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Hamiltonian system theory is an important reflearch tool for nonlinear systems, and has been widely used in motor speed regulation and control during reflent years. Aiming at the chaotic phenomenon in permanent magnet synchronous motors, a design method of robust controller based on the Hamiltonian function is preflented for the chaotic systems. The dynamic model of permanent magnet synchronous motor is transformed into a model similar to the Lorenz chaotic equation, and the model is chaotic at certain parameters according to the Lyapunov exponent and the Lyapunov dimension calculated. Let the rotator speed of the motor track a set of values, an error equation is obtained accordingly. Because the error equation does not satisfy the standard form of Hamilton exactly, it can be transformed into the Hamiltonian system containing uncertain disturbance terms. While the uncertain disturbance terms as well as the load term are regarded as a total disturbance term to the system, a kind of robust controller is designed. The controller consists of two parts. One part is based on the method of interconnection and damping assignment, and can make the rotator speed track any value well; The other part is used as a disturbance compensator. Simulation result shows that the controller drives the permanent magnet synchronous motor out of the chaotic state rapidly and the rotator speed tracks the set of values well. It is proven that the controller is feasible and effective. The method mentioned in this paper extends the range of application of Hamiltonian function and has a certain advantage.
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Keywords:
- permanent magnet synchronous motors /
- Hamiltonian function /
- chaos /
- robust control
[1] Krishnan R, Bharadwaj A S 1991 IEEE Trans. Power Electron. 6 695
[2] Li C L, Yu S M 2011 Acta Phys. Sin. 60 120505 (in Chinese) [李春来, 禹思敏 2011 60 120505]
[3] Tang C S, Dai Y H 2013 Acta Phys. Sin. 62 180504 (in Chinese) [唐传胜, 戴跃洪 2013 62 180504]
[4] Tang C S, Dai Y H, Zhen W X 2014 Control Theory Appl. 31 404 (in Chinese) [唐传胜, 戴跃洪, 甄文喜 2014 控制理论与应用 31 404]
[5] Zhang X H, Ding S G 2009 Control Theory Appl. 26 661 (in Chinese) [张兴华, 丁守刚 2009 控制理论与应用 26 661]
[6] Yao Q G 2011 IEEE International Conference on Computer Science and Automation Engineering (CSAE) Shanghai, China, June 10-12, 2011 p104
[7] Yu J P, Yu H S, Chen B, Gao J W, Qin Y 2012 Nonlinear Dynam. 70 1879
[8] Zeng Y, Zhang L X, Yu F R, Qian J 2009 Proceedings of the CSEE. 29 54 (in Chinese) [曾云, 张立翔, 于凤荣, 钱晶 2009 中国电机工程学报 29 54]
[9] Wu C, Qi R, Gao F 2014 Control and Decision. 29 895 (in Chinese) [吴春, 齐蓉, 高峰 2014 控制与决策 29 895]
[10] Wu Z Q, Zhuang S Y, Han Y G 2013 Chinese Journal of Scientific Instrument. 34 344 (in Chinese) [吴忠强, 庄述燕, 韩延光 2013 仪器仪表学报 34 344]
[11] Ren L N, Liu F C, Jiao X H, Li J Y 2012 Acta Phys. Sin. 61 060506 (in Chinese) [任丽娜, 刘福才, 焦晓红, 李俊义 2012 61 060506]
[12] Guo Y, Xi Z, Cheng D 2007 IET Control Theory Appl. 1 281
[13] Zhang B, Li Z, Mao Z Y 2002 Control Theory Appl. 19 545 (in Chinese) [张波, 李忠, 毛宗源 2002 控制理论与应用 19 545]
[14] Ortega R, Van der Schaft A J, Mareels I, Maschke B 2001 IEEE Control. Syst. Mag. 21 18
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[1] Krishnan R, Bharadwaj A S 1991 IEEE Trans. Power Electron. 6 695
[2] Li C L, Yu S M 2011 Acta Phys. Sin. 60 120505 (in Chinese) [李春来, 禹思敏 2011 60 120505]
[3] Tang C S, Dai Y H 2013 Acta Phys. Sin. 62 180504 (in Chinese) [唐传胜, 戴跃洪 2013 62 180504]
[4] Tang C S, Dai Y H, Zhen W X 2014 Control Theory Appl. 31 404 (in Chinese) [唐传胜, 戴跃洪, 甄文喜 2014 控制理论与应用 31 404]
[5] Zhang X H, Ding S G 2009 Control Theory Appl. 26 661 (in Chinese) [张兴华, 丁守刚 2009 控制理论与应用 26 661]
[6] Yao Q G 2011 IEEE International Conference on Computer Science and Automation Engineering (CSAE) Shanghai, China, June 10-12, 2011 p104
[7] Yu J P, Yu H S, Chen B, Gao J W, Qin Y 2012 Nonlinear Dynam. 70 1879
[8] Zeng Y, Zhang L X, Yu F R, Qian J 2009 Proceedings of the CSEE. 29 54 (in Chinese) [曾云, 张立翔, 于凤荣, 钱晶 2009 中国电机工程学报 29 54]
[9] Wu C, Qi R, Gao F 2014 Control and Decision. 29 895 (in Chinese) [吴春, 齐蓉, 高峰 2014 控制与决策 29 895]
[10] Wu Z Q, Zhuang S Y, Han Y G 2013 Chinese Journal of Scientific Instrument. 34 344 (in Chinese) [吴忠强, 庄述燕, 韩延光 2013 仪器仪表学报 34 344]
[11] Ren L N, Liu F C, Jiao X H, Li J Y 2012 Acta Phys. Sin. 61 060506 (in Chinese) [任丽娜, 刘福才, 焦晓红, 李俊义 2012 61 060506]
[12] Guo Y, Xi Z, Cheng D 2007 IET Control Theory Appl. 1 281
[13] Zhang B, Li Z, Mao Z Y 2002 Control Theory Appl. 19 545 (in Chinese) [张波, 李忠, 毛宗源 2002 控制理论与应用 19 545]
[14] Ortega R, Van der Schaft A J, Mareels I, Maschke B 2001 IEEE Control. Syst. Mag. 21 18
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