Dual mode steering feedback torque fusion algorithm for steer-by-wire systems considering uneven-road conditions

The design of steering feedback torque in steer-by-wire (SBW) systems requires both high estimation accuracy and low signal delay, especially under uneven-road conditions. To address this challenge, this paper proposes a steering feedback torque reconstruction method based on multi-source weighted fusion. The proposed strategy integrates an observer-based rack-force estimation component with a dynamic-model-based aligning-torque calculation component, thereby combining the advantages of the two torque sources. First, a rack-force estimation method based on the SBW system model is developed using an unscented Kalman filter (UKF) observer. To improve estimation accuracy, the parameters of the UKF are optimized using the black kite algorithm (BKA). In parallel, a nonlinear bicycle model combined with the Magic Formula tire model is employed to calculate the aligning torque. The observer-based rack force and the model-based aligning torque are converted into two main road-feel torque components through assist torque modules and then fused using road-feel weighting factors. Compared with using either torque source alone, the proposed fusion strategy combines the low-delay and smooth characteristics of the dynamic-model-based component with the stronger uneven-road feedback capability of the observer-based component. In addition, two weighting strategies corresponding to the Comfort and Sport modes are designed to provide different levels of steering comfort and road-surface information feedback, thereby satisfying personalized road-feel preferences under different driving conditions. Finally, the proposed method is validated through CarSim–Simulink co-simulation and hardware-in-the-loop experiments. The results demonstrate that the proposed fusion strategy effectively reduces the delay associated with the observer-based torque source while preserving uneven-road information. Multi-speed road-feel evaluations further show that the Comfort mode provides smoother steering feedback and lower steering effort, whereas the Sport mode retains clearer road-surface information and stronger steering feel. These results confirm that the proposed method improves the realism and adaptability capability of SBW road-feel control.