Delayed feedback control for chaotic vibration in nonlinear impact dynamics of bouncing agricultural tractor.

Agricultural tractors often lose contact and recollide with the ground surface while driving on narrow paddy fields and bumpy farm roads owing to excessive vibrations. These nonlinear impact dynamics can cause chaotic vibrations during tractor operation. Chaotic vibrations are random complex motions that can deteriorate tractor stability and lead to tractor overturning accidents, causing damage to machinery and risk of injury to the operator. This study investigates the theoretical feasibility of chaos control to eliminate chaotic vibrations in tractor dynamics. Delayed feedback (DF) control is employed to eliminate complex vibrations in tractor dynamics. First, the frequency response, bifurcation diagram, and largest Lyapunov exponent are obtained to investigate the nonlinear dynamics of the tractor and identify the parametric region in which chaotic vibrations occur. Subsequently, the DF control is designed based on the trial-and-error method and applied to the tractor dynamics as the driving force control input. The numerical results demonstrate that the DF control can successfully eliminate chaotic vibration and reduce the vibration level. Therefore, this study is expected to contribute to improving the tractor safety by reducing the risk of overturning.