Reliable and safe Redundant Steering System (RSS) equipped with Dual-Winding Permanent Magnet Synchronous Motor (DW-PMSM) is considered an ideal actuator for future autonomous vehicle chassis. The built-in DW-PMSM of the RSS is required to identify various winding’s faults such as disconnection, open circuit, and grounding. When achieving redundant control through winding switching, it is necessary to suppress speed fluctuations during the process of winding switching to ensure angle control precision. In this paper, a steering angle safety control for RSS considering motor winding’s faults is proposed. First, we analyze working principle of RSS. Corresponding steering system model and fault model of DW-PMSM have been established. Next, we design the fault diagnosis and fault tolerance strategy of RSS. Considering the difference in amplitude frequency characteristics of phase current during DW-PMSM winding faults, the Hanning window and Short-Time Fourier Transform (STFT) is comprehensively used to extract the third harmonic components. These components are then compared with the peak values of the third harmonic under DW-PMSM winding fault-free conditions to diagnose faults. Furthermore, in the main loop and the redundant loop of the RSS, we utilize the backstepping control and the sliding-mode control theory to design precise steering angle following method considering the unmodeled disturbance, which ensures smooth switching of two-circuit windings. Finally, a simulation platform based on MATLAB/Simulink is established. The test results demonstrate that the designed steering angle safety control strategy could accurately identify winding faults in the DW-PMSM, reduce speed fluctuations during two-circuit winding switching, and ensures RSS maintains a steady-state following error within 3° under winding fault conditions.