Road Feel Simulation Strategy for Steer-by-Wire System in Electric Vehicles Based on an Improved Nonlinear Second-Order Sliding Mode Observer

Addressing the shortcoming that steer-by-wire (SBW) system cannot directly transmit road feel, this study investigates a SBW system dynamics model, steering angle tracking control, and road feel simulation algorithm design. This study proposes a high-precision observer-based road feel simulation method that achieves road feel feedback torque design through the real-time estimation of system disturbance torque based on accurate front-wheel angle tracking. The methodology employs an improved nonlinear second-order sliding mode observer (INSOSMO) to estimate the system disturbance torque. This observer incorporates proportional–integral terms into the super-twisting algorithm to enhance dynamic response, replaces the sign function with a Sigmoid function to eliminate chattering, and utilizes the sparrow search algorithm (SSA) for global parameter optimization. Meanwhile, a two-stage filter combining a strong tracking Kalman filter (STKF) and first-order low-pass filtering processes the observer values to generate road feel feedback torque. Additionally, for the active return control of the steering wheel, a backstepping sliding mode control (BSSMC) integrated with an extended state observer (ESO) is employed, where the ESO enhances the robustness of BSSMC through real-time nonlinear disturbance estimation and compensation. MATLAB/Simulink-CarSim co-simulation demonstrates that, under sinusoidal testing, the INSOSMO reduces mean absolute error (MAE) by 34.7%, 62.5%, and 60.1% compared to the ESO, Kalman filter observer (KFO), and conventional sliding mode observer (SMO), respectively. The designed road feel feedback torque meets operational requirements. The active return controller maintains accurate steering wheel repositioning across various speed ranges.