| 摘要 | 本文探讨了板凳龙沿阿基米德螺线盘入过程中, 各把手位置的确定方法。首先, 根据各把手盘入的行径特征, 确定对应极角的定量搜索范围, 为后续算法提供初值。随后, 提出了一种用于计算后一把手位置的动态反馈算法, 该算法有效避免了在求解非线性方程组时出现的多解问题。此外, 为提高计算效率, 研究了不同极角与迭代参数的函数设计。在仿真环境下, 验证了该动态反馈算法的有效性。 |
| Abstract | The paper considers the problem of determining the position of each handle as the bench dragon coils along the spiral. First, the quantitative searching range of the corresponding polar angle of the handle is given according to the traveling path characteristics of each handle coiled in, offering the initial value for the proposed algorithm. Then, a dynamical feedback algorithm for calculating the position of the latter handle is proposed, which avoids the multi-solution problem of solving nonlinear equations. Furthermore, to promote the computational efficiency, the design of iterative parameters based on varying polar angles is discussed. In the simulation environment, the effectiveness of the proposed dynamical feedback algorithm is illustrated. |
| DOI | 10.48014/bcam.20241118001 |
| 文章类型 | 研究性论文 |
| 收稿日期 | 2024-11-18 |
| 接收日期 | 2024-12-15 |
| 出版日期 | 2025-03-28 |
| 关键词 | 动态反馈算法, 迭代参数, 板凳龙 |
| Keywords | Dynamical feedback algorithm, iterative parameter, bench dragon |
| 作者 | 郑雯欢1, 郑姝艺1, 陈森1,*, 郑姝琳2 |
| Author | ZHENG Wenhuan1, ZHENG Shuyi1, CHEN Sen1,*, ZHENG Shulin2 |
| 所在单位 | 1. 陕西师范大学数学与统计学院, 西安 710119 2. 陕西师范大学物理学与信息技术学院, 西安 710119 |
| Company | 1. School of Mathematics and Statistics, Shaanxi Normal University, Shaanxi, Xi' an 710119, China 2. School of Physics and Information Technology, Shaanxi Normal University, Shaanxi, Xi' an 710119, China |
| 浏览量 | 152 |
| 下载量 | 62 |
| 基金项目 | This work is supported by the Young Talent Fund of Association for Science and Technology in Shaanxi,China,under grant No.20230513. |
| 参考文献 | [1] Liu C. Historical changes of Jiangxi folk sports “Ta Chengxiang bench dragon”[J]. World of Archives, 2014,(35): 154-155.(in Chinese) https://doi.org/10.16565/j.cnki.1006-7744.2014.35.018. [2] Wu L. Aesthetic Review of Huizhou Folk Sports: Based on the Field Investigation of Bench Dragon of Youlong Village[J]. Sports Research and Education, 2021, 36(04): 76-80.(in Chinese) https://doi.org/10.16207/j.cnki.2095-235x.2021.04.013 [3] Liu S. Investigation and Study on Pu Jiang Bench Dragon[J]. Ethnic Art, 2009,(04): 106-108+115.(in Chinese) https://doi.org/10.16564/j.cnki.1003-2568.2009.04.022.(inChinese) [4] Mao R, Wang Q, Wang Z, et al. On the Living Inheritance of Huizhou Bench Dragon in the View of Intangible Cultural Heritage Protection[J]. Martial Arts Studies, 2021, 6(01): 131-132.(in Chinese) https://doi.org/10.13293/j.cnki.wskx.008789. [5] Luo J. The Inheritance of Bench Dragon Folk Culture in the Context of Social Development[J]. Todays Literature and Art Creation, 2022,(40): 104-106.(in Chinese) https://doi.org/10.20024/j.cnki.CN42-1911/I.2022.40.033. [6] Ibrahim H A, Homidan A S. A derivative-free projection method with double inertial effects for solving nonlinear equations[J]. Applied Numerical Mathematics, 2025, 20955-67. https://doi.org/10.1016/J.APNUM.2024.11.006 [7] Li X, Liu M. Solving Nonlinear Equation Systems Based on Improved Whale Optimization Algorithm[J]. Engineering and Management Science, 2024, 6(11).(in Chinese) https://doi.org/10.12238/EMS.V6I11.10005 [8] Popkov S Y. Analytic Method for Solving One Class of Nonlinear Equations[J]. Doklady Mathematics, 2024: 1- 4.(prepublish) https://doi.org/10.1134/S1064562424601392 [9] Mittal K S, Panday S, Jäntschi L. Enhanced Ninth-Order Memory-Based Iterative Technique for Efficiently Solving Nonlinear Equations[J]. Mathematics, 2024, 12(22): 3490-3490. https://doi.org/10.3390/MATH12223490 [10] Ozbay H. Introduction to feedback control theory[M]. CRC Press, 2019. https://doi.org/10.1201/9780203750117 [11] Ross I M, Sekhavat P, Fleming A, et al. Optimal Feedback Control: Foundations, Examples, and Experimental Results for a New Approach[J]. Journal of Guidance, Control, and Dynamics, 2008, 31(2): 307-321. https://doi.org/10.2514/1.29532 [12] Khalil H K, Praly L. High-gain Observers in Nonlinear Feedback Control[J]. International Journal of Robust and Nonlinear Control, 2014, 24(6): 993-1015. https://doi.org/10.1002/rnc.3156 [13] Peng N, Yao B, Wang F. Research of H2 Dynamic Output Feedback Reliable Control Against any Fault[J]. Computer Technology and Automation, 2016, 35(01): 1-4.(in Chinese) https://doi.org/10.16339/j.cnki.jsjsyzdh.2016.01.001. [14] Wei A, Zhao K. Analysis and Design for Linear Systems with Saturation by Linear Feedback[J]. Control and Decision, 2005,(01): 59-61+68.(in Chinese) https://doi.org/10.13195/j.cd.2005.01.59.weiar.013. [15] Long Y, Fan Y. Multiple and Sign-Changing Solutions for Boundary Value Problems of Second-Order Nonlinear Difference Equations[J]. Applied Mathematics, 2018, 31(03): 522-532.(in Chinese) https://doi.org/10.13642/j.cnki.42-1184/o1.2018.03.034. |
| 引用本文 | 郑雯欢, 郑姝艺, 陈森, 等. 板凳龙行径位置计算的动态反馈算法[J]. 中国应用数学通报, 2025, 3(1): 1-9. |
| Citation | ZHENG Wenhuan, ZHENG Shuyi, CHEN Sen, et al. Dynamical feedback algorithm for calculating the moving position of bench dragon' s path[J]. Bulletin of Chinese Applied Mathematics, 2025, 3(1): 1-9. |