Stability control of towed two-wheeled trailers with an improved model and different contact force models

This study investigates the nonlinear dynamics of towed two-wheeled trailers using a 4-DoF spatial mechanical model. That is, yaw, pitch, and roll motions are all taken into account. The nonlinear governing equations are derived using the Lagrange equation of the second kind. Geometrical nonlinearities and the non-smooth nature of the lateral tire forces are considered. The normal loads at the wheels are precisely calculated based on free-body diagrams, resulting in an improved trailer model. To extend the globally stable towing speed range, stability control is applied. Namely, a differential braking scheme is implemented based on the sign of the yaw rate of the trailer. A numerical bifurcation analysis is performed to investigate the large-amplitude vibrations and unsafe (bistable) zones, where stable rectilinear motion coexists with stable limit cycles. Bifurcation diagrams show that with appropriately chosen control gains, the size of the bistable region can be limited. Since the modeling of the tire-ground contact has a significant impact on the resulting vibrations, different contact force models are considered. Namely, the widely used Magic Formula and the brush tire models are implemented and investigated. Additionally, a family of analytical creep models is presented, which can capture the essential properties of tire forces and are easier to construct. Mathematics Subject Classification (2020) 70E50 · 70E60 · 70H03