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针对一类多项式形式的Hopf分岔系统, 提出了一种鲁棒稳定的控制器设计方法. 使用该方法设计控制器时不需要求解出系统在分岔点处的分岔参数值, 只需要估算出分岔参数的上下界, 然后设计一个参数化的控制器, 并通过Hurwitz判据和柱形代数剖分技术求解出满足上下界条件的控制器参数区域, 最后在得到的这个区域内确定出满足鲁棒稳定的控制器参数值. 该方法设计的控制器是由包含系统状态的多项式构成, 形式简单, 具有通用性, 且添加控制器后不会改变原系统平衡点的位置. 本文首先以Lorenz系统为例说明了控制器的推导和设计过程, 然后以van der Pol振荡系统为例, 进行了工程应用. 通过对这两个系统的控制器设计和仿真, 说明了文中提出的控制器设计方法能够有效地应用于这类Hopf分岔系统的鲁棒稳定控制, 并且具有通用性.
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[6] Wang F Q, Ma X K 2013 Chin. Phys. B 22 120504
[7] Yfoulis C, Giaouris D, Stergiopoulos F, Ziogou C, Voutetakis S, Papadopoulou S 2015 Control Eng. Pract. 35 67
[8] Zhao H Y, Xie W 2011 Nonlinear Dyn. 63 345
[9] Wu Z, Yu P 2006 IEEE Trans. Automat. Control 51 1019
[10] Mohammadi A, Marvdasht I 2012 Problems of Cybernetics and Informatics (PCI), 2012 IV International Conference Baku, September 12-14, 2012 p1
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[12] Cao G Y, Hill D J 2010 IET Gener. Transm. Dis. 4 873
[13] Inoue M, Imura J, Kashima K, Aihara K 2015 Analysis and Control of Complex Dynamical Systems 7 3
[14] Hu J, Liu L, Ma D W 2014 J. Korean Phys. Soc. 65 2132
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[16] Yue M, Schlueter R 2005 IEEE Trans. Power Syst. 20 301
[17] Chen D W, Gu H B, Liu H 2010 J. Vib. and Shock 29 30 (in Chinese) [陈大伟, 顾宏斌, 刘晖 2010 振动与冲击 29 30]
[18] He C M, Jin L, Chen D G, Geiger R 2007 IEEE Trans. Circ. Syst. 54 964
[19] Liu S, Zhao S S, Wang Z L, Li H B 2015 Chin. Phys. B 24 014501
[20] Li H Y, Che Yan Q, Wang J, Jin Q T, Deng B, Wei X L, Dong F 2012 The 10th World Congress on Intelligent Control and Automation (WCICA) Beijing, July 6-8, 2012 p4953
[21] Yang T B, Chen X 2008 Proceedings of the 47th IEEE Conference on Decision and Control(CDC) Cancun, Mexico, December 9-11, 2008 p4103
[22] LaValle S M 2006 Planning Algorithms (Cambridge: Cambridge University Press) pp 280-290
[23] Gandy S, Kanno M, Anai H, Yokoyama K 2011 Math. Comput. Sci. 5 209
[24] England M, Bradford R, Chen C, Davenport J H, Maza M M, Wilson D 2014 Intellig. Comput. Math. 8543 45
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[1] Wu Z Q, Sun L M 2011 Acta Phys. Sin. 60 050504 (in Chinese) [吴志强, 孙立明 2011 物理学报 60 050504]
[2] Zhu L H, Zhao H Y 2014 Acta Phys. Sin. 63 090203 (in Chinese) [朱霖河, 赵洪涌 2014 物理学报 63 090203]
[3] Wang J S, Yuan R X, Gao Z W, Wang D J 2011 Chin. Phys. B 20 090506
[4] Pei Y, Chen G R 2004 Int. J. Bifurcat. Chaos 14 1683
[5] Nguyen L, Hong K 2012 Phys. Lett. A 376 442
[6] Wang F Q, Ma X K 2013 Chin. Phys. B 22 120504
[7] Yfoulis C, Giaouris D, Stergiopoulos F, Ziogou C, Voutetakis S, Papadopoulou S 2015 Control Eng. Pract. 35 67
[8] Zhao H Y, Xie W 2011 Nonlinear Dyn. 63 345
[9] Wu Z, Yu P 2006 IEEE Trans. Automat. Control 51 1019
[10] Mohammadi A, Marvdasht I 2012 Problems of Cybernetics and Informatics (PCI), 2012 IV International Conference Baku, September 12-14, 2012 p1
[11] Kishida M, Braatz R 2014 American Control Conference (ACC), Portland, OR, June 4-6, 2014 p5085
[12] Cao G Y, Hill D J 2010 IET Gener. Transm. Dis. 4 873
[13] Inoue M, Imura J, Kashima K, Aihara K 2015 Analysis and Control of Complex Dynamical Systems 7 3
[14] Hu J, Liu L, Ma D W 2014 J. Korean Phys. Soc. 65 2132
[15] Liang J S, Chen Y S, Leung A Y T 2004 Appl. Math. Mech. 25 263
[16] Yue M, Schlueter R 2005 IEEE Trans. Power Syst. 20 301
[17] Chen D W, Gu H B, Liu H 2010 J. Vib. and Shock 29 30 (in Chinese) [陈大伟, 顾宏斌, 刘晖 2010 振动与冲击 29 30]
[18] He C M, Jin L, Chen D G, Geiger R 2007 IEEE Trans. Circ. Syst. 54 964
[19] Liu S, Zhao S S, Wang Z L, Li H B 2015 Chin. Phys. B 24 014501
[20] Li H Y, Che Yan Q, Wang J, Jin Q T, Deng B, Wei X L, Dong F 2012 The 10th World Congress on Intelligent Control and Automation (WCICA) Beijing, July 6-8, 2012 p4953
[21] Yang T B, Chen X 2008 Proceedings of the 47th IEEE Conference on Decision and Control(CDC) Cancun, Mexico, December 9-11, 2008 p4103
[22] LaValle S M 2006 Planning Algorithms (Cambridge: Cambridge University Press) pp 280-290
[23] Gandy S, Kanno M, Anai H, Yokoyama K 2011 Math. Comput. Sci. 5 209
[24] England M, Bradford R, Chen C, Davenport J H, Maza M M, Wilson D 2014 Intellig. Comput. Math. 8543 45
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