Constrained Nonlinear Estimation of Road Friction Coefficient and Wheel Slip for Control of Anti-Lock Braking System

In designing the anti-lock braking system (ABS), some states and parameters of vehicle system such as road friction of coefficient and wheel slip should be estimated due to lack of cost effective and reliable sensors for direct measurement. Because of nonlinear characteristics of vehicle dynamics and tire forces, development of a nonlinear estimation algorithm is necessary. However, consideration of physical constraints can enhance the accuracy and reliability of estimation algorithm in real situations. In this paper, the extended Kalman filter (EKF) is applied for the ABS and its algorithm is modified in way that the physical limitations of road friction and wheel slip could be considered. The performance of the modified EKF in the constrained case is compared with the conventional EKF. At the rest of paper, a nonlinear predictive-based controller is analytically designed for the ABS and combined with the proposed constrained estimation algorithm. In order to decrease the effect of estimation errors on tracking performance, the integral feedback technique is combined with the control strategy. The simulation results indicate that not only the proposed algorithm improves the tracking accuracy in the presence of uncertainties, but also the control signal oscillations with high frequency will be prevented.