Combined Algebraic Estimator and Extremum Seeking for Estimation of Tire Force and Optimal Slip Ratio

Abstract

This paper presents an optimal adaptive method for slip ratio optimization in electric vehicles using extremum seeking. The extremum seeking algorithm tracks the optimal slip ratio value that maximizes the tire longitudinal force, which is observed using algebraic estimation. Firstly, a wheel slip control based on a gain-scheduled proportional-integral-derivative controller is proposed. A linearized slip ratio model is developed and utilized to allocate the desired control dynamics, defining the control gains as functions of vehicle speed. Secondly, an algebraic estimator is employed to estimate the longitudinal force applied to the tire, utilizing a gray-box model of the wheel dynamics. Finally, the extremum seeking optimization method is applied to maximize the longitudinal force, a gain dependent on the vehicle speed is proposed to account for disturbances caused by road roughness and imperfections. The results of this application are validated using the CarSim automotive simulator, along with MATLAB/Simulink. The effectiveness of the implemented method is demonstrated for the study case.