Zhang, Z., Huang, M., Ji, M., and Zhu, S., "Design of the Linear Quadratic Control Strategy and the Closed-Loop System for the Active Four-Wheel-Steering Vehicle," SAE Int. J. Passeng. Cars - Mech. Syst. 8(1):354-363, 2015, doi:10.4271/2015-01-9107.
In the field of active safety, the active four-wheel-steering (4WS) system seems to be an attractive alternative and an effective tool to improve the vehicles' handling stability in lane-keeping control performance. Under normal using condition, the vehicle's lateral acceleration is comparatively small, and the mathematic relationship between the small side force excitation and the small slip angle of the tire is in the linear region. Furthermore, the effects of roll, heave, and pitch motions are neglected as well as the dynamic characteristics of the tires and suspension system in this work. Therefore, the linear quadratic control (LQC) theory is used to ensure that the output of the 4WS control system can keep track of the desired yaw rate and zero-sideslip-angle response can also be realized at the same time.Due to the development of Steer-by-Wire (SBW) technology, the driver's steering input can be easily converted into digital signals and calculated by the SBW conversion mechatronic control system, which utilize these digital signals to regulate the front and rear wheel steering angle to achieve the ideal steering responses. And the attention is paid to the more fundamental aspects of the vehicle's horizontal motions. Based on these statements, the differential equations of 2DOF linear model for the 4WS vehicle is derived to describe the vehicle's horizontal motions with relatively high precision in essence. In addition, a numerical method is presented to evaluate the steering characteristics and handling stability. Output results show that the 4WS system with LQC algorithms has higher accuracy in path tracking and better performance in improving the active safety.