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Existence and stability of limit cycles in control of anti-lock braking systems with two boundaries via perturbation theory. (English) Zbl 1366.93421

Summary: 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.

MSC:

93C95 Application models in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C73 Perturbations in control/observation systems
93D99 Stability of control systems
93C10 Nonlinear systems in control theory
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