Extended Nonlinear Two-Time Scale Estimation Approach for Antilock Braking Systems

This article is motivated by an interesting recent result on antilock braking system (ABS) design using two-time scale (TTS)-based estimation. In this article, the basic method of TTS is extended to estimate not only the disturbances but also their derivatives, improving the accuracy of estimation by an order of magnitude. Further, the problem of ABS is extended to an eight-DOF vehicle model to include the effects of load transfer, steering dynamics, and actuator dynamics. Since analysis showed that the use of basic TTS to ABS design results in a poor transient in the estimation error dynamics, this article proposes a new formulation of the TTS method specifically for ABS. Two new ABS-specific sliding surfaces are proposed to compensate the actuator dynamics where the second sliding surface is proposed as an improvement over the first one. The stability, and convergence of estimation, and tracking errors are analyzed. The proposed methods are validated on MATLAB/Simulink, and CarSim platforms for a D-class sedan car. The results are also validated on an experimental ABS platform in the laboratory.