主动磁力轴承鲁棒控制算法研究及其控制系统设计
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摘要
磁力轴承作为一种高科技产品,是支承领域的重大变革。因为其一系列独特的性能使它拥有广泛的应用前景和很高的实用价值。本文的研究对象主要是针对主动磁力轴承转子控制系统,研究的主要目标是应用鲁棒H_∞原理设计磁力轴承控制器,同时给出主动磁力轴承系统的硬件设计框架。
首先,本文简要的介绍了磁力轴承的基本工作原理,对磁力轴承磁场中的电磁力进行了计算推导,同时建立了磁力轴承系统的数学模型,为后面的分析奠定基础。
其次,通过磁力轴承系统的不确定性分析,介绍了关于H_∞控制标准设计问题的描述,进而利用H_∞控制理论的混合灵敏度方法,根据系统受扰情况选择合适的加权函数,设计出能使该系统稳定且具有良好鲁棒性的H_∞控制器,其中对加权函数的选择原则作了比较详尽的阐述。
再次,借用MATLAB工具,通过计算机仿真将H_∞控制器和PID控制器的控制效果进行了对比,并分析了各种情况下系统的起浮性能。仿真实验验证了利用H_∞混合灵敏度理论设计的单自由度H_∞控制器的闭环系统具有良好稳定性和鲁棒性,对干扰信号和不确定参数具有令人满意的抑制效果。
最后,介绍了基于DSP芯片TMS320LF2812设计的磁力轴承系统的控制器,并以其为中心详尽地对A/D通道设计,D/A通道设计作出必要的说明。为了构成完整的磁力轴承控制系统,本文也给出了包括滤波电路在内的各种必要的外围电路,如电源电路,仿真接口等。除此之外,传感器和功率放大器也是构成磁力轴承系统的重要组成部分,在文章中给出了选择和设计的方法。
在文章的最后对本论文做了思考性的总结,同时对课题进一步要开展的工作作出一些思考。
Magnetic Bearings, as one kind of high tech products, is called as a important technology revolution of the supporting domain. Because of a series of unique properties, it has wide application potential and inestimable practical value. The main objective of research of this paper is designing control system with the robust H_∞principle for active magnetic bearings rotor system, Simultaneously ,the hardware design frame of the active magnetic bearings system has been given in the paper.
Firstly the principle of the magnetic bearing is introduced briefly and themagnetic force of the magnetic bearing magnetic field is analysed and computed,and mathematical model of the magnetic bearing systems is established in this paper,all this is making foundation for the following analysis and the next works.
Secondly, by analysising the uncertainty of the magnetic bearing system,the paper introduced the standard H_∞control designing question description, then use the mixed sensitivity function of H_∞control theory designing H_∞controller, which has good robustness and can enable the system to stabilize, according to the disturbed situation in choosing suitable weighting function. In addition, the article introduced the Selection principle of weighting function in detail.
Thirdly, using MATLAB tools and computer simulation the control effect of the H_∞controller and the PID controller were compared, then the floating system performance from a variety of circumstances is analyzed. Simulation results verify the active magnetic bearing system which is designed whit H_∞mixed sensitivity theory has good stability and robustness .It can be very good suppression of low frequency interference signals.
Finally, the paper introduced the designing of the magnetic bearing system controller based on the chip DSP named TMS320LF2812 . On this basis, the A/D channel designing and the D/A channels designing had a detailed presentation. In order to construct a complete magnetic bearing system control system, the paper also presents the filter circuit, including the necessary peripheral circuits, such as power supply circuit, simulation interface. In addition, sensors and power amplifier is an important component of a magnetic bearing system, the article finally given the selection and design methods.
At the end of the article, I has made the ponder summary to the present paper, simultaneously the work which further must develop to the topic has made the ponder.
首先,本文简要的介绍了磁力轴承的基本工作原理,对磁力轴承磁场中的电磁力进行了计算推导,同时建立了磁力轴承系统的数学模型,为后面的分析奠定基础。
其次,通过磁力轴承系统的不确定性分析,介绍了关于H_∞控制标准设计问题的描述,进而利用H_∞控制理论的混合灵敏度方法,根据系统受扰情况选择合适的加权函数,设计出能使该系统稳定且具有良好鲁棒性的H_∞控制器,其中对加权函数的选择原则作了比较详尽的阐述。
再次,借用MATLAB工具,通过计算机仿真将H_∞控制器和PID控制器的控制效果进行了对比,并分析了各种情况下系统的起浮性能。仿真实验验证了利用H_∞混合灵敏度理论设计的单自由度H_∞控制器的闭环系统具有良好稳定性和鲁棒性,对干扰信号和不确定参数具有令人满意的抑制效果。
最后,介绍了基于DSP芯片TMS320LF2812设计的磁力轴承系统的控制器,并以其为中心详尽地对A/D通道设计,D/A通道设计作出必要的说明。为了构成完整的磁力轴承控制系统,本文也给出了包括滤波电路在内的各种必要的外围电路,如电源电路,仿真接口等。除此之外,传感器和功率放大器也是构成磁力轴承系统的重要组成部分,在文章中给出了选择和设计的方法。
在文章的最后对本论文做了思考性的总结,同时对课题进一步要开展的工作作出一些思考。
Magnetic Bearings, as one kind of high tech products, is called as a important technology revolution of the supporting domain. Because of a series of unique properties, it has wide application potential and inestimable practical value. The main objective of research of this paper is designing control system with the robust H_∞principle for active magnetic bearings rotor system, Simultaneously ,the hardware design frame of the active magnetic bearings system has been given in the paper.
Firstly the principle of the magnetic bearing is introduced briefly and themagnetic force of the magnetic bearing magnetic field is analysed and computed,and mathematical model of the magnetic bearing systems is established in this paper,all this is making foundation for the following analysis and the next works.
Secondly, by analysising the uncertainty of the magnetic bearing system,the paper introduced the standard H_∞control designing question description, then use the mixed sensitivity function of H_∞control theory designing H_∞controller, which has good robustness and can enable the system to stabilize, according to the disturbed situation in choosing suitable weighting function. In addition, the article introduced the Selection principle of weighting function in detail.
Thirdly, using MATLAB tools and computer simulation the control effect of the H_∞controller and the PID controller were compared, then the floating system performance from a variety of circumstances is analyzed. Simulation results verify the active magnetic bearing system which is designed whit H_∞mixed sensitivity theory has good stability and robustness .It can be very good suppression of low frequency interference signals.
Finally, the paper introduced the designing of the magnetic bearing system controller based on the chip DSP named TMS320LF2812 . On this basis, the A/D channel designing and the D/A channels designing had a detailed presentation. In order to construct a complete magnetic bearing system control system, the paper also presents the filter circuit, including the necessary peripheral circuits, such as power supply circuit, simulation interface. In addition, sensors and power amplifier is an important component of a magnetic bearing system, the article finally given the selection and design methods.
At the end of the article, I has made the ponder summary to the present paper, simultaneously the work which further must develop to the topic has made the ponder.
引文
[1]G.Schweiter,H.Bleuler,A.Traxler.Active Magnetic Bearings Basics Properties and Application of Active magnetic Bearings.ETH,Switzerland,1994
[2]Eamshaw S.On the nature of molecular forces which regulate the constitution of luminiferous ether[J].Tran Camb Phil Soc 7,1983:97-112
[3]EM097新技术系列报道之二,电主轴--当前最热门的功能部件.世界机电市场,1998.2
[4]M.Brunet,B.Wagner.Analysis of performance of an AMB spindle in creep feed grinding.Proceedings of the Fourth International Symposium on Magnetic Bearings,ETH Zurich,Switzerland,August 23-26,1994
[5]江伟.磁轴承数字控制系统的研究.博士论文,清华大学,1990
[6]G.施韦策,H.布鲁勒,A.特拉克斯勒著,虞烈,袁崇军译.主动磁轴承基础性能及应用,北京:新时代出版社,1997
[7]Michael Scharfe,Karl Meizer,Ralf Zimmermann.Development of a Magnetic-Bearing Momentum Wheel
[8]G.Schweitzer.Proceedings of the First International Symposium on Magnetic Beatings,Zurich,Switzerland:June 1988
[9]赵鸿宾.磁悬浮技术综述.国际学术动态.1992,(5):43-47
[10]徐安,李永善.磁悬浮技术在德国的发展.城市轨道交通研究.2001,(2):64-68
[11]Moon FC.Magento-soldmechanics.New York:Comelluniversity,1984
[12]陈立群.电磁轴承精度控制及其应用研究.博士论文,西安交通大学,1990
[13]戴政.磁悬浮技术综述.中小型电机.2000,27(2):24-26
[14]F.Carrere,S.Font.H_∞ control design of flexible rotor magnetic bearing system.Proceedings of the Fourth International Symposium on Magnetic Bearings,ETH Zurich.Switzerland:August 23-26,1994
[15]K.Yamashita,P.E.Allair,C.R.Knospe.Rotor disturbance attenuation using H_∞ controller for active magnetic bearings.Proceedings of the Fifth International Symposium on Magnetic Bearings.Kanazawa Japan:August 28-30,1996
[16]M.Hirata,K.Nonami.Robust control of a magnetic beating system using constantly scaled H_∞ control.Proceedings of the sixth International Symposium on Magnetic Bearings,MIT.USA:August 5-7,1998
[17]汪希平,袁崇军,谢友柏.磁力轴承系统的控制策略与功放电路的设计.西安交通大学学报,1995,29(12):68-74
[18]C.Doyle著,周克敏译.鲁棒与最优控制.北京:国防工业出版社,2002
[19]朱秋,孙玉坤.最优控制理论在磁轴承控制系统中的应用研究.控制理论与应用,2002,19(3):479-483
[20]Zames G.Feedback and optimal sensitivity,model reference transformations,multiplicative seminars,and approximate inverses.IEEE Transaction on Automatic Control,1981,26:301-320.
[21]J.C.Doyle,K.Glover,P.P.Khargonekar and B.A.Francis.State-space solutions to standard H_2 and H_∞ control problems.IEEE Transactions on Automatic Control,1989,34(8):831-847
[22]解学书,钟宜生.H_∞控制理论.北京:清华人学出版社,1994
[23]C.Doyle著,周克敏译.鲁棒与最优控制.北京:国防工业出版社,2002
[24]申铁龙,耳控制理论及应用.北京:清华大学出版社,1996
[25]吴旭东,解学书.H_∞鲁棒控制中的加权阵选择.清华人学学报(自然科学版),1997,37(1):27-30
[26]马瑞,卢毅.控制器设计中的相关问题讨论.西北工业大学学报,1996,14(2):259-264
[27]工曦,曾庆福.频域不确定系统加权混合灵敏度函数频域整形.航空学报,1999,20(4):358-361
[28]陶涛,阎文博.航空发动机混合灵敏度控制中权阵的选取.推进技术,1999,20(4):66-70
[29]付丽强.磁力轴承的鲁棒控制和神经网络控制.[硕士学位论文],福州,福州大学,2001
[30]Conrad Gahler.Rotor Dynamic Testing and Control with Active Magnetic Bearings,Swiss Federal Institute of Technology,ETH,Zurich,1998,29-34.
[31]张金淼.H_∞控制理论在磁力轴承系统中的应用研究.[硕士学位论文],南京航空航天大学,2005.
[32]范素香.基于H_∞控制理论的磁悬浮系统控制研究.[硕士学位论文],中南大学,2004.
[33]苏义鑫,龙祥,张丹红.主动磁轴承的神经网络自适应PID控制.华中师范大学学报,2004,38(3):304-307
[34]Fittro R L,Knospe C R.μ-Synthesis Control Design Applied of a High-speed Machining Spindle with Active Magnetic Beatings.Proceedings of 6th International Symposium on Magnetic Beatings,Cambrige,USA,1998
[35]Fujita M.Loop Shaping Based Robust Control of a Magnetic Bearing.IEEE Control System Magazine,1993,13(4):57-65
[36]Yamashita K,Allaire P E,Knospe C R.Rotor Disturbance Attenuation Using H_∞ Cont roller for Active Magnetic Bearings.Proceedings of 5th International Symposium on Magnetic Beatings,Kanazaw
[37]薛定宇.控制系统计算机辅助设计---MATLAB语言及应用.北京:清华大学出版社
[38]王士杰.常规PID调节系统的研究进展.中国纺织大学学报,1994,4:104-112
[39]Zhuang M.and Atherton D.P.Automatic tuning of optimum PID controllers,proc.IEE,Pt.D,1993,35.329-331
[40]恒庆海,王广雄.SISO系统混合灵敏度的鲁棒性能设计.控制与决策,1995,14(3):269-271
[41]马瑞,卢毅.H_∞控制器设计中的相关问题讨论.西北工业大学学报,1996,14(2):259-264
[42]周晓宏,刘红军,武雅丽,汤娟.基于MATLAB的H_∞鲁棒控制器的设计.交通运输工程学报,2002,2(3):12-15
[43]王广雄,袁欣.H_∞设计中两块还是三块问题.电机与控制学报,2001 5(2):81-830
[44]TexasInstrumentsIncozporated.SM320F2810-EP/SM320F2811-EP/SM320-F2812-EP/SM320C2810-EP/SM320C2811-EP/SM320C2812-EP Digital Signal Processors DataManual.Literature Number:SGUSO51 A March 2004一Revised October 2004
[45]刘迎春,叶湘滨等.传感器原理设计与应用(第四版)[M].长沙:国防科技大学出版社2004.
[46]苏义鑫,周祖德,胡业发,张丹红.磁力轴承功率放大器的研究.武汉理工大学报,2003,25(6):43-45
[47]V.Gondhalekar,G.Schweitzer.Dynamics and magnetic control of a microgravity platform.Rep.Inst.ETH Zurich,1984
[2]Eamshaw S.On the nature of molecular forces which regulate the constitution of luminiferous ether[J].Tran Camb Phil Soc 7,1983:97-112
[3]EM097新技术系列报道之二,电主轴--当前最热门的功能部件.世界机电市场,1998.2
[4]M.Brunet,B.Wagner.Analysis of performance of an AMB spindle in creep feed grinding.Proceedings of the Fourth International Symposium on Magnetic Bearings,ETH Zurich,Switzerland,August 23-26,1994
[5]江伟.磁轴承数字控制系统的研究.博士论文,清华大学,1990
[6]G.施韦策,H.布鲁勒,A.特拉克斯勒著,虞烈,袁崇军译.主动磁轴承基础性能及应用,北京:新时代出版社,1997
[7]Michael Scharfe,Karl Meizer,Ralf Zimmermann.Development of a Magnetic-Bearing Momentum Wheel
[8]G.Schweitzer.Proceedings of the First International Symposium on Magnetic Beatings,Zurich,Switzerland:June 1988
[9]赵鸿宾.磁悬浮技术综述.国际学术动态.1992,(5):43-47
[10]徐安,李永善.磁悬浮技术在德国的发展.城市轨道交通研究.2001,(2):64-68
[11]Moon FC.Magento-soldmechanics.New York:Comelluniversity,1984
[12]陈立群.电磁轴承精度控制及其应用研究.博士论文,西安交通大学,1990
[13]戴政.磁悬浮技术综述.中小型电机.2000,27(2):24-26
[14]F.Carrere,S.Font.H_∞ control design of flexible rotor magnetic bearing system.Proceedings of the Fourth International Symposium on Magnetic Bearings,ETH Zurich.Switzerland:August 23-26,1994
[15]K.Yamashita,P.E.Allair,C.R.Knospe.Rotor disturbance attenuation using H_∞ controller for active magnetic bearings.Proceedings of the Fifth International Symposium on Magnetic Bearings.Kanazawa Japan:August 28-30,1996
[16]M.Hirata,K.Nonami.Robust control of a magnetic beating system using constantly scaled H_∞ control.Proceedings of the sixth International Symposium on Magnetic Bearings,MIT.USA:August 5-7,1998
[17]汪希平,袁崇军,谢友柏.磁力轴承系统的控制策略与功放电路的设计.西安交通大学学报,1995,29(12):68-74
[18]C.Doyle著,周克敏译.鲁棒与最优控制.北京:国防工业出版社,2002
[19]朱秋,孙玉坤.最优控制理论在磁轴承控制系统中的应用研究.控制理论与应用,2002,19(3):479-483
[20]Zames G.Feedback and optimal sensitivity,model reference transformations,multiplicative seminars,and approximate inverses.IEEE Transaction on Automatic Control,1981,26:301-320.
[21]J.C.Doyle,K.Glover,P.P.Khargonekar and B.A.Francis.State-space solutions to standard H_2 and H_∞ control problems.IEEE Transactions on Automatic Control,1989,34(8):831-847
[22]解学书,钟宜生.H_∞控制理论.北京:清华人学出版社,1994
[23]C.Doyle著,周克敏译.鲁棒与最优控制.北京:国防工业出版社,2002
[24]申铁龙,耳控制理论及应用.北京:清华大学出版社,1996
[25]吴旭东,解学书.H_∞鲁棒控制中的加权阵选择.清华人学学报(自然科学版),1997,37(1):27-30
[26]马瑞,卢毅.控制器设计中的相关问题讨论.西北工业大学学报,1996,14(2):259-264
[27]工曦,曾庆福.频域不确定系统加权混合灵敏度函数频域整形.航空学报,1999,20(4):358-361
[28]陶涛,阎文博.航空发动机混合灵敏度控制中权阵的选取.推进技术,1999,20(4):66-70
[29]付丽强.磁力轴承的鲁棒控制和神经网络控制.[硕士学位论文],福州,福州大学,2001
[30]Conrad Gahler.Rotor Dynamic Testing and Control with Active Magnetic Bearings,Swiss Federal Institute of Technology,ETH,Zurich,1998,29-34.
[31]张金淼.H_∞控制理论在磁力轴承系统中的应用研究.[硕士学位论文],南京航空航天大学,2005.
[32]范素香.基于H_∞控制理论的磁悬浮系统控制研究.[硕士学位论文],中南大学,2004.
[33]苏义鑫,龙祥,张丹红.主动磁轴承的神经网络自适应PID控制.华中师范大学学报,2004,38(3):304-307
[34]Fittro R L,Knospe C R.μ-Synthesis Control Design Applied of a High-speed Machining Spindle with Active Magnetic Beatings.Proceedings of 6th International Symposium on Magnetic Beatings,Cambrige,USA,1998
[35]Fujita M.Loop Shaping Based Robust Control of a Magnetic Bearing.IEEE Control System Magazine,1993,13(4):57-65
[36]Yamashita K,Allaire P E,Knospe C R.Rotor Disturbance Attenuation Using H_∞ Cont roller for Active Magnetic Bearings.Proceedings of 5th International Symposium on Magnetic Beatings,Kanazaw
[37]薛定宇.控制系统计算机辅助设计---MATLAB语言及应用.北京:清华大学出版社
[38]王士杰.常规PID调节系统的研究进展.中国纺织大学学报,1994,4:104-112
[39]Zhuang M.and Atherton D.P.Automatic tuning of optimum PID controllers,proc.IEE,Pt.D,1993,35.329-331
[40]恒庆海,王广雄.SISO系统混合灵敏度的鲁棒性能设计.控制与决策,1995,14(3):269-271
[41]马瑞,卢毅.H_∞控制器设计中的相关问题讨论.西北工业大学学报,1996,14(2):259-264
[42]周晓宏,刘红军,武雅丽,汤娟.基于MATLAB的H_∞鲁棒控制器的设计.交通运输工程学报,2002,2(3):12-15
[43]王广雄,袁欣.H_∞设计中两块还是三块问题.电机与控制学报,2001 5(2):81-830
[44]TexasInstrumentsIncozporated.SM320F2810-EP/SM320F2811-EP/SM320-F2812-EP/SM320C2810-EP/SM320C2811-EP/SM320C2812-EP Digital Signal Processors DataManual.Literature Number:SGUSO51 A March 2004一Revised October 2004
[45]刘迎春,叶湘滨等.传感器原理设计与应用(第四版)[M].长沙:国防科技大学出版社2004.
[46]苏义鑫,周祖德,胡业发,张丹红.磁力轴承功率放大器的研究.武汉理工大学报,2003,25(6):43-45
[47]V.Gondhalekar,G.Schweitzer.Dynamics and magnetic control of a microgravity platform.Rep.Inst.ETH Zurich,1984