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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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