Xia, X. and Law, E., "Nonlinear Analysis of Closed Loop Driver/Automobile Performance with Four Wheel Steering Control," SAE Technical Paper 920055, 1992, doi:10.4271/920055.
A nonlinear 8 degree-of-freedom (DOF) four wheel automobile model and a multi-loop quasi-linear driver model were used to investigate both conventional front wheel (FWS) and four wheel steering (4WS) automobiles during (a) crosswind disturbances and (b) collision avoidance maneuvers resulting from combined steering and braking commands. Two different 4WS control laws were used. The first was an open loop control law (OL4) where the rear wheel steer angle was determined by the front wheel steer angle. The second was a closed loop law (CL4) where the rear wheel steer angle was determined by both the front wheel steer angle and the vehicle yaw rate. Both of these linear control laws were proposed by previous investigators and were originally developed using 2 DOF linear “bicycle” models. These linear control laws were modified for application to the situations described above.Simulation results indicate that the CL4 system significantly improves the driver/vehicle performance in response to cross wind disturbances and during the collision avoidance maneuver. Specifically, the benefits of the CL4 system include: (a) reduction of the driver's work load and reduced yaw rate response as compared to that for either the FWS or the OL4 car in response to a cross wind; (b) more stable response of the driver/vehicle system and reduction of the driver's work load during collision avoidance maneuvering as compared to the other two configurations. The driver/vehicle system with the OL4 exhibits a more stable response than that with the FWS during collision avoidance maneuvering.