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基于电容和电感都是分数阶的事实，采用分数阶微积分理论，建立了电感电流伪连续模式下Boost变换器的分数阶状态空间平均模型. 针对其分数阶模型具有仿射非线性系统的特点，根据分数阶的类Lyapunov稳定性理论，设计了适用于分数阶电感电流伪连续模式下Boost变换器的一种分数阶非线性控制器. 依据分抗链及改进的Oustaloup分数阶近似算法，得到了分数阶电感和电容的等效电路模型，用Matlab/Simulink软件对所设计的控制器进行了仿真验证. 结果表明：所设计的分数阶非线性控制器对分数阶电感电流伪连续模式下的Boost变换器的动态和稳态性能有显著的提高，并且在输入电压和负载大幅度波动的情况下，仍然能够确保系统具有良好的稳定性和动态性能.
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关键词:
- 分数阶 /
- Boost变换器 /
- 伪连续模式(三态模式) /
- 非线性控制
[1] Koeller R C 1986 Acta Mech. 58 251
[2] Sun H H, Abdelwahab A A, Onaral B 1984 IEEE Trans. Automatic Control 29 441
[3] Bagley R L, Torvik P J 1983 J. Rheol. 27 201
[4] Suwat K 2012 Comput. Math. Appl. 63 183
[5] Wu X J, Wang H, Lu H T 2012 Nonlin. Anal. Real World Appl. 13 1441
[6] 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]
[7] Shokooh A, Suarez L 1999 J. Vib. Control 5 331
[8] Jonscher A K 1999 J. Phys. D: Appl. Phys. 32 R57
[9] Westerlund S, Ekstam L 1994 IEEE Trans. Dielectr. Electr. Insulat. 1 826
[10] Westerlund S 1991 Phys. Scripta 43 174
[11] 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
[12] Westerlund S 2002 Dead Matter Has Memory (Kalmar, Sweden: Causal Consulting) chapt. 7
[13] Wang F Q, Ma X K 2013 Sci. Sin. Technol. 43 368 (in Chinese) [王发强, 马西奎 2013 中国科学: 技术科学 43 368]
[14] Tan C, Liang Z S 2014 Acta Phys. Sin. 63 070502 (in Chinese) [谭程, 梁志珊 2014 物理学报 63 070502]
[15] Zhang F, Xu J P, Yang P 2012 Proceedings of the CSEE 32 56 (in Chinese) [张斐, 许建平, 杨平 2012 中国电机工程学报 32 56]
[16] Kanakadabai V 2002 IEEE Trans. Power Electron. 17 677
[17] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press) chapt 1-2, 4
[18] Matigon D 1996 IMACS IEEE SMC Proceeding Conference Lille, France, July 9-12, 1996 p963
[19] Hu J B, Zhao L D 2013 Acta Phys. Sin. 62 240504 (in Chinese) [胡建兵, 赵灵冬 2013 物理学报 62 240504]
[20] Wang F Q, Ma X K 2013 Chin. Phys. B 22 030506
[21] Xue D Y, Chen Y Q 2007 MATLAB Solutions to Mathematical Problems in Control (Beijing: Tsinghua University Press) pp435-460 (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435–460页]
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[1] Koeller R C 1986 Acta Mech. 58 251
[2] Sun H H, Abdelwahab A A, Onaral B 1984 IEEE Trans. Automatic Control 29 441
[3] Bagley R L, Torvik P J 1983 J. Rheol. 27 201
[4] Suwat K 2012 Comput. Math. Appl. 63 183
[5] Wu X J, Wang H, Lu H T 2012 Nonlin. Anal. Real World Appl. 13 1441
[6] 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]
[7] Shokooh A, Suarez L 1999 J. Vib. Control 5 331
[8] Jonscher A K 1999 J. Phys. D: Appl. Phys. 32 R57
[9] Westerlund S, Ekstam L 1994 IEEE Trans. Dielectr. Electr. Insulat. 1 826
[10] Westerlund S 1991 Phys. Scripta 43 174
[11] 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
[12] Westerlund S 2002 Dead Matter Has Memory (Kalmar, Sweden: Causal Consulting) chapt. 7
[13] Wang F Q, Ma X K 2013 Sci. Sin. Technol. 43 368 (in Chinese) [王发强, 马西奎 2013 中国科学: 技术科学 43 368]
[14] Tan C, Liang Z S 2014 Acta Phys. Sin. 63 070502 (in Chinese) [谭程, 梁志珊 2014 物理学报 63 070502]
[15] Zhang F, Xu J P, Yang P 2012 Proceedings of the CSEE 32 56 (in Chinese) [张斐, 许建平, 杨平 2012 中国电机工程学报 32 56]
[16] Kanakadabai V 2002 IEEE Trans. Power Electron. 17 677
[17] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press) chapt 1-2, 4
[18] Matigon D 1996 IMACS IEEE SMC Proceeding Conference Lille, France, July 9-12, 1996 p963
[19] Hu J B, Zhao L D 2013 Acta Phys. Sin. 62 240504 (in Chinese) [胡建兵, 赵灵冬 2013 物理学报 62 240504]
[20] Wang F Q, Ma X K 2013 Chin. Phys. B 22 030506
[21] Xue D Y, Chen Y Q 2007 MATLAB Solutions to Mathematical Problems in Control (Beijing: Tsinghua University Press) pp435-460 (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435–460页]
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