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基于电感和电容本质上是分数阶的事实，采用分数阶微积分理论建立了电感电流伪连续模式下Boost变换器的区间分数阶数学模型. 依据状态平均建模方法，建立了Boost变换器工作于电感电流伪连续模式下的分数阶状态平均模型. 通过所建的分数阶数学模型对其电感电流和输出电压进行了理论分析以及传递函数的推导，并比较了与整数阶数学模型的区别. 根据改进的Oustaloup分数阶微积分滤波器近似算法，采用电感和电容的等效分数阶电路模型，在Matlab/Simulink的仿真环境下，对其数学模型和电路模型进行了仿真对比，分析了模型误差产生的原因，验证了所建的分数阶数学模型以及对其理论分析的正确性. 最后，指出了分数阶Boost变换器工作于电感电流伪连续模式与连续模式、断续模式的区别与联系.
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关键词:
- 分数阶 /
- Boost变换器 /
- 伪连续模式(三态模式) /
- 数值仿真
Based on the fact that the inductor and the capacitor are fractional in nature, the fractional order mathematical model of the Boost converter in pseudo-continuous conduction mode is established by using fractional order calculus theory. According to the state average modeling method, the fractional order state average model of Boost converter in pseudo-continuous conduction mode is built. In view of the mathematical model, the inductor current and the output voltage are analyzed and the transfer functions are derived. Then the differences between the integer order and the fractional order mathematical models are analyzed. On the basis of the improved Oustaloup fractional order calculus for filter approximation algorithm and the model of fractional order inductance and capacitance, the simulation results have been compared between the mathematical model and circuit model with Matlab/Simulink software; the origins of model error are analyzed and the correctness of the modeling in fractional order and the theoretical analysis is verified. Finally, the differences and the relations of Boost converter among the continuous conduction mode, the discontinuous conduction mode, and the pseudo-continuous conduction mode are indicated.-
Keywords:
- fractional order /
- Boost converter /
- pseudo continuous conduction mode(tri-state mode) /
- numerical simulation
[1] Yang S P, Zhang R X 2008 Acta Phys. Sin. 57 6837 (in Chinese)[杨世平, 张若洵2008 物理学报57 6837]
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[4] Kenneth S M, Bertram R 1993 An Introduction to the Fractional Calculus and Fractiona Differential Equations (New Jersey: John Wiley & Sons) p21
[5] Shockooh A, Suarez L 1999 Journal of Viberation and Control. 5 331
[6] Bohannan G W 2002 Proceedings of the 41st IEEE International Conference on Decision and Control, Tutorial Workshop 2:Fractional Calculus Applications in Automatic Control and Robotics Las Vegas, USA, December 10-13, 2002 p1
[7] Westerlund S, Ekstam L 1994 IEEE Trans. Dielectr. Electr. Insulat. 1 826
[8] Westerlund S 2002 Dead matter has memory (Kalmar, Sweden: Causal Consulting)chapt. 7
[9] Ahmad W 2003 Proceedings of the 2003 International Symposium on Circuits and Systems Bangkok, Thailand, May 25-28, 2003 3 p5
[10] Martinez R, Bolea Y, Grau A, Martinez H 2009 IEEE Conference on Emerging Technologies & Factory Automation Palma de Mallorca, Spain, September 22-25, 2009 p1
[11] Wang F Q, Ma X K 2011 Acta Phys. Sin. 60 070506 (in Chinese)[王发强, 马西奎2011 物理学报60 070506]
[12] Wang F Q, Ma X K 2013 Scientia Sinica Technological. 43 368 (in Chinese)[王发强, 马西奎2013 中国科学: 43 368]
[13] Ma D S, Ki W H 2007 IEEE Trans. Circuit and Systtems Ⅱ: Express Briefs. 54 825
[14] Kanakasabai V, Ramesh O, Dipti S 2002 IEEE Trans. Power Electronics. 17 677
[15] Podlubny I 1999 Fractional differential equations (New York: Academic Press) chapt 1-2,4
[16] Yu H K 2010 M. S. Thesis. (Sichuan: Southeast Jiaotong University) (in Chinese) [于海坤2010 硕士学位论文 (四川: 西南交通大学)]
[17] Wang F Q, Ma X K 2013 Chin. Phys. B 22 236
[18] Xue D Y, Chen Y Q 2007 MATLAB Solutions to Mathematical Problems in Control (Beijing: Tsinghua University Press) p435 (in Chinese) [薛定宇, 陈阳泉2007 控制数学问题的MATLAB 求解(北京: 清华大学出版社) 第 435 页]
[19] Cao W S, Yang Y X 2007 Journal of System Simulation. 19 1329 (in Chinese) [曹文思, 杨育霞2007 系统仿真学报 19 1329]
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[1] Yang S P, Zhang R X 2008 Acta Phys. Sin. 57 6837 (in Chinese)[杨世平, 张若洵2008 物理学报57 6837]
[2] Zhang C F, Gao J F, Xu L 2007 Acta Phys. Sin. 56 5124 (in Chinese)[张成芬, 高金峰, 徐磊2007 物理学报56 5124]
[3] Li C L, Yu S M, Luo X S 2012 Chin. Phys. B 21 172
[4] Kenneth S M, Bertram R 1993 An Introduction to the Fractional Calculus and Fractiona Differential Equations (New Jersey: John Wiley & Sons) p21
[5] Shockooh A, Suarez L 1999 Journal of Viberation and Control. 5 331
[6] Bohannan G W 2002 Proceedings of the 41st IEEE International Conference on Decision and Control, Tutorial Workshop 2:Fractional Calculus Applications in Automatic Control and Robotics Las Vegas, USA, December 10-13, 2002 p1
[7] Westerlund S, Ekstam L 1994 IEEE Trans. Dielectr. Electr. Insulat. 1 826
[8] Westerlund S 2002 Dead matter has memory (Kalmar, Sweden: Causal Consulting)chapt. 7
[9] Ahmad W 2003 Proceedings of the 2003 International Symposium on Circuits and Systems Bangkok, Thailand, May 25-28, 2003 3 p5
[10] Martinez R, Bolea Y, Grau A, Martinez H 2009 IEEE Conference on Emerging Technologies & Factory Automation Palma de Mallorca, Spain, September 22-25, 2009 p1
[11] Wang F Q, Ma X K 2011 Acta Phys. Sin. 60 070506 (in Chinese)[王发强, 马西奎2011 物理学报60 070506]
[12] Wang F Q, Ma X K 2013 Scientia Sinica Technological. 43 368 (in Chinese)[王发强, 马西奎2013 中国科学: 43 368]
[13] Ma D S, Ki W H 2007 IEEE Trans. Circuit and Systtems Ⅱ: Express Briefs. 54 825
[14] Kanakasabai V, Ramesh O, Dipti S 2002 IEEE Trans. Power Electronics. 17 677
[15] Podlubny I 1999 Fractional differential equations (New York: Academic Press) chapt 1-2,4
[16] Yu H K 2010 M. S. Thesis. (Sichuan: Southeast Jiaotong University) (in Chinese) [于海坤2010 硕士学位论文 (四川: 西南交通大学)]
[17] Wang F Q, Ma X K 2013 Chin. Phys. B 22 236
[18] Xue D Y, Chen Y Q 2007 MATLAB Solutions to Mathematical Problems in Control (Beijing: Tsinghua University Press) p435 (in Chinese) [薛定宇, 陈阳泉2007 控制数学问题的MATLAB 求解(北京: 清华大学出版社) 第 435 页]
[19] Cao W S, Yang Y X 2007 Journal of System Simulation. 19 1329 (in Chinese) [曹文思, 杨育霞2007 系统仿真学报 19 1329]
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