Dynamic model of steer-by-wire system for driver handwheel feedback

Ait-Oufroukh, N.; Messaoudène, K.; Mammar, S. · 2013 · Crossref

DOI: 10.1109/icnsc.2013.6548837

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Summary

This paper presents a dynamic model for a steer-by-wire system designed to provide realistic handwheel feedback to drivers, specifically addressing the scenario of a stopped vehicle. The research is motivated by the development of an innovative brake handwheel prototype, initially intended for paraplegic drivers but applicable to all users, which integrates steering and braking functions. The primary objective is to establish the dynamic equations governing the forces and torques exchanged between the handwheel and the front wheels, ensuring that the driver receives appropriate tactile feedback despite the absence of mechanical linkages. The proposed architecture replaces traditional mechanical connections with two DC electric motors: one for steering actuation connected to the rack-and-pinion via a hydraulic assistance valve, and another for restitution connected to the handwheel to simulate feedback. The modeling process incorporates tire behavior during stationary steering, where front tires are sheared by driver torque and friction forces until reaching a saturation zone. The authors derive state-space representations for both the restitution block (handwheel) and the steering block (front wheels). Key parameters include inertias, viscous friction, stiffness of torsion bars, and tire lateral stiffness. The model accounts for hydraulic assistance linearized around an operating point and calculates the torque required from the steering engine to mimic conventional steering column dynamics. Additionally, an adjustable torque term is included to fine-tune the handwheel feeling and inertia. Simulation results validate the model using two distinct driver torque profiles. The first profile, a saw-tooth waveform, demonstrates the relationship between the front wheel steering angle and the tire’s sheared surface angle, highlighting the delay caused by tire deformation before the wheels physically turn. The second profile, a right-left steering maneuver, illustrates the hysteresis phenomenon inherent in stationary steering, where the handwheel position depends on the history of applied torque due to friction saturation limits. These simulations confirm that the model accurately captures the complex interaction between driver input, tire friction, and hydraulic assistance. The significance of this work lies in its contribution to the design of safe and ergonomic steer-by-wire systems, particularly for specialized vehicles requiring integrated control interfaces. By providing a rigorous mathematical framework for handwheel feedback in stationary conditions, the study enables the development of control laws that replicate the natural feel of mechanical steering. This enhances driver confidence and comfort, supporting the broader adoption of X-by-wire technologies in automotive engineering. The model serves as a foundation for future experimental validation using the described prototype.

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• steering pattern
• haptic feedback

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• Theoretical Contribution: computational model