The Design and Stable Delay Range Analysis of TD-H₂/H∞ Controller for SbW Systems

With the advancement of X-by-wire chassis technology, the number of controller area network (CAN) bus-mounted nodes in steering-by-wire (SbW) vehicles has increased, resulting in an increase of input time delay (ITD) in the SbW system’s control input. When the maximum ITD (MITD) exceeds the ITD critical value (ITD-CV) that the SbW controller can tolerate, the SbW system would diverge, causing a major accident. In order to improve the control performance of SbW systems, a novel strategy is proposed, containing an analysis part and a controller design part. In the analysis part, a novel critical eigenroot-based ITD-CV and stable delay range (SDR) analysis method, using the Hurwitz stability criterion to analyze the direction where the eigenroots cross the imaginary axis with ITD varying, is built to evaluate and optimize the SbW system controller. In the controller design part, a novel $\text{TD-H}_{2} / \text{H}_{\mathrm {\infty }}$ controller is established. Specifically, an SbW model with implicit ITD is derived utilizing state transformation theory, and an angle tracking controller (ATC) is developed using H2 and $\text{H}_{\mathrm {\infty }}$ norm constraints to ensure tracking and robustness performance. Finally, simulation and hardware-in-the-loop (HIL) experiment are carried out to verify that the proposed method can efficiently calculate SDR and achieve superior control performance.