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arXiv 2602.08757eess.SYcs.SY
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具有分布式轮胎摩擦动力学的半线性单轨车辆模型的稳定性与镇定 via 奇异摄动分析

Stability and stabilization of semilinear single-track vehicle models with distributed tire friction dynamics via singular perturbation analysis

Linköping University(林雪平大学);Norwegian University of Science and Technology(挪威科技大学);University of California San Diego(加州大学圣地亚哥分校)

Luigi Romano, Ole Morten Aamo, Miroslav Krstić, Jan Åslund, Erik Frisk

AI总结:

本文通过奇异摄动分析,建立了首个将分布式轮胎模型与传统车辆动力学严格联系的数学框架,为车辆稳定性与镇定提供了理论基础。

摘要:

本文研究了具有分布式轮胎摩擦动力学的半线性单轨车辆模型的稳定性与镇定问题,该模型被建模为常微分方程(ODEs)和双曲偏微分方程(PDEs)的互连。受长期以来在车辆建模和控制中忽略瞬态轮胎动力学的实践启发,本文利用奇异摄动理论提供了这种简化方法的严格证明。引入了一个定义为特征滚动接触长度与车辆纵向速度比值的摄动参数,以正式表征刚体运动与轮胎动力学之间的时间尺度分离。对于该参数足够小的情况下,证明标准有限维技术可以应用于分析平衡点的局部稳定性并设计稳定化控制器。考虑了状态反馈和输出反馈设计,假定标准可稳定性和可检测性假设。尽管所提出的控制器遵循经典方法,但该工作的创新之处在于建立了首个将分布式轮胎模型与传统车辆动力学严格联系起来的数学框架。结果将数十年的经验发现与正式理论基础相结合,并为汽车应用中ODE-PDE系统的分析和控制开辟了新的视角。

英文摘要:

This paper investigates the stability and stabilization of semilinear single-track vehicle models with distributed tire friction dynamics, modeled as interconnections of ordinary differential equations (ODEs) and hyperbolic partial differential equations (PDEs). Motivated by the long-standing practice of neglecting transient tire dynamics in vehicle modeling and control, a rigorous justification is provided for such simplifications using singular perturbation theory. A perturbation parameter, defined as the ratio between a characteristic rolling contact length and the vehicle's longitudinal speed, is introduced to formalize the time-scale separation between rigid-body motion and tire dynamics. For sufficiently small values of this parameter, it is demonstrated that standard finite-dimensional techniques can be applied to analyze the local stability of equilibria and to design stabilizing controllers. Whilst the proposed controllers build on classical approaches, the novelty of this work lies in establishing the first singular perturbation framework for ODE-PDE vehicle models with distributed tire dynamics, providing a theoretical justification for their quasi-static reduction and for the use of finite-dimensional tools for analysis and control design.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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