Steer-by-wire (SBW) is a crucial chassis electronic control system. Accurate and rapid wheel angle control is key to enhancing system performance. This paper first establishes a dynamics model of the steering actuator. Then, a co-simulation vehicle model with CarSim and Simulink is built, and the feasibility of the SBW model is experimentally verified. Based on this, a front wheel angle compensation difference tracking strategy is proposed using the front wheel steering angle control method. This strategy compensates for the difference between the actual and ideal front wheel steering angles to achieve the desired front wheel angle progressively. A dual-layer controller is designed in the Simulink module and integrated with the CarSim module to achieve closed-loop feedback control of the front wheel angle. The upper layer controller employs a fuzzy PID control method to execute the front wheel angle compensation strategy, enabling two corrections of the front wheel angle and yaw rate. The lower layer controller corrects wheel angle information to improve control effects. Simulation results under double lane change and single lane change conditions show that the fuzzy PID controller with front wheel angle compensation significantly enhances vehicle steering stability. Notably, at high speeds, the peak yaw rate is lower, convergence speed is faster, and response time is shorter.