Invariant set based vehicle handling improvement at tire saturation using fuzzy output feedback

This paper firstly reviews of the analysis of the nonlinear behavior of the vehicle lateral dynamics. The (α_f, α_f) phase plane is used in order to quantify the stability region of the vehicle under different forward speed, steering angle and road adhesion. The tire-road interaction forces are modeled using Pacejka´s magic formula. In a second step, the exact linear sectors procedure is used for representation of nonlinear functions in order to derive a Takagi-Sugeno (TS) fuzzy model. This model copes the behavior of the lateral tire forces including the linear, decreasing and saturated regions. Thereafter, a Takagi-Sugeno fuzzy output feedback is designed for yaw motion control. The controller acts through the steering of the front wheels and the differential braking torque generation. The computation of the controller is performed in such a way that the trajectories of the controlled vehicle remain inside an invariant set even when it is under disturbance input. This is achieved using quadratic boundedness theory and Lyapunov stability. Simulation tests show that the controlled car is able to satisfactorily perform standard maneuvers such as the ISO3888-2 transient maneuver and the roundabout maneuver.