Delayed feedback active suspension control for chaos in quarter car model with jumping nonlinearity

Vehicles that operate on off-road terrain, such as rough and unpaved roads, sometimes suffer from severe vibrations. This vibration causes vehicle tires to lose contact with the supporting ground and subsequently collide with it. This jumping leads to nonlinear impact dynamics similar to those of a bouncing ball. In this study, a quarter car model with jumping nonlinearity is newly developed to represent the impact dynamics of an off-road vehicle under harsh terrain conditions. Subsequently, complicated vibrations, such as quasi-periodic and chaotic vibrations in the developed model, are identified using a bifurcation diagram and Lyapunov exponents. Additionally, delayed feedback (DF) control of the active suspension is designed for the developed model. The numerical results show that DF control is effective at eliminating chaos and reducing vibration levels. The noise robustness of the DF control is validated for sinus excitation and small random road noise. The results indicate that DF is effective even when road noise exists. Thus, this study demonstrates the feasibility of DF active suspension control for future suspension control design of the off-road vehicle.