Nonlinear Dynamics of a Controlled Two-Wheeled Trailer

The nonlinear dynamics of towed two-wheeled trailers is investigated using a spatial, 4-DoF model. Namely, the yaw, pitch, and roll motions are all taken into account. Geometrical nonlinearities and the non-smooth characteristics of the tire forces are considered. A linear state feedback controller with feedback delay is designed to enhance the stability performance of the trailer. Numerical bifurcation analysis is performed to investigate the large amplitude vibrations and unsafe (bistable) zones, where the stable rectilinear motion and the stable limit cycle coexist with each other. The effects of the control gain and the feedback delay of the controller are presented on bifurcation diagrams. It is shown, that with appropriately chosen control gains, the size of the bistable region can be limited.