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## Fractional order modeling and simulation analysis of Boost converter in continuous conduction mode operation

Wang Fa-Qiang, Ma Xi-Kui
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#### Abstract

Based on fractional calculus and the fact that the capacitor and the inductor are fractional in nature, the fractional mathematical model and the fractional state averaged model of the Boost converter in continuous conduction mode operation are built and analyzed. Also, the condition for the continuous conduction mode operation of the Boost converter is given. Finally, in order to verify the theoretical analysis, the simulation model of the Boost converter in continuous conduction mode operation is established by using the software of Matlab/Simulink.

#### 作者及机构信息

###### 1. 西安交通大学电气工程学院电力设备电气绝缘国家重点实验室,西安 710049
• 基金项目: 国家自然科学基金(批准号:51007068),高等学校博士学科点专项科研基金(批准号:20100201120028),中央高校基本科研业务专项资金和电力设备电气绝缘国家重点实验室(批准号:EIPE10303)资助的课题.

#### 参考文献

 [1] Zhang W P 2006 Modeling and control of switching converter (Bejing: China Electric Power Press) chapt. 1,6 (in Chinese) [张卫平 2006 开关变换器的建模与控制(北京:中国电力出版社)第一,六章] [2] Zhao Y B, Luo X S, Fang J Q, Wang B H 2005 Acta Phys. Sin. 54 5022 (in Chinese) [赵益波、罗晓曙、方锦清、汪秉宏 2005 物理学报 54 5022] [3] Jonscher A K 1983 Dielectric relaxation in solids (London: Chelsea Dielectric Press) chapt. 3 [4] Bohannan G W 2002 Proc. of the 41st IEEE Int. Conf. on Decision and Control, Tutorial Workshop 2: Fractional Calculus Applications in Automatic Control and Robotics 1 [5] Westerlund S, Ekstam L 1994 IEEE Trans. Dielectr. Electr. Insul. 1 826 [6] Westerlund S 2002 Dead matter has memory (Kalmar, Sweden: Causal Consulting) chapt. 7 [7] Petr I 2008 Chaos Soliton. Fract. 38 140 [8] Jesus I S, Tenreiro Machado J A 2009 Nonlinear Dyn. 56 45 [9] Ahmad W 2003 Proc. of the 2003 Int. Symposium on Circuits and Systems 3 III.5 [10] Martínez R, Bolea Y, Grau A, Martínez H 2009 IEEE Conf. on Emerging Technologies & Factory Automation 1 [11] Podlubny I 1999 Fractional differential equations (New York: Academic Press) chapt. 1-2,4. [12] Zhang Z S, Cai X S 2006 The Principle and Design of Switching Power Supply (Beijing: Publishing House of Electronics Industry) chapt. 2 (in Chinese) [张占松、蔡宣三 2006 开关电源的原理与设计 (北京:电子工业出版社)第二章] [13] Duan J S, An J Y, Xu M Y 2007 Appl. Math. J. Chinese Univ. Ser. B 22 7 [14] Yang Y, Pei Y Q, Wang Z A 2004 Switching Power supply technology (Beijing: China Machine Press) chapt. 4 (in Chinese) [杨旭、裴云庆、王兆安 2004 开关电源技术(北京:机械工业出版社)第四章] [15] Oustaloup A, Levron F, Mathieu B, Nanot F M 2000 IEEE Trans. Circuits Syst.-I 47 25 [16] Xue D Y, Chen Y Q 2007 MATLAB Solutions to Mathematical Problems in Control (Tsinghua University Press) chapt. 9 (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)第九章]

#### 施引文献

•  [1] Zhang W P 2006 Modeling and control of switching converter (Bejing: China Electric Power Press) chapt. 1,6 (in Chinese) [张卫平 2006 开关变换器的建模与控制(北京:中国电力出版社)第一,六章] [2] Zhao Y B, Luo X S, Fang J Q, Wang B H 2005 Acta Phys. Sin. 54 5022 (in Chinese) [赵益波、罗晓曙、方锦清、汪秉宏 2005 物理学报 54 5022] [3] Jonscher A K 1983 Dielectric relaxation in solids (London: Chelsea Dielectric Press) chapt. 3 [4] Bohannan G W 2002 Proc. of the 41st IEEE Int. Conf. on Decision and Control, Tutorial Workshop 2: Fractional Calculus Applications in Automatic Control and Robotics 1 [5] Westerlund S, Ekstam L 1994 IEEE Trans. Dielectr. Electr. Insul. 1 826 [6] Westerlund S 2002 Dead matter has memory (Kalmar, Sweden: Causal Consulting) chapt. 7 [7] Petr I 2008 Chaos Soliton. Fract. 38 140 [8] Jesus I S, Tenreiro Machado J A 2009 Nonlinear Dyn. 56 45 [9] Ahmad W 2003 Proc. of the 2003 Int. Symposium on Circuits and Systems 3 III.5 [10] Martínez R, Bolea Y, Grau A, Martínez H 2009 IEEE Conf. on Emerging Technologies & Factory Automation 1 [11] Podlubny I 1999 Fractional differential equations (New York: Academic Press) chapt. 1-2,4. [12] Zhang Z S, Cai X S 2006 The Principle and Design of Switching Power Supply (Beijing: Publishing House of Electronics Industry) chapt. 2 (in Chinese) [张占松、蔡宣三 2006 开关电源的原理与设计 (北京:电子工业出版社)第二章] [13] Duan J S, An J Y, Xu M Y 2007 Appl. Math. J. Chinese Univ. Ser. B 22 7 [14] Yang Y, Pei Y Q, Wang Z A 2004 Switching Power supply technology (Beijing: China Machine Press) chapt. 4 (in Chinese) [杨旭、裴云庆、王兆安 2004 开关电源技术(北京:机械工业出版社)第四章] [15] Oustaloup A, Levron F, Mathieu B, Nanot F M 2000 IEEE Trans. Circuits Syst.-I 47 25 [16] Xue D Y, Chen Y Q 2007 MATLAB Solutions to Mathematical Problems in Control (Tsinghua University Press) chapt. 9 (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)第九章]
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##### 出版历程
• 收稿日期:  2011-03-02
• 修回日期:  2011-03-22
• 刊出日期:  2011-07-15

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