Simulation specifications.

An EPS system is used to improve the stability and safety of the car when steering while also simplifying the steering process. This article introduces a novel control solution for the EPS system called BSSMCPID. This algorithm combines two nonlinear techniques, BS and SMC, with the input signal corrected by a PID technique. This algorithm provides three new contributions compared to existing algorithms: reducing system errors and eliminating phase differences, ensuring stability even when exposed to external disturbances, and reducing power consumption. The system’s stability is evaluated according to the Lyapunov criterion, while the algorithm’s performance is evaluated based on numerical simulation results. According to the article findings, the RMS error of the steering column angle and steering motor angle values (controlled objects) is approximately zero, and the RMS error of the steering column speed and steering motor speed is about 0.01 rad/s, which is much lower than the results obtained with traditional BS and PID controllers. When the EPS system is controlled by the integrated nonlinear method proposed in this work, the output values always closely follow the reference values with negligible errors under all investigated conditions. Additionally, power steering performance increases as speed decreases or driver torque increases, which follows the ideal assisted power steering curve. In general, the responsiveness and stability of the system are always ensured when applying this algorithm.