Ding, N., Zhang, Y., Gao, F., and Xu, G., "A Gain-Scheduled PID Controller for Automatic Path Following of a Tractor Semi-Trailer," SAE Int. J. Commer. Veh. 6(1):110-117, 2013, doi:10.4271/2013-01-0687.
Improving driving safety and freeway capacity is an indispensable research issue for road vehicles, especially for tractor semi-trailers, which on the one hand exhibit unstable motion modes at high speeds due to their articulated configurations and undertake the largest part of freight transportation on freeways. Automatic driving is rated as the ultimate solution of vehicle safety since it can significantly reduce accidents resulting from human driver errors.Proposed in this paper is a gain-scheduled PID controller for automatic path-following of a tractor semi-trailer. The PID controller minimizes the vehicle's predicted lateral deviation and heading error with respect to the desired path at a preview point, and gains of the controller are scheduled with respect to vehicle speed. The gains of the controller at several given vehicle speeds are tuned using the orthogonal experimental design method (OEDM), based on comprehensive evaluation of lateral path deviation, steering angle input and vehicle stability index under a double lane change maneuver. The tuned gains are further fitted using linear and quadratic functions to form a gain-scheduled control system. The controller is evaluated by simulations using a high-fidelity nonlinear tractor semi-trailer model built in the TruckSim software. Simulation results show that the automatic path following controller can control the tractor semi-trailer to follow the desired path with quite small tracking errors and keep the vehicle stable at various vehicle speeds and road friction conditions with a reasonable steering input.