Nonlinear control of an antilock braking system in the presence of tire–road friction uncertainties

An Antilock Braking System (ABS) is characterized by nonlinear dynamics, which render more difficult the design of a controller for high performance. The problem is even harder due to the uncertainties on the parameters appearing in its dynamics. In this paper, an ABS laboratory setup is considered, which mimics a quarter car model. A super–twisting controller is proposed to overcome the problem due to parameter uncertainties. This controller is designed in order to impose a reference value of the tire slip. Two cases are considered: in the first, nominal ABS parameters are used in the controller, whereas in the second the controller embeds an estimator of the tire–road friction coefficient, which is one of most critical parameters. The friction coefficient is estimated in finite–time by means of a high–order sliding mode differentiator. The original contributions of the paper are the real–time implementation of the super–twisting controller for the laboratory setup under study, and the use of a super–twisting estimator to provide a finite–time estimation of the friction coefficient between the tire and the road, along with a comparison with classical PI–like and super–twisting controllers, available in the literature. The ABS laboratory setup allows checking experimentally the performance of the proposed nonlinear dynamic controller, showing a considerable increase of the efficiency of the control system.