{"title":"Balancing riderless electric scooters at zero speed in the presence of a feedback delay","authors":"Hanna Zsofia Horvath, Denes Takacs","doi":"10.1007/s11044-024-10019-z","DOIUrl":null,"url":null,"abstract":"<p>The nonlinear dynamics of electric scooters are investigated using a spatial mechanical model. The equations of motion are derived with the help of Kane’s method. Two control algorithms are designed in order to balance the e-scooter in a vertical position at zero forward speed. Hierarchical, linear state feedback controllers with feedback delay are considered. In the case of a delay-free controller, the linear stability properties are analyzed analytically, with the help of the Routh–Hurwitz criteria. The linear stability charts of the delayed controllers are constructed with the help of the D-subdivision method and semi-discretization. The control gains of the controllers are optimized with respect to the robustness against perturbations. The effects of the feedback delay of the controllers, the rake angle, the trail, and the center of gravity of the handlebar on the linear stability are shown. The performance of the control algorithms is verified by means of numerical simulations.</p>","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Multibody System Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s11044-024-10019-z","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The nonlinear dynamics of electric scooters are investigated using a spatial mechanical model. The equations of motion are derived with the help of Kane’s method. Two control algorithms are designed in order to balance the e-scooter in a vertical position at zero forward speed. Hierarchical, linear state feedback controllers with feedback delay are considered. In the case of a delay-free controller, the linear stability properties are analyzed analytically, with the help of the Routh–Hurwitz criteria. The linear stability charts of the delayed controllers are constructed with the help of the D-subdivision method and semi-discretization. The control gains of the controllers are optimized with respect to the robustness against perturbations. The effects of the feedback delay of the controllers, the rake angle, the trail, and the center of gravity of the handlebar on the linear stability are shown. The performance of the control algorithms is verified by means of numerical simulations.
本文利用空间机械模型研究了电动滑板车的非线性动力学。运动方程是在凯恩法的帮助下推导出来的。设计了两种控制算法，以平衡电动滑板车在零前进速度下的垂直位置。考虑了有反馈延迟的分层线性状态反馈控制器。在无延迟控制器的情况下，借助 Routh-Hurwitz 准则对线性稳定性特性进行了分析。延迟控制器的线性稳定性图是借助 D 细分法和半离散化构建的。根据对扰动的鲁棒性，对控制器的控制增益进行了优化。图中显示了控制器的反馈延迟、车耙角、车道和车把重心对线性稳定性的影响。通过数值模拟验证了控制算法的性能。
期刊介绍：
The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations.
The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
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