Optimal control for anti-lock braking system: Output feedback adaptive controller design and processor in the loop validation test

In this paper, the problem of controlling anti-lock braking system (ABS) was considered. Based on LuGre friction model, an output-feedback adaptive controller that enjoys good braking performances whatever the road conditions, was developed. Specifically, the controller tracks the optimal slip coefficient and, unlike previous work, the reference slip ratio is online estimated according to road conditions as well as longitudinal vehicle speed. The adaptive feature of the controller proves to be crucial for compensating the uncertainty on the changing road characteristics. The controller consists of: (i) a generator of the reference signal for the slip coefficient designed in the form of a neural network; (ii) a nonlinear observer for estimating the internal friction state; (iii) a backstepping adaptive control law, designed on the basis of a quarter-car model, that ensures tracking of the optimal slip value and providing estimates of the model unknown parameters. The controller stability properties are analyzed using Lyapunov stability tools. The theoretical stability results are confirmed by processor-in-the-loop (PIL) experiments in different road conditions. A comparative study, a robustness test, and a co-simulation involving CarSim and MATLAB/Simulink were made to highlight the much better performances, in terms of stability, tracking, robustness, and practicability of the new controller.