Vehicle handling improvement by fuzzy explicit nonlinear tire forces parametrization

This paper presents the design and the simulation test of a Takagi-Sugeno (TS) fuzzy output feedback for yaw motion control. The control synthesis is conducted on a nonlinear model in which tire-road interactions are modeled using Pacejka's magic formula. Using sector approximation, a TS fuzzy model is obtained. It is able to handle explicitly the nonlinear Pacejka lateral tire forces including the decreasing or saturated region. The controller acts through the steering of the front wheels and the differential braking torque generation. The computation of the controller takes into account the constraints that the trajectories of the controlled vehicle remain inside an invariant set. This is achieved using quadratic boundedness theory and Lyapunov stability. Some design parameters can be adjusted to handle the trade-off between safety constraints and comfort specifications. The solution to the associated problem is obtained using Linear and Bilinear Matrix Inequalities (LMI-BMI) methods. Simulation tests show the controlled car is able to well achieve standard maneuvers such as the ISO3888-2 transient maneuver and the sine with dwell maneuver.