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A new method based on symbobic dynamics and relative entropy theory is proposed to examine the nonlinear behaviours of converters. Firstly, the discrete numerical sequence is obtained from iteration map, which is then transferred to a symbol-time series according to the topological conjugation, and the relative entropy is calculated by means of forward and backward probabilities. This paper takes a first one-order voltage feedback DCM Boost converter as an example, and the result shows that the relative entropy, which can measure quantitatively the distance apart from equilibrium when converter lies in a chaotic state, is a new and quantified nonlinear dynamic behaviours which has not been used in converters yet.
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Keywords:
- symbolic dynamics /
- converters /
- relative entropy /
- time irreversibility
[1] Laugesen J L, Mosekilde E, Zhusubaliyev Z T 2012 Phys. D 241 488
[2] Xie L L, Gong R X, Zhao H Z, Ma X H 2012 Acta Phys. Sin. 61 058401 (in Chinese)[谢玲玲, 龚仁喜, 卓浩泽, 马献花 2012 61 058401]
[3] Giaouris D, Banerjee S, Imrayed O, Mandal, K, Zahawi B, Pickert V 2012 IEEE Trans. Circuit and Syst. I 59 207
[4] Xie F, Yang R, Zhang B 2012 Acta Phys. Sin. 61 110504 (in Chinese)[谢帆, 杨汝, 张波 2012 61 110504]
[5] Yao T L, Liu H F, Xu J L, Li W F 2012 Chaos 22 033102
[6] Chen X, Qiu S S 2010 Acta Phys. Sin. 59 7630 (in Chinese)[陈旭, 丘水生 2010 59 7630]
[7] Yang R, Zhang B 2006 Acta Phys. Sin. 55 5667 (in Chinese)[杨汝, 张波 2006 55 5667]
[8] Wang X M, Zhang B, Qiu D Y 2011 IEEE Trans. on Power Electronics 26 2101
[9] Xu H M, Jin Y G, Gou S X 2013 Acta Phys. Sin. 62 248401 (in Chinese)[徐红梅, 金永镐, 郭树旭 2013 62 248401]
[10] Porporato A, Rigby J R, Daly E 2007 Phys. Rev. Lett. 98 094101
[11] Costa M, Goldberger A L, Peng C K 2010 Phys. Rev. Lett. 95 198102
[12] Camillo C, Enrico R 2007 Chaos 32 1649
[13] Bian C H, Ning X B 2004 Chin. Phys. 13 633
[14] Yang R, Zhang B, Zhao S B, Lao Y J 2010 Acta Phys. Sin. 59 3756 (in Chinese)[杨汝, 张波, 赵寿柏, 劳裕锦 2010 59 3756]
[15] Rached Z, Alajaji F, Campbell L L 2004 IEEE Trans. on Information Theory. 50 917
[16] Andrieux D, Gaspard P 2007 Phys. Rev. Lett. 98 150601
[17] Muriel A 2013 Phys. Lett. A 377 1161
[18] Zhang M, Wang J 2013 Acta Phys. Sin. 62 038701 (in Chinese)[张梅, 王俊 2013 62 038701]
[19] Huang J H, Liu N H, Liu J T, Yu T B, He X 2010 Chin. Phys. B 19 110312
[20] Lu H X, Zhao Bo 2006 Chin. Phys. 15 1914
[21] Tse C K 1994 IEEE Trans. Circuit and Syst. I 41 16
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[1] Laugesen J L, Mosekilde E, Zhusubaliyev Z T 2012 Phys. D 241 488
[2] Xie L L, Gong R X, Zhao H Z, Ma X H 2012 Acta Phys. Sin. 61 058401 (in Chinese)[谢玲玲, 龚仁喜, 卓浩泽, 马献花 2012 61 058401]
[3] Giaouris D, Banerjee S, Imrayed O, Mandal, K, Zahawi B, Pickert V 2012 IEEE Trans. Circuit and Syst. I 59 207
[4] Xie F, Yang R, Zhang B 2012 Acta Phys. Sin. 61 110504 (in Chinese)[谢帆, 杨汝, 张波 2012 61 110504]
[5] Yao T L, Liu H F, Xu J L, Li W F 2012 Chaos 22 033102
[6] Chen X, Qiu S S 2010 Acta Phys. Sin. 59 7630 (in Chinese)[陈旭, 丘水生 2010 59 7630]
[7] Yang R, Zhang B 2006 Acta Phys. Sin. 55 5667 (in Chinese)[杨汝, 张波 2006 55 5667]
[8] Wang X M, Zhang B, Qiu D Y 2011 IEEE Trans. on Power Electronics 26 2101
[9] Xu H M, Jin Y G, Gou S X 2013 Acta Phys. Sin. 62 248401 (in Chinese)[徐红梅, 金永镐, 郭树旭 2013 62 248401]
[10] Porporato A, Rigby J R, Daly E 2007 Phys. Rev. Lett. 98 094101
[11] Costa M, Goldberger A L, Peng C K 2010 Phys. Rev. Lett. 95 198102
[12] Camillo C, Enrico R 2007 Chaos 32 1649
[13] Bian C H, Ning X B 2004 Chin. Phys. 13 633
[14] Yang R, Zhang B, Zhao S B, Lao Y J 2010 Acta Phys. Sin. 59 3756 (in Chinese)[杨汝, 张波, 赵寿柏, 劳裕锦 2010 59 3756]
[15] Rached Z, Alajaji F, Campbell L L 2004 IEEE Trans. on Information Theory. 50 917
[16] Andrieux D, Gaspard P 2007 Phys. Rev. Lett. 98 150601
[17] Muriel A 2013 Phys. Lett. A 377 1161
[18] Zhang M, Wang J 2013 Acta Phys. Sin. 62 038701 (in Chinese)[张梅, 王俊 2013 62 038701]
[19] Huang J H, Liu N H, Liu J T, Yu T B, He X 2010 Chin. Phys. B 19 110312
[20] Lu H X, Zhao Bo 2006 Chin. Phys. 15 1914
[21] Tse C K 1994 IEEE Trans. Circuit and Syst. I 41 16
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