Multiple model adaptive back-stepping control for antilock braking system based on LuGre dynamic tyre model

Vehicle stability control systems play an essential role in helping the driver maintain vehicle control. This paper addresses a control scheme for antilock braking system (ABS). In this control scheme, first, a quarter model of the vehicle's longitudinal dynamic system is developed, which includes the LuGre tyre/road dynamic friction model. Then, a non-linear controller is developed using the multiple models adaptive controls (MMAC) methodology. The control system models are divided into high adhesion, middle adhesion, low adhesion fixed models and an adaptive model. Backstepping and adaptive back-stepping controller are designed for fixed and adaptive models, respectively. The index function is used to switch the control rule by searching the minimum index value. Our proposed ABS controller's stability is proved by the Lyapunov stability theorem. Finally, the results of the simulation in the different surface conditions show that MMAC is better than other controllers and achieves great and robust braking performance.