Bifurcation Analysis of a Lane Keeping Controller With Feedback Delay

Illés Vörös, D. Takács
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引用次数: 2

Abstract

The aim of this study is to highlight nonlinear behaviors and periodic orbits of the single-track vehicle model with a delayed feedback controller. Two widely used tire models, namely a linear tire characteristic and Pacejka’s Magic Formula are considered. Linearly stable domains of parameters such as the vehicle speed and the control gains are determined. Periodic solutions originating from Hopf bifurcation points are followed using numerical continuation and the results obtained with the two different tire models are compared. It is shown that neglecting the saturation of the tire lateral forces at total sliding might change the sense of certain Hopf bifurcations from subcritical to supercritical. The results are verified by numerical simulations. The resulting bifurcation diagrams aim to quantify the degree of robustness of these controllers with regards to the initial conditions at various parameter ranges in order to assure stable and safe operation.
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一类具有反馈时滞的车道保持控制器的分岔分析
本研究的目的是突出具有延迟反馈控制器的单轨车辆模型的非线性行为和周期轨道。考虑了两种常用的轮胎模型,即线性轮胎特性模型和Pacejka魔术公式模型。确定了车辆速度和控制增益等参数的线性稳定域。采用数值延拓法对Hopf分岔点的周期解进行了跟踪,并对两种轮胎模型的结果进行了比较。结果表明,忽略全滑动时轮胎侧力的饱和可能会使某些Hopf分岔的意义由亚临界变为超临界。数值模拟验证了结果。所得到的分岔图旨在量化这些控制器在不同参数范围内的初始条件下的鲁棒性程度,以确保稳定和安全运行。
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