Composite sliding mode control of a steer-by-wire road-feel motor using spatial-domain iterative learning and an extended state observer

In steer-by-wire systems, delivering accurate and smooth steering feedback is challenging due to periodic torque ripples, friction nonlinearities, and external disturbances. This paper proposes a layered composite control strategy for the steering feel motor, integrating sliding mode control, spatial-domain iterative learning control, and an extended state observer. First, a comprehensive dynamic model is developed, incorporating vehicle self-aligning torque, permanent magnet synchronous motor electromagnetics, periodic harmonic disturbances, and LuGre dynamic friction, providing a unified basis for controller design. The control architecture is hierarchical: an outer-loop sliding mode control ensures robust torque tracking, and an inner-loop third-order extended state observer estimates aperiodic disturbances in real time for feed-forward compensation. Unlike traditional time-domain methods that deteriorate under variable-speed steering, a middle-layer spatial-domain iterative learning control is introduced to iteratively compensate for angle-dependent periodic torque ripples, maintaining a fixed iteration period in the spatial domain regardless of speed variations. This achieves decoupled and precise mitigation of highly coupled multi-source disturbances. Lyapunov stability analysis proves the closed-loop stability of the composite control system and the convergence of the spatial-domain iterative learning control law. Simulation results demonstrate that the proposed strategy outperforms conventional methods, reducing the root-mean-square error to 0.039 N m and attenuating the dominant 6th- and 12th-order torque harmonics to 45.8 and 48.10 dB, respectively. This achieves high-precision road-feel torque control with minimal chatter.