A second-order slip model for constraint backstepping control of antilock braking system based on Burckhardt’s model

Abstract

This paper is concerned with the problem of constraint control for an Antilock Braking System (ABS) with asymmetric slip ratio constraints. A nonlinear backstepping control method based on Barrier Lyapunov Function (BLF) is proposed not only to track the optimal slip ratio but also to guarantee no violation on the slip ratio constraints. A second order slip rate model is established based on a quarter vehicle braking model and a Burckhardt’s tire model. The Asymmetric Barrier Lyapunov Function (ABLF) is introduced into the backstepping controller for solving the asymmetric slip ratio constraint problems. The proposed controller can implement ABS zero steady state error tracking of the optimal wheel slip ratio and make slip ratio constraints flexible for various runway surfaces and runway transitions. Simulation results show that the control scheme can guarantee no violation on slip ratio constraints and avoid self-locking.