MIMO Controller Design for Stabilizing Vehicle Drifting

The presence of highly automated vehicles and driver assistance systems is expected to grow in the future. In recent years, these systems offer assistance for the driver but, in the future, the human driver will be increasingly replaced by automated vehicle functions. In order to achieve this, the vehicle must be able to plan and safely follow a trajectory. In this paper, a MIMO linear quadratic regulator was designed for stabilizing the vehicle during steady-state drifting. The research can be utilized in different fields of applications. Namely, the driving capabilities of an automated vehicle must be at least as good as a human driver. Hence, these systems must be able to drive the car at friction limits. Furthermore, a better understanding of the dynamics of drifting and the equilibrium conditions can be used in motorsports. A three-state bicycle model has been implemented, supplemented with two different tire models. A brush tire model was used at front wheels. A combined slip brush tire model was used at rear wheels, considering lateral-longitudinal force coupling. During drift, the rear tires are saturated, the front tires are not. The complete vehicle model containing the tire models described by eight equations, the system of equations has been solved numerically for equilibrium points. The nonlinear vehicle model was Jacobian linearized in a parametric form. Based on the results, a MIMO LQ system was designed. The control inputs include the steering angle at front wheels and longitudinal drive force at rear wheels. Finally, the controller performance was demonstrated using the nonlinear model in MATLAB/Simulink environment. The proposed controller found able to regulate steady-state drifting with predefined sideslip angles and longitudinal velocities.