results of bifurcation analysis indicate that the hysteretic nonlinear characteristics of the damping forces produce codimension-two bifurcation, resulting in homoclinic orbits and pitchfork bifurcation. We also characterized the complex dynamics of vehicle suspension systems using a bifurcation diagram, phase portraits, Poincaré maps, and frequency spectra. Furthermore, the largest Lyapunov exponent was used to identify the onset of chaotic motion and to verify the results of bifurcation analysis. We also developed a continuous feedback control method based on synchronization characteristics to eliminate chaotic oscillations. Finally, we conducted analysis on the robustness of parametric perturbation in suspension systems with synchronization control using Lyapunov stability theory and numerical simulations.

Numerical continuation applied to internal combustion engine models

“…In addition, the lateral dynamics of a vehicle driving straight ahead was also studied. 14 The methods are also shown to be useful in the analysis of wheels, tyres and suspension dynamics, with the damping force shown to dramatically affect the behaviour of the suspension 15 and the slip angle and vehicle speed shown to play major roles in the development of vibration. 14 Shimmy behaviour has also been studied, with limit cycles being observed under bisectional road conditions 16 and bistable parameter ranges were found for towed wheels.…”

“…14 The methods are also shown to be useful in the analysis of wheels, tyres and suspension dynamics, with the damping force shown to dramatically affect the behaviour of the suspension 15 and the slip angle and vehicle speed shown to play major roles in the development of vibration. 14 Shimmy behaviour has also been studied, with limit cycles being observed under bisectional road conditions 16 and bistable parameter ranges were found for towed wheels. 17 Furthermore, the approach was used in determining the stability of permanent synchronous motors 18 and regions of dynamic behaviour in braking dynamics.…”

Controlling Chaos through Period-Doubling Bifurcations in Attitude Dynamics for Power Systems

“…is approach has been used in numerous chaotic systems [19,20]. Chang and Hu [19] used synchronization to lessen chaotic behavior in an automotive suspension system.…”

“…is approach has been used in numerous chaotic systems [19,20]. Chang and Hu [19] used synchronization to lessen chaotic behavior in an automotive suspension system. Chang and Lue [20] used synchronization to achieve stable equilibrium in a magnetic levitation system.…”