Existence and stability of limit cycles in control of anti-lock braking systems with two boundaries via perturbation theory

This paper presents a two-phase control logic for anti-lock braking systems (ABS). ABS are by now a standard component in every modern car, preventing the wheels from going into a lock situation where the wheels are fixed by the brake and the stopping distances are greatly prolonged. There are different approaches to such control logics. An ABS design proposed in recent literature controls the wheel's slip by creating stable limit cycles in the corresponding phase space. This design is modified via an analytical approach that is derived from perturbation theory. Simulation results document shorter braking distance compared to available tests in the literature.