Lin, X., Ding, N., Xu, G., and Gao, F., "High Speed Optimal Yaw Stability of Tractor-Semitrailers with Active Trailer Steering," SAE Technical Paper 2014-01-0093, 2014, doi:10.4271/2014-01-0093.
Most tractor-semitrailers are fitted with multi-axle trailers which cannot be actively steered, and such vehicles with an articulated configuration are inclined to exhibit instability such as trailer swing, jack-knifing, and rollover at high speed. Proposed in this paper is an optimal control of the yaw stability of tractor-semitrailers at high speed by applying an active trailer's steering angle. An optimal control algorithm is designed by employing a 3-DOF vehicle model in the yaw plane. The optimal linear quadratic regulator (LQR) approach is used with a cost function including sideslip angles, yaw rates of both tractor and trailer, and trailer's steering angle. The yaw stability at the high speed is also quantified by the dynamic performance measurements of lateral path deviation, hitch angle and rearward amplification (RA). The algorithm is evaluated by co-simulations using TruckSim and Matlab/Simulink softwares. Simulation results under double lane change maneuvers show that trailer swing and jack-knifing are suppressed with a small path-tracking error and it is concluded that the optimal control of semi-trailer steering can improve the yaw stability at high speed.