Nonlinear Disturbance Observer-Based Adaptive Anti-Lock Braking Control of Electro-Hydraulic Brake Systems with Unknown Tire–Road-Friction Coefficient

This paper addresses a recursive adaptive anti-lock braking (AB) control design problem for electro-hydraulic brake (EHB) systems subject to unknown tire–road-friction coefficients and disturbances. Compared with the relevant literature, the primary contributions are (i) the development of a novel nonlinear AB model integrated with a bond-graph-based EHB (BGEHB) system, and (ii) the proposal of an adaptive neural AB control approach incorporating a nonlinear disturbance observer (NDO). The AB and BGEHB models are unified into a single nonlinear braking model, with the wheel speed as the system output and the duty ratios of the BGEHB inlet and outlet valves as control inputs. To maintain an optimal slip ratio during braking, we design the NDO-based adaptive AB controller to regulate the wheel speed in a recursive manner. The designed controller incorporates a delay-compensation term to address the time-delay characteristics of the hydraulic system, employs a neural-network function approximator in the NDO and controller to compensate for the unknown tire–road-friction coefficient, and applies NDOs to compensate for disturbances due to the vehicle motion and BGEHB dynamics. The stability of the proposed control scheme is established via the Lyapunov theory, and a simulation comparison is presented to demonstrate the effectiveness of the proposed design approach.