大功率分数阶电感的电路实现
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摘要
现有研究结果表明,自然界中的许多物理现象本质上都具有分数阶的特性,如电感实际上是一种分数阶元件,理想的整数阶电感并不存在。目前普遍采用的分数阶电感等效电路均存在功率等级受限、电感阶数和感值不易调节等缺点,为此,利用电压型逆变器,构造了一种大功率分数阶电感电路的等效模型,通过更改逆变器的控制参数,可以实现分数阶电感阶数和感值的灵活调节。此外,该分数阶电感等效电路模型的功率等级取决于逆变器,故可适用于各种不同的应用场合。最后,将提出的大功率分数阶电感等效模型应用到分数阶RLβC并联谐振电路中,验证了该模型的工作性能。
At present, the existing research results show that lots of physical phenomena in nature have fractional characteristics indeed. For example, an inductor is actually a fractional-order component, while the ideal integral-order inductor does not exist. However, the commonly used circuit models of fractional inductor have some drawbacks, such as limitation on the power level, and difficulties in the adjustment of fractional orders and inductance. Accordingly, an equivalent circuit model of high-power fractional inductor is constructed in this paper by means of a voltage sourced inverter, thus different fractional orders and inductances can be adjusted flexibly by changing the control parameters of the inverter. In addition, as the power level of the proposed equivalent circuit model is determined by the inverter, this model is suitable for various application scenarios. Finally, the equivalent model of high-power fractional inductor is applied to a fractional RLβC parallel resonant circuit, which verifies the performance of this model.
At present, the existing research results show that lots of physical phenomena in nature have fractional characteristics indeed. For example, an inductor is actually a fractional-order component, while the ideal integral-order inductor does not exist. However, the commonly used circuit models of fractional inductor have some drawbacks, such as limitation on the power level, and difficulties in the adjustment of fractional orders and inductance. Accordingly, an equivalent circuit model of high-power fractional inductor is constructed in this paper by means of a voltage sourced inverter, thus different fractional orders and inductances can be adjusted flexibly by changing the control parameters of the inverter. In addition, as the power level of the proposed equivalent circuit model is determined by the inverter, this model is suitable for various application scenarios. Finally, the equivalent model of high-power fractional inductor is applied to a fractional RLβC parallel resonant circuit, which verifies the performance of this model.
引文
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[2]Rastogi A,Tiwari P.Optimal tuning of fractional order PIDcontroller for DC motor speed control using particle swarm optimization[J].International Journal of Soft Computing&Engineering,2013,3(2):150-157.
[3]Chen Yangquan,Sun Rongtao,Zhou Anhong,et al.Fractional order signal processing of electrochemical noises[J].Journal of Vibration&Control,2008,14(9-10):1443-1456.
[4]Schfer I,Krüger K.Modelling of coils using fractional derivatives[J].Journal of Magnetism&Magnetic Materials,2006,307(1):91-98.
[5]马龙,梁贵书,董华英.含分数阶电抗元件网络的灵敏度分析[J].华北电力大学学报:自然科学版,2013,40(3):6-10.Ma Long,Liang Guishu,Dong Huaying.Sensitivity analysis of the networks with fractional order reactance[J].Journal of North China Electric Power University:Natural Science,2013,40(3):6-10(in Chinese).
[6]Radwan A G,Salama K N.Passive and active elements using fractional LβCαcircuit[J].IEEE Transactions on Circuits&Systems I Regular Papers,2011,58(10):2388-2397.
[7]PetráI,Chen Yangquan,Coopmans C.Fractional-order memristive systems[C]//2009 IEEE Conference on Emerging Technologies and Factory Automation.Palma De Mallorca,Spain,2009:1-8.
[8]El-Khazali R,Tawalbeh N.Realization of fractional-order capacitors and inductors[C]//5th-IFAC Symposium on Fractional Diff.and its Applications.Nanjing,China,2012.
[9]谭程,梁志珊.电感电流伪连续模式下Boost变换器的分数阶建模与分析[J].物理学报,2014,63(7):50-59.Tan Cheng,Liang Zhishan.Modeling and simulation analysis of fractional-order Boost converter in pseudo-continuous conduction mode[J].Acta Phys Sin,2014,63(7):50-59.
[10]马冬冬,王志强,王进君,等.单相逆变器分数阶建模及分析[J].电测与仪表,2017,54(6):106-112.Ma Dongdong,Wang Zhiqiang,Wang Jinjun,et al.Fractional modeling and analysis of single-phase inverter[J].Electrical Measurement&Instrumentation.2017,54(6):106-112.
[11]Tsirimokou G,Psychalinos C,Freeborn T J,et al.Emulation of current excited fractional-order capacitors and inductors using OTA topologies[J].Microelectronics Journal,2016,55(9):70-81.
[12]Tripathy M C,Mondal D,Biswas K,et al.Experimental studies on realization of fractional inductors and fractionalorder bandpass filters[J].International Journal of Circuit Theory&Applications,2014,43(9):1183-1196.
[13]Nakagawa M.Basic characteristics of a fractance device[J].Ieice Trans Fundamentals,1992,75(12):1814-1819.
[14]王东东,张波,丘东元,等.分数阶电路的相量分析法及正弦稳态特性研究[J].电源学报,2017,15(4):34-40.Wang Dongdong,Zhang Bo,Qiu Dongyuan,et al.Phasor analysis method and study of sinusoidal steady state characteristics of the fractional-order circuits[J].Journal of Power Supply,2017,15(4):34-40(in Chinese).
[15]Herrmann R.Fractional calculus:an introduction for physicists[J].2nd ed.World Scientific,2014,152(6):846-850.