A Kalman Filter-Based Disturbance Observer for Steer-by-Wire Systems

TL;DR

This paper addresses high-frequency driver-impedance disturbances in Steer-by-Wire (SbW) systems by designing a Kalman filter-based disturbance observer (DOB) that estimates the passive driver torque $T_d$ from motor-state measurements. Driver torque is modeled as a PT1 element and integrated into both linear and nonlinear hand-wheel dynamics, with discrete KF and EKF variants used to estimate $T_d$ and enable disturbance rejection within the control loop. The study finds that the EKF-based DOB outperforms the linear KF in nonlinear friction regimes, achieving an estimation delay of approximately $14\,\mathrm{ms}$ and enabling effective disturbance rejection when embedded in an MPC-based steering controller. While the results are based on simulations, they demonstrate the potential to reject high-frequency driver impedance without direct torque sensing, highlighting the need for further robustness analyses and real-world validation in HiL and in-vehicle experiments.

Abstract

Steer-by-Wire systems replace mechanical linkages, which provide benefits like weight reduction, design flexibility, and compatibility with autonomous driving. However, they are susceptible to high-frequency disturbances from unintentional driver torque, known as driver impedance, which can degrade steering performance. Existing approaches either rely on direct torque sensors, which are costly and impractical, or lack the temporal resolution to capture rapid, high-frequency driver-induced disturbances. We address this limitation by designing a Kalman filter-based disturbance observer that estimates high-frequency driver torque using only motor state measurements. We model the drivers passive torque as an extended state using a PT1-lag approximation and integrate it into both linear and nonlinear Steer-by-Wire system models. In this paper, we present the design, implementation and simulation of this disturbance observer with an evaluation of different Kalman filter variants. Our findings indicate that the proposed disturbance observer accurately reconstructs driver-induced disturbances with only minimal delay 14ms. We show that a nonlinear extended Kalman Filter outperforms its linear counterpart in handling frictional nonlinearities, improving estimation during transitions from static to dynamic friction. Given the study's methodology, it was unavoidable to rely on simulation-based validation rather than real-world experimentation. Further studies are needed to investigate the robustness of the observers under real-world driving conditions.

Figures (10)

• Figure 1: Schematic architecture of a SbW-system with consideration of driver impedance and resulting passive driver torque rejection.
• Figure 2: 2-mass spring damper HW system model (no gear displayed)
• Figure 3: Control structure of the HW module using MPC and Kalman filter-based DOB
• Figure 4: Bode plots of the driver torque estimation for KF and EKF, identified via Matlab's tfestimate.
• Figure 5: Evolution of steering wheel angle and angular velocity of the nonlinear system and EKF-based estimations without disturbance rejection