Fuzzy proportional-integral state feedback controller For vehicle traction control system

In this paper, a fuzzy proportional integral (PI) state feedback controller has been developed in order to improve vehicle traction on slippery roads. A nonlinear model has been formulated from the vehicle longitudinal dynamics, the drivetrain model and the wheel motion. Takagi-Sugeno (TS) representation has been used in order to take into account the nonlinearities of the obtained model and to simplify the controller design. The objective of the proposed controller is to compute the optimal engine torque so that the longitudinal slip ratio does not exceed a desired value which is the limit of the optimal traction and the vehicle stability. Lypunov and H_∞ approaches have been used in the controller design and stability conditions are given in terms of Linear Matrix Inequalities (LMI). In order to show the effectiveness of the developed approaches, the vehicle model has been simulated on a slippery road with and without traction control system.