LMI-Based H∞ Controller of Vehicle Roll Stability Control Systems with Input and Output Delays

Redondo, Jonatan Pajares; Boada, Beatriz L.; Díaz, Vicente · 2021 · Crossref

DOI: 10.3390/s21237850

archive: archived pipeline: cataloged verified

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Summary

This paper addresses the challenge of maintaining vehicle roll stability in commercial vehicles equipped with low-cost embedded systems, which often introduce significant input and output delays due to networked communication. While previous research has demonstrated the feasibility of using low-cost sensors for roll angle estimation, these systems suffer from delays and noise that can compromise safety-critical control performance. The authors propose a novel Linear Matrix Inequality (LMI)-based $H_\infty$ output-feedback controller specifically designed to compensate for both sensor-side (output) and actuator-side (input) delays in Roll Stability Control (RSC) systems. The methodology utilizes a validated vehicle model based on a Mercedes Benz Sprinter, characterized by a state-space representation of roll motion. The system accounts for external disturbances, including lateral acceleration and road bank angle, as well as unknown vector disturbances. The controller design incorporates bounded time delays for both the control input ($h$) and the measured roll rate output ($\rho$). The authors derive stability conditions using a Lyapunov–Krasovskii functional and formulate the controller synthesis as a set of LMIs. This approach ensures asymptotic stability and a guaranteed $H_\infty$ performance index despite the presence of network-induced delays. The control input is defined as an anti-roll moment generated by an active suspension, while the roll rate serves as the measured output. The proposed controller was evaluated through simulation tests using TruckSim® software. The study compares the performance of the delay-compensating $H_\infty$ controller against a conventional controller that does not account for delays but is subjected to the same delay conditions. The results demonstrate that the proposed LMI-based controller effectively mitigates the destabilizing effects of input and output delays. By explicitly modeling the delays in the control loop, the system maintains robust stability and improved roll angle control compared to the non-delay-aware counterpart, which experiences degraded performance under similar network conditions. The significance of this work lies in its contribution to the development of reliable, low-cost Networked Control Systems (NCS) for heavy-duty vehicles. By providing a rigorous mathematical framework for handling delays in both sensing and actuation, the study enables the integration of affordable embedded systems without sacrificing safety or stability. This approach supports the broader goal of reducing rollover incidents in commercial vehicles by ensuring that control systems remain effective even when constrained by the latency inherent in cost-effective communication networks.

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