Bifurcation and chaos in sliding mode controlled first-order h-bridge inverter based on pulse width modulation

Hao Xiang; Xie Rui-Liang; Yang Xu; Liu Tao; Huang Lang

doi:10.7498/aps.62.200503

Abstract

Sliding mode control (SMC) is recognized as a robust controller with fast dynamic response and high stability in a wide range of operating conditions, and therefore it is widely used in the control of inverter. The sliding mode controlled inverter is in nature a nonlinear controlled time-varying nonlinear system, and it has complicated nonlinear behaviors in practice. In this paper the sliding mode controlled first-order H-bridge inverter based on pulse width modulation is taken for example. First, through observation of the waveforms under different SMC parameters, a new type of bifurcation is discovered for the first time, in which diverse multi-period bifurcations exist at the same time. Second, the discrete time iterative model is established for the system and the folded diagram is employed to observe the waveforms. These analyses of current waveforms prove that the new type of bifurcation proposed in this paper is not a route to chaos. Moreover, the stability of the system is much concerned in engineering applications. However, because of the nonlinear characteristics of sliding mode controller, the method using eigenvalues of Jacobian matrix and other analytical methods are unsuitable for the system, and the graphic methods are not accurate enough. Finally, a criterion of fast-scale stability which can accurately distinguish the stability of the system is proposed, and it can be used to provide reliable reference for the parameter design of sliding mode controller.

Keywords:

Authors and contacts

1.
State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51177129) and the National High Technology Research and Deve-lopment Program of China (Grant No. 2011AA05A305).

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[19]	Hu J, Shang L, He Y, Zhu Z Q 2011 IEEE Trans. Power Electron. 26 210
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[21]	Kukrer O, Komurcugil H, Doganalp.A 2009 IEEE Trans. Ind. Electron. 56 3477
[22]	Abrishamifar A, Ahmad A A, Mohamadian M 2012 IEEE Trans. Power Electron. 27 2507
[23]	Chen Y, Kang Y 2011 IEEE Trans. Power Electron. 26 2727
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[25]	Chen D Y, Liu Y X, Ma X Y, Zhang R F 2011 Chin. Phys. B 20 120506
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Cited By

[1]	Ma X K, Li M, Dai D, Zhang H, Zou J L 2006 Trans. CES 21 1 (in Chinese) [马西奎, 李明, 戴栋, 张浩, 邹建龙 2006 电工技术学报 21 1]
[2]	Iu H H C, Zhou Y, Tse C K 2003 Int. J. Circ. Theor. Appl. 31 611
[3]	Wang X M, Zhang B, Qiu D Y 2009 Acta Phys. Sin. 58 2248 (in Chinese) [王学梅, 张波, 丘东元 2009 物理学报 58 2248]
[4]	Zhang B, Qu Y 2003 Proc. CSEE 23 99 (in Chinese) [张波, 曲颖 2003 电工技术学报 23 99]
[5]	Luo X S, Wang B H, Chen G R, Quan H J, Fang J Q, Zou Y L, Jiang P Q 2003 Acta Phys. Sin. 52 12 (in Chinese) [罗晓曙, 汪秉宏, 陈关荣, 全宏俊, 方锦清, 邹艳丽, 蒋品群 2003 物理学报 52 12]
[6]	Aroudi A, Debbat M, Giral R, Oliver G, Benadero L, Toribio E 2005 Int. J. Bifurcation and Chaos 15 1549
[7]	Yang R, Zhang B 2007 Acta Phys. Sin. 56 3789 (in Chinese) [杨汝, 张波 2007 物理学报 56 3789]
[8]	Liu W Z, Zhang H, Ma X K 2005 Proc. CSEE 25 43 (in Chinese) [刘伟增, 张浩, 马西奎 2005 电机工程学报 25 43]
[9]	Ma X K, Liu W Z, Zhang H 2005 Proc. CSEE 25 61 (in Chinese) [马西奎, 刘伟增, 张浩 2005 电机工程学报 25 61]
[10]	Dai D, Zhang B, Li S N, Ma X K 2008 Trans. CES 23 65 (in Chinese) [戴栋, 张波, 李胜男, 马西奎 2008 电工技术学报 23 65]
[11]	Robert B, Feki M, Iu H H C 2006 Int. J. Bifurcation and Chaos 16 113
[12]	Lei B, Xiao G C, Wu X L, Qi Y R 2011 Acta Phys. Sin. 60 122 (in Chinese) [雷博, 肖国春, 吴旋律, 齐元瑞 2011 物理学报 60 122]
[13]	Lei B, Xiao G C, Wu X L 2012 Acta Phys. Sin. 61 153 (in Chinese) [雷博, 肖国春, 吴旋律 2012 物理学报 61 153]
[14]	Liu T, Hao X, Yang X, Liu J, Zhang B, Huang L 2012 Proc. IEEE IPEMC Harbin, China, June, 2012, 1 p626
[15]	Liu T, Hao X, Yang X, Zhao M, Huang Q, Huang L 2012 Proc. IEEE IPEMC Harbin, China, June, 2012, 1 p335
[16]	Liu T, Hao X, Yang X, Zhao M, Xiong L 2012 Proc. IEEE ISIE Hangzhou, China, May, 2012, p86
[17]	Hao X, Liu T, Yang X, Huang L 2012 Proc. IEEE IPEMC Harbin, China, June, 2012, 2 p831
[18]	Hao X, Yang X, Liu T, Huang L, Chen W 2013 IEEE Trans. Power Electron. 28 793
[19]	Hu J, Shang L, He Y, Zhu Z Q 2011 IEEE Trans. Power Electron. 26 210
[20]	Wai R J, Wang W H 2008 IEEE Trans. Circuits Syst. 55 240
[21]	Kukrer O, Komurcugil H, Doganalp.A 2009 IEEE Trans. Ind. Electron. 56 3477
[22]	Abrishamifar A, Ahmad A A, Mohamadian M 2012 IEEE Trans. Power Electron. 27 2507
[23]	Chen Y, Kang Y 2011 IEEE Trans. Power Electron. 26 2727
[24]	Yu D C, Wu A G, Yang C P 2005 Chin. Phys. 14 914
[25]	Chen D Y, Liu Y X, Ma X Y, Zhang R F 2011 Chin. Phys. B 20 120506
[26]	Mohammad P A, Hassan F 2012 Chin. Phys. B 21 060506
[27]	Wang X M, Zhang B 2009 Proc. CSEE 29 22 (in Chinese) [王学梅, 张波 2009 电机工程学报 29 22]
[28]	Wang X M, Zhang B 2009 Trans. CES 24 101 (in Chinese) [王学梅, 张波 2009 电工技术学报 24 101]

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Vol. 62, Issue 20 - 2013-10-20

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