用虚功平衡原理求解无损耗系统的主谐波
Solving the Main Harmonic of Lossless System Using the Reactive Power Balance Principle

作者: 黄炳华 * , 卫雅芬 :集美大学信息工程学院; 李广明 :东莞理工学院;

关键词: 虚功功率无损耗:主谐波:哈密顿圈混沌Reactive Power Lossless Main Harmonic Hamiltonian Cycle Chaos

摘要: 含耗能元件的非自治电路,自振分量的存在性取决于实功率能否保持平衡。具有激励源不含耗能元件的非自治电路是一个无损耗系统。自振与受迫两振荡分量无条件同时共存。激励源只输出虚功率,谐振回路不消耗任何实功率,谐振回路的储能每一瞬时都在变化,但经历一周期后其储能保持原值。根据虚功平衡条件可以求出自振频率与两个电压振幅值的关系,主谐波解不但与外激源有关,还与初始条件有关,本文以含有压控非线性电感的谐振电路为例,论证自激与受迫两振荡分量的非线性耦合能产生混沌。

Abstract:

In the nonautonomous circuit which contains the dissipative element, the existence of self excited oscillation depends upon whether or not active power can maintain balance. The nonautonomous circuit with excited source has no dissipative element. It is a lossless system. The forced and self-excited oscillation components can simultaneously coexist unconditionally. The excited source export only reactive power. The resonant circuit does not consume any active power. The energy stored in this resonant circuit varies at all time; but after a cycle, the energy stored maintains original quantity. The relation between self-oscillation frequency and two voltage amplitude of oscillation can be found from the condition for reactive power balance. The main harmonic solutions are relative to both excited source and the initial condition. Taking the resonant circuit which contains the voltage-controlled nonlinear inductor as example, this paper demonstrates that the chaos can be produced by nonlinear coupling of forced and self-excited oscillation components.

文章引用: 黄炳华 , 李广明 , 卫雅芬 (2012) 用虚功平衡原理求解无损耗系统的主谐波。 现代物理, 2, 60-69. doi: 10.12677/MP.2012.23011

参考文献

[1] 黄炳华. 埃米特矩阵和集成网络的稳定性[J]. 固体电子学研究和进展, 1997, 17(3): 235-241.

[2] 黄炳华. 埃米特矩阵的第二形式及其应用[J]. 通信学报, 1999, 2: 53-57.

[3] 黄炳华. 用埃米特式计算复功率[J]. 电路与系统学报, 1999, 4(2): 45-52.

[4] 黄炳华, 卫雅芬, 黄莹. 非线性振荡每一谐波成份的复功率守恒[A]. 第23届电路与系统学术年会论文集[C], 桂林电子科技大学, 2011.

[5] S.-M. Yu, S.-S. Qiu and Q.-H. Lin. New results of study on generating multiple-scroll chaotic attractors. Science in China (Series F), 2003, 46(2): 104-115.

[6] M. P. Kennedy. Chaos in the colpitts oscillator. IEEE Transactions on CAS-1, 1994, 41(11): 771-774.

[7] G. M. Maggio, O. De Feo and M. P. Kennedy. Nonlinear analysis of the colpitts oscillator and applications to design. IEEE Transactions on CAS, 1999, 46(9): 1118-1130.

[8] D. D. Ganji, M. Esmaeilpour and S. Soleimani. Approximate solutions to Van der Pol damped nonlinear oscillators by means of He’s energy balance method. Computer Mathematics, 2010, 87(9): 2014-2023.

[9] Y. M. Chen, J. K. Liu. A new method based on the harmonic balance method for nonlinear oscillators. Physics Letters A, 2007, 368(5): 371-378.

[10] 黄炳华, 黄新民, 张海明. 各类自激振荡的基波分析法[J]. 固体电子学研究和进展, 2005, 25(1): 102-107.

[11] 黄炳华, 黄新民, 王庆华. 用基波平衡原理分析非线性电子网络的稳定性[J]. 固体电子学研究和进展, 2006, 26(1): 43- 48.

[12] 黄炳华, 黄新民, 韦善革. 用基波平衡原理分析非线性振荡与混沌[J]. 通信学报, 2008, 29(1): 65-70.

[13] 黄炳华, 钮利荣, 蔺兰峰. 功率平衡基础上的基波分析法[J]. 电子学报, 2007, 35(10): 1994-1998.

[14] 黄炳华, 陈辰, 韦善革. 基波平衡原理的推广[J]. 固体电子学研究和进展, 2008, 28(1): 57-62.

[15] 黄炳华, 黄新民, 李晖. 基于功率平衡的谐波分析法[A]. 22届电路与系统学术年会论文集[C], 上海复旦大学, 2010.

[16] B.-H. Huang, X.-M. Huang and H. Li. Main components of harmonic solutions. International Conference on Electric Information and Control Engineering, Nanning, 15-17 April 2011: 2307-2310.

[17] B.-H. Huang, X.-M. Huang and H. Li. Main components of harmonic solutions of nonlinear oscillations. Procedia Engineering, 2011, 16: 325-332.

[18] S. M. Yu, W. K. S. Tang, J. Lu, et al. Generating 2n-wing attrac- tors from Lorenz-like systems. International Journal of Circuit Theory and Applications, 2010, 38(3): 243-258.

[19] Mathematica程序(按出现先后排序):①Tab1.nb; ②Leq.nb; ③whwh.nb; ④Tab2.nb; ⑤wh35.nb; ⑥Tab3.nb; ⑦Tab4.nb.

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