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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
Based on the fact that the inductor and the capacitor are of fractional order in nature, the mathematical model of the fractional order boost converter in pseudo continuous conduction mode is established by using the fractional order calculus theory. Due to the affine non-linear nature in this mathematical model and a similar Lyapunov stability theorem of the fractional order system, a fractional order non-linear controller is designed. On the basis of chain fractance and the improved Oustaloup algorithm, the circuit model of fractional order inductor and capacitor are built. The fractional order controller is verified by the Matlab/Simulink software. Simulation results show that the controller enhances the dynamic and steady-state performance, so as to realize the stability and achieve good dynamic performance of the fractional order system during large fluctuation of power supply and load disturbance.-
Keywords:
- fractional order /
- boost converter /
- pseudo continuous conduction mode (tri-state mode) /
- non-linear control
[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 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 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 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 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 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 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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