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为解决用示波器观测单变量非线性系统难的问题, 本文提出了一种45线法, 该方法能将随时间变化的连续信号以特殊的方式转换成直角坐标上45线上的点图, 并可用通用双踪示波器 (模拟或数字均可)直接显示出来, 从而达到直接方便地观测和分析单变量被测系统运行时的各种状态, 如周期稳定态, 局部和全局不稳定态. 文中详细阐述了该方法的机理. 同时, 研究和解决了设计实现该方法物理电路的关键问题, 即从连续变化的信号中提取出能反映系统状态的有用信号. 由于蔡氏电路是典型的非线性系统, 且能随参数的变化产生各种丰富的状态, 本文选用该电路作为被测系统进行了大量的物理实验, 实验结果证实了该方法的有效性和实用性.In order to solve the problem why it was hard to observe the single-variable nonlinear system, this article proposed the 45 line method. In this method, the continuous signal changing with time was transformed into dots on the 45 line of the rectangular coordinates, so that it could be directly displayed on a general dual-trace oscilloscope (either analog or digital). In this way, it is convenient to directly observe and analyze various states of single-variable system while the system is running, such as the periodical stable states, the local and global non-stable states. The mechanism of this method was expounded in this paper. In addition, the key issues in physical circuit design and implementation of this method were researched and solved, i.e., the useful signal which reflected the state of the system could be extracted from the continuously changing signal. Since the Chuas circuit is a typical nonlinear system, and it could produce abundant states with variation of parameters, so it was chosen as the system under test to conduct a great number of physical experiments. The experimental results confirmed the effectiveness and practicability of this method.
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Keywords:
- 45line method /
- single-variable system /
- system state /
- dual trace oscilloscope
[1] Cao Z C, Han D F, Wang Y J 2012 Acta Electronica Sin. 40 2062 (in Chinese) [曹政才, 韩丁富, 王永吉 2012 电子学报 40 2062]
[2] Jiang H F, Chen S F 2009 Systems Engineering 27 116 (in Chinese) [蒋慧峰, 陈森发 2009 系统工程 27 116]
[3] Zhang W C, Tan S C, Gao P Z 2013 Acta Phys. Sin. 62 060502 (in Chinese) [张文超, 谭思超, 高璞珍 2013 物理学报 62 060502]
[4] Tang J, Zhang X 2012 Acta Phys. Sin. 61 169601 (in Chinese) [唐洁, 张雄 2012 物理学报 61 169601]
[5] Wang W K, Zeng Z M, Li Y B, Jin S J 2012 Nanotechnology and Precision Engineering 10 531 (in Chinese) [王伟魁, 曾周末, 李一博, 靳世久 2012 纳米技术与精密工程 10 531]
[6] Zhang Y, Guan W 2009 Acta Phys. Sin. 58 756 (in Chinese) [张勇, 关伟 2009 物理学报 58 756]
[7] Yang H, Wu W 2012 Automation of Electric Power Systems 36 103 (in Chinese) [杨浩, 吴畏 2012 电力系统自动化 36 103]
[8] Chen H, Wu L 2013 Acta Phys. Sin. 62 020507 (in Chinese) [陈红, 吴玲 2013 物理学报 62 020507]
[9] Nie C Y 2009 Chaotic Systems and Weak Signal Detection (Beijing: Tsinghua University Press) p41 (in Chinese) [聂春燕 2009 混沌系统与弱信号检测 (北京: 清华大学出版社) 第41页]
[10] Chen H, Gao M Z, Ding Q 2010 ICIC Express Letters Part B: Applications 1 221
[11] Rana K P S, Singh R, Sayann K S 2010 Measurement 43 299
[12] Matsumoto T, Chua L O, Komuro M 1985 IEEE Trans on Circuits and Systems 32 797
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[1] Cao Z C, Han D F, Wang Y J 2012 Acta Electronica Sin. 40 2062 (in Chinese) [曹政才, 韩丁富, 王永吉 2012 电子学报 40 2062]
[2] Jiang H F, Chen S F 2009 Systems Engineering 27 116 (in Chinese) [蒋慧峰, 陈森发 2009 系统工程 27 116]
[3] Zhang W C, Tan S C, Gao P Z 2013 Acta Phys. Sin. 62 060502 (in Chinese) [张文超, 谭思超, 高璞珍 2013 物理学报 62 060502]
[4] Tang J, Zhang X 2012 Acta Phys. Sin. 61 169601 (in Chinese) [唐洁, 张雄 2012 物理学报 61 169601]
[5] Wang W K, Zeng Z M, Li Y B, Jin S J 2012 Nanotechnology and Precision Engineering 10 531 (in Chinese) [王伟魁, 曾周末, 李一博, 靳世久 2012 纳米技术与精密工程 10 531]
[6] Zhang Y, Guan W 2009 Acta Phys. Sin. 58 756 (in Chinese) [张勇, 关伟 2009 物理学报 58 756]
[7] Yang H, Wu W 2012 Automation of Electric Power Systems 36 103 (in Chinese) [杨浩, 吴畏 2012 电力系统自动化 36 103]
[8] Chen H, Wu L 2013 Acta Phys. Sin. 62 020507 (in Chinese) [陈红, 吴玲 2013 物理学报 62 020507]
[9] Nie C Y 2009 Chaotic Systems and Weak Signal Detection (Beijing: Tsinghua University Press) p41 (in Chinese) [聂春燕 2009 混沌系统与弱信号检测 (北京: 清华大学出版社) 第41页]
[10] Chen H, Gao M Z, Ding Q 2010 ICIC Express Letters Part B: Applications 1 221
[11] Rana K P S, Singh R, Sayann K S 2010 Measurement 43 299
[12] Matsumoto T, Chua L O, Komuro M 1985 IEEE Trans on Circuits and Systems 32 797
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