Robust $H_{\infty}$ Position Controller for Steering Systems

TL;DR

The paper tackles robust steering control in EPAS and steer-by-wire systems by incorporating a multi-variable $H_{\infty}$ design that includes sensed torque feedback to counteract driver-induced coupling inertia. It develops a 2-DOF model, performs system identification, and then derives both a static-torque-feedback approach and a full LMIs-based $H_{\infty}$ controller, achieving a favorable low-frequency tracking gain while reducing high-frequency sensitivity for robustness. Empirical results on real hardware show improved reference tracking and robustness over classical position controllers, with the $H_{\infty}$ solution offering the best overall performance under arm inertia uncertainty. The work enhances haptic feedback fidelity and steering control reliability in semi- and fully automated driving contexts, and points to future extensions using advanced $H_{\infty}$ techniques such as 2-DOF scheduling and mu-synthesis.

Abstract

This paper presents a robust position controller for electric power assisted steering and steer-by-wire force-feedback systems. A position controller is required in steering systems for haptic feedback control, advanced driver assistance systems and automated driving. However, the driver's \textit{physical} arm impedance causes an inertial uncertainty during coupling. Consequently, a typical position controller, i.e., based on single variable, becomes less robust and suffers tracking performance loss. Therefore, a robust position controller is investigated. The proposed solution is based on the multi-variable concept such that the sensed driver torque signal is also included in the position controller. The subsequent solution is obtained by solving the LMI$-H_{\infty}$ optimization problem. As a result, the desired loop gain shape is achieved, i.e., large gain at low frequencies for performance and small gain at high frequencies for robustness. Finally, frequency response comparison of different position controllers on real hardware is presented. Experiments and simulation results clearly illustrate the improvements in reference tracking and robustness with the proposed $H_\infty$ controller.

Figures (9)

• Figure 1: A typical illustration of: (a) an electric power assisted steering and (b) a steer-by-wire system.
• Figure 2: (a) Simplified $2$-DOF EPAS and SbW-FFb models, where $M_{mot,eff} = i_{mot} M_{mot}$. The system identification frequency response plots for EPAS: (b) $\omega_{p}(j\omega)/M_{mot}(j\omega)$, (c) $M_{tb}(j\omega)/M_{mot}(j\omega)$; and for FFb: (d) $\omega_{p}(j\omega)/M_{mot}(j\omega)$ and (e) $M_{tb}(j\omega)/M_{mot}(j\omega)$.
• Figure 3: A relative % change in bandwidth due to: (a) coupling stiffness $c_{p}$ at $\theta_{p}/M_{d}$ port and (b) coupling inertia $J_{arm}$ at $\theta_{s}/M_{s}$ port.
• Figure 4: The closed-loop $H_{\infty}$ control configuration with different exogenous input-output channels for the reference position tracking problem. $g_{\Delta}(t) = J_{arm} \dot{\omega}_{s}(t)$ is the inverse additive parametric uncertainty. This $P$-$K$ structure is based on a general formulation, described in Skogestad2001.
• Figure 5: Closed-loop EPAS and FFb frequency response with the position control laws in Equations \ref{['eq:PosCtrlSingleVar']} and \ref{['eq:PosCtrlMultiVar']}. This formed the basis to design the $H_{\infty}$ targets (and subsequently the respective weighting functions), as shown for $\omega_{s}/\theta_{p,ref}$, $e_{\theta}/\theta_{p,ref}$ and $M_{tb}/\theta_{p,ref}$ respectively.