Hybrid modeling, control and estimation in ABS applications based on In-Wheel electric motors

Abstract

The problems of tire slip control and peak friction estimation for Anti-lock Braking Systems are formulated and solved in the framework of hybrid control techniques. The hybrid systems model of the vehicle dynamics arises from approximating the nonlinear behavior of the tire-road frictioncoefficient with a Piecewise Linear Function (PLF). The problem of tyre slip control is formulated as an invariance problem. The invariance control problem is solved with the help of a simple hysteretic controller which takes advantage of the fast torque response from the in-wheel electric motor. The controllers properties, such as necessary conditions to ensure invariance, robustness to disturbances, convergence and limit cycle period are analyzed in detail. The problem of the estimating the peak friction for the tire-road interface is solved using properties of the limit cycles arising in the hybrid model. Monitoring the duty cycle, imposed by hysteretic controller, was found to be sufficient to extract information regarding the conditions of adhesion in the road. The controller and estimator were evaluated under variable grip levels, in a vehicle dynamics simulation software, obtaining a good performance for both the tire slip regulation and for the peak friction estimationd.