Optimal Disturbance-Observer-Based Fuzzy PID Back-Stepping Control of a Self-Driving Car with a Steer-by-Wire System

This paper presents a robust dual-loop control strategy for the lateral motion and heading-angle regulation of an autonomous vehicle equipped with a Steer-By-Wire (SBW) system under unknown time-varying disturbances. The proposed framework comprises a fuzzy PID controller in the inner loop to generate the motor torque and track the front-wheel steering angle, and an optimal backstepping controller in the outer loop—integrated with a finite-time disturbance observer—to ensure lateral trajectory tracking and wind-disturbance rejection. The PID gains are tuned online by a Mamdani-type fuzzy inference system, while the backstepping parameters are optimized offline via a genetic algorithm. Beyond the bicycle-model-based design, the controller is evaluated through supplementary simulations using a 6-degree-of-freedom (6-DOF) vehicle model, as well as through a detailed robustness analysis that includes measurement noise and increasing lateral disturbance forces. The results demonstrate that the closed-loop system achieves precise path tracking, finite-time convergence of both tracking and estimation errors, and effective compensation of road vibrations and wind disturbances. Furthermore, the controller maintains stable performance under significant measurement noise and tolerates lateral disturbance forces up to at least 10,000 N without violating safety constraints. The effectiveness of the proposed method is consistently confirmed across both the reduced-order bicycle model and the higher-fidelity 6-DOF validation environment.