高速电主轴主动磁轴承温度场参数设计及控制研究
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摘要
磁悬浮轴承(简称磁轴承)具有无机械接触、无磨损、无需润滑、无污染、高精度、寿命长等优点,在洁净空间、压缩机和卫星等多种需要无接触支承的场合起到了很重要的作用。本课题组研究了一种新型的交流主动磁轴承,与传统的直流磁轴承相比,它具有结构紧凑、成本低、便于驱动与控制等优点。论文设计了新型结构的五自由度交流主动磁轴承支承的电主轴系统,建立了状态方程,并以降温为目标,运用有限元方法对磁轴承进行参数优化设计,得出了满意的设计方案。在此基础上,采用改进H∞输出反馈控制算法抑制磁轴承的径向和轴向扰动,最后构建了五自由度交流主动磁轴承支承的电主轴数字控制系统,并对电主轴的五自由度悬浮支承技术进行了基础理论和PID参数鲁棒稳定域典型实验研究。论文工作是在国家自然科学基金(60974053)和江苏省自然科学基金(BK2012707)等资助下开展的。本文主要研究工作及取得的成果如下：
1.设计了用于高速电主轴一端悬浮支承的三相交流主动磁轴承,采用等效磁路法对磁轴承的磁路进行了计算,导出了悬浮力数学模型。依据数学模型及性能要求,给出了相关设计参数的方法,并研究了其控制策略。
2.提出了径向主动磁轴承温度场参数化有限元分析方法。建立定子绕组线圈的等效导热模型,降低了计算难度。解决了定转子之间的气隙热交换问题。给出了定子线圈绕组传热途径,建立了等效热路图模型,合理处理了温升对线圈绕组阻值的影响。计算了定子磁极绕组的等效体积,在此基础上得出了准确的线圈铜耗的生热率。对温度场和热损耗进行分析,给出了径向主动磁轴承三维全域温度场模型。采用三因素三水平的正交试验设计方法,在满足静态悬浮力和最大悬浮力性能要求的前提下,分析并研究了交流主动磁轴承的结构参数优化设计方法,给出了关于温度的最佳参数水平组合。仿真结果证明了所选用模型的正确性和所采用方法的实用性和有效性。
3.提出一种抑制交流主动磁轴承径向和轴向扰动的最优H∞输出反馈控制算法。在本文中,分别采用了最优输出反馈控制和最优H∞输出反馈控制改善磁轴承的径向和轴向位移调节。通过求解Riccati方程得到满足最小性能指标的输出反馈控制增益矩阵,并将该增益矩阵反馈到系统中,用来改善系统性能。上述两种控制方法可以有效调节磁轴承的径向和轴向位移输出,并通过使用Matlab和Simulink工具箱对其进行了验证。仿真结果表明文中提出的最优H∞输出反馈控制在有扰动存在情况下,其效果优于最优输出反馈控制。
4.提出仅依靠频率响应确定轴向磁轴承的PID参数鲁棒稳定域的方法。首先根据小增益定理得到闭环系统的鲁棒稳定性条件,由此推导出加性不确定性的内部稳定H∞指标,再由边界穿越定理和D-分割技术,推导了满足H∞指标的PID控制器的鲁棒参数稳定域边界的解析表达式。在稳定域中选择PID参数,可以使得系统稳定并满足鲁棒性能约束条件。该方法降低了轴向磁轴承PID控制器参数稳定域设计的难度,对时滞系统PID参数调节具有良好的鲁棒性和可操作性。仿真实验证明了本章方法的有效性。
5.设计了基于数字信号处理器TMS320F2812DSP的五自由度交流主动磁轴承数字控制系统软、硬件方案,给出了软件总体流程图以及各中断子流程图,进行了局部实验,以实例对所第五章中提出算法的有效性进行了验证,实现了交流主动磁轴承稳定悬浮。提出了详细的实验及测试方案,为进一步开展各项参数调试与功能测试奠定了基础。
For the demands of high speed and high accuracy, the use of active magnetic bearings (AMBs) plays a key role in various situations such as clean room, compressor, satellite and so on, due to their contactless nature, no lubricated, no pollution, high-precision, long service life, and etc.. A new-style AC active magnetic bearing is proposed in the dissertation. Compared with the traditional DC magnetic bearing, the AC AMB has many advantages, such as compact configuration, low cost, convenient driving and control, and so on. A new-style construction of electric spindle supported by five degrees of freedom AC active magnetic bearings is designed in this paper, state equation was established. Aim for lower temperatures, the optimum design for structural parameters of active magnetic bearing was discussed by using finite element method, and we get complete design parameters. On this basis, we adopted the improved H∞output feedback control method to suppress the radial and axial directions position perturbation of AMB systems effectively. The digital control system of electric spindle supported by five degrees of freedom AC AMBs is developed. The basic theory and proportional integral derivation (PID) robustness stability region tests of electric spindle system's five degrees of freedom suspension supporting technology are researched. The dissertation research is supported by National Natural Science Foundation of China project (60974053) and Jiangsu Province Natural Science Fund (BK2012707). The main contents of the dissertation and the achievements are as follows:
1. A three-phase AC active magnetic bearing was designed which was used in high speed electric spindle's suspension, respectively. The flux path of this magnetic bearing was calculated by using equivalent magnetic circuit, and the mathematical models of suspension forces were deduced respectively. Then based on the mathematics models, the relatively design parameters were given. The control strategy of three-phase AC active magnetic bearing was also proposed, respectively.
2. Radial active magnetic bearing's thermal field parametric finite element method is proposed. A model of equivalent thermal conductivity of the stator coil winding is set up, by means of which the difficulty in calculating the active magnetic bearing thermal field is reduced to some extent. The air gap heat exchange between the stator and rotor is worked out. By means of setting up the equivalent thermal circuit, the way to heat dissipation of the stator coil winding is given and temperature rise influence on coil winding is legitimately treated. On the basis of the equivalent volume of the stator is calculated, heat generation rate of winding copper loss is precisely calculated. According to the electromagnetic field design parameters, the active magnetic bearing's temperature field and thermal loss is further analyzed, so, thermal Field numerical calculation of the radial active magnetic bearing is given, which could help optimum design of active magnetic bearing in the future. Based on the orthogonal design method which has three three levels factors, a parameters optimum design method was researched in this thesis. On the premise that the product design could satisfy the demands of maximum static suspension forces and maximum suspension forces, an optimization design method about active magnetic bearing was studied and the best combination of the parameters about temperature are given. The simulation proved the validity of the model and the practicability of the method used in the research.
3. We propose the improved H∞output feedback control method for suppressing the radial and axial directions position perturbation of AC AMB systems. In this research, two other control options for high speed machine were designed based on the optimal output feedback and the improved H∞output feedback control methods to improve the radical and axial position regulation of AMB. The output feedback control gain matrix with the minimum performance index is obtained by solving the Riccati equation and fed back to the system in order to achieve the system's performance. The above designed controllers can efficiently regulate the radial and axial directions position deviation of for AMB systems. Simulations for the two control methods were carried out using Matlab and Simulink for AMB system models. Results show that the improved H∞output feedback controller has a better position deviation control performance over the optimal output feedback under condition of decreasing the disturbance of reaction.
4. A method is proposed for finding all PID controllers that satisfy a robust performance constraint for a given transfer function of any order with time-delay by using the frequency response. The H-infinity index of additive weight uncertainty on the basis of robustness stability condition of closed loop system is first get by small gain theorem. Then, Based on the boundary crossing theorem, the parameter boundaries with the expected decay ratio index of PID controller are derived. The system can be stabilized and robustly meet the performance requirements by choosing PID controllers parameter in the stability region. The proposed method avoids the complexity of stability regions of PID parameters, the closed-loop system has strong robustness for any order time-delay system with no accurate model. The simulation results demonstrate the validity of this method.
5. Finally, the five degrees of freedom AC AMBs system's software and hardware circuits based on digital signal processor TMS320F2812DSP have been designed, the flow charts for main program and interrupt programs have been listed too. Local experiment is done. The verification on the effectiveness of the being proposed algorithm in chapter five was put forward by a living example to realize the AC active magnetic bearing stably suspension. The detailed experimental and testing procedures have been proposed, which establishes a good foundation for the next parameters debugging and function test.
1.设计了用于高速电主轴一端悬浮支承的三相交流主动磁轴承,采用等效磁路法对磁轴承的磁路进行了计算,导出了悬浮力数学模型。依据数学模型及性能要求,给出了相关设计参数的方法,并研究了其控制策略。
2.提出了径向主动磁轴承温度场参数化有限元分析方法。建立定子绕组线圈的等效导热模型,降低了计算难度。解决了定转子之间的气隙热交换问题。给出了定子线圈绕组传热途径,建立了等效热路图模型,合理处理了温升对线圈绕组阻值的影响。计算了定子磁极绕组的等效体积,在此基础上得出了准确的线圈铜耗的生热率。对温度场和热损耗进行分析,给出了径向主动磁轴承三维全域温度场模型。采用三因素三水平的正交试验设计方法,在满足静态悬浮力和最大悬浮力性能要求的前提下,分析并研究了交流主动磁轴承的结构参数优化设计方法,给出了关于温度的最佳参数水平组合。仿真结果证明了所选用模型的正确性和所采用方法的实用性和有效性。
3.提出一种抑制交流主动磁轴承径向和轴向扰动的最优H∞输出反馈控制算法。在本文中,分别采用了最优输出反馈控制和最优H∞输出反馈控制改善磁轴承的径向和轴向位移调节。通过求解Riccati方程得到满足最小性能指标的输出反馈控制增益矩阵,并将该增益矩阵反馈到系统中,用来改善系统性能。上述两种控制方法可以有效调节磁轴承的径向和轴向位移输出,并通过使用Matlab和Simulink工具箱对其进行了验证。仿真结果表明文中提出的最优H∞输出反馈控制在有扰动存在情况下,其效果优于最优输出反馈控制。
4.提出仅依靠频率响应确定轴向磁轴承的PID参数鲁棒稳定域的方法。首先根据小增益定理得到闭环系统的鲁棒稳定性条件,由此推导出加性不确定性的内部稳定H∞指标,再由边界穿越定理和D-分割技术,推导了满足H∞指标的PID控制器的鲁棒参数稳定域边界的解析表达式。在稳定域中选择PID参数,可以使得系统稳定并满足鲁棒性能约束条件。该方法降低了轴向磁轴承PID控制器参数稳定域设计的难度,对时滞系统PID参数调节具有良好的鲁棒性和可操作性。仿真实验证明了本章方法的有效性。
5.设计了基于数字信号处理器TMS320F2812DSP的五自由度交流主动磁轴承数字控制系统软、硬件方案,给出了软件总体流程图以及各中断子流程图,进行了局部实验,以实例对所第五章中提出算法的有效性进行了验证,实现了交流主动磁轴承稳定悬浮。提出了详细的实验及测试方案,为进一步开展各项参数调试与功能测试奠定了基础。
For the demands of high speed and high accuracy, the use of active magnetic bearings (AMBs) plays a key role in various situations such as clean room, compressor, satellite and so on, due to their contactless nature, no lubricated, no pollution, high-precision, long service life, and etc.. A new-style AC active magnetic bearing is proposed in the dissertation. Compared with the traditional DC magnetic bearing, the AC AMB has many advantages, such as compact configuration, low cost, convenient driving and control, and so on. A new-style construction of electric spindle supported by five degrees of freedom AC active magnetic bearings is designed in this paper, state equation was established. Aim for lower temperatures, the optimum design for structural parameters of active magnetic bearing was discussed by using finite element method, and we get complete design parameters. On this basis, we adopted the improved H∞output feedback control method to suppress the radial and axial directions position perturbation of AMB systems effectively. The digital control system of electric spindle supported by five degrees of freedom AC AMBs is developed. The basic theory and proportional integral derivation (PID) robustness stability region tests of electric spindle system's five degrees of freedom suspension supporting technology are researched. The dissertation research is supported by National Natural Science Foundation of China project (60974053) and Jiangsu Province Natural Science Fund (BK2012707). The main contents of the dissertation and the achievements are as follows:
1. A three-phase AC active magnetic bearing was designed which was used in high speed electric spindle's suspension, respectively. The flux path of this magnetic bearing was calculated by using equivalent magnetic circuit, and the mathematical models of suspension forces were deduced respectively. Then based on the mathematics models, the relatively design parameters were given. The control strategy of three-phase AC active magnetic bearing was also proposed, respectively.
2. Radial active magnetic bearing's thermal field parametric finite element method is proposed. A model of equivalent thermal conductivity of the stator coil winding is set up, by means of which the difficulty in calculating the active magnetic bearing thermal field is reduced to some extent. The air gap heat exchange between the stator and rotor is worked out. By means of setting up the equivalent thermal circuit, the way to heat dissipation of the stator coil winding is given and temperature rise influence on coil winding is legitimately treated. On the basis of the equivalent volume of the stator is calculated, heat generation rate of winding copper loss is precisely calculated. According to the electromagnetic field design parameters, the active magnetic bearing's temperature field and thermal loss is further analyzed, so, thermal Field numerical calculation of the radial active magnetic bearing is given, which could help optimum design of active magnetic bearing in the future. Based on the orthogonal design method which has three three levels factors, a parameters optimum design method was researched in this thesis. On the premise that the product design could satisfy the demands of maximum static suspension forces and maximum suspension forces, an optimization design method about active magnetic bearing was studied and the best combination of the parameters about temperature are given. The simulation proved the validity of the model and the practicability of the method used in the research.
3. We propose the improved H∞output feedback control method for suppressing the radial and axial directions position perturbation of AC AMB systems. In this research, two other control options for high speed machine were designed based on the optimal output feedback and the improved H∞output feedback control methods to improve the radical and axial position regulation of AMB. The output feedback control gain matrix with the minimum performance index is obtained by solving the Riccati equation and fed back to the system in order to achieve the system's performance. The above designed controllers can efficiently regulate the radial and axial directions position deviation of for AMB systems. Simulations for the two control methods were carried out using Matlab and Simulink for AMB system models. Results show that the improved H∞output feedback controller has a better position deviation control performance over the optimal output feedback under condition of decreasing the disturbance of reaction.
4. A method is proposed for finding all PID controllers that satisfy a robust performance constraint for a given transfer function of any order with time-delay by using the frequency response. The H-infinity index of additive weight uncertainty on the basis of robustness stability condition of closed loop system is first get by small gain theorem. Then, Based on the boundary crossing theorem, the parameter boundaries with the expected decay ratio index of PID controller are derived. The system can be stabilized and robustly meet the performance requirements by choosing PID controllers parameter in the stability region. The proposed method avoids the complexity of stability regions of PID parameters, the closed-loop system has strong robustness for any order time-delay system with no accurate model. The simulation results demonstrate the validity of this method.
5. Finally, the five degrees of freedom AC AMBs system's software and hardware circuits based on digital signal processor TMS320F2812DSP have been designed, the flow charts for main program and interrupt programs have been listed too. Local experiment is done. The verification on the effectiveness of the being proposed algorithm in chapter five was put forward by a living example to realize the AC active magnetic bearing stably suspension. The detailed experimental and testing procedures have been proposed, which establishes a good foundation for the next parameters debugging and function test.
引文
[1]诸德宏.交流磁轴承支承电主轴系统设计与控制研究[D].镇江：江苏大学,2009
[2]孙传余.新型低功耗永磁偏置混合磁轴承的研究[D].济南：山东大学,2010
[3]戴大海.磁悬浮轴承数字控制器的研究与设计[D].南京：南京航空航天大学,2006
[4]K. Jiro, S. Tadahiko, L. Lichuan, S. Akira. Miniaturization of a one-Axis-controlled magnetic bearing[J]. Precision Engineering,2005,29(2):208-218
[5]A. M. Mohamed, F. P. Emad. Conical Magnetic Bearings with Radial and Thrust Control[C]// Proceedings of the IEEE Conference on Decision and Control Including the Symposium on Adaptive Processes,1989:554-561
[6]A. C. Lee, F. Z. Hsiao, D. Ko. Analysis and testing of magnetic bearing wish permanent magnets for bias[J]. JSME International Journal,1994,37(4):774-782
[7]Y. H. Fan, A. C. Lee. Design of a permanent/electromagnetic magnetic bearing-controlled rotor system[J]. Journal of the Franklin Institute,1997,334(3):337-359
[8]Schweitzer G, Traxler A, Bleuler H. Magnetlager [M]. Berlin:Springer-Verlag Berlin Heidelberg, 1993.
[9]S. Fukata, S. Matsuoka. Control system and dynamics of cone shaped magnetic bearings actuated by five electromagnets[C]//Fourth International Symposium on Magnetic Bearings, Zurich,Sweitzland,1994:245-250
[10]S. L. Chen, C. T. Hsu. Optimal design of a three-pole active magnetic bearing[J]. IEEE Transactions on Magnetics,2002,38(5):3458-3466
[11]C.T. Hsu, S. L. Chen. Exact linearization of a voltage-controlled three-pole active magnetic bearing system[J]. IEEE Transactions on Control Systems Technology,2002,10(5):618-625
[12]N. C. Tsai, S. L. Hsu. On sandwiched magnetic bearing design[J]. Electromegnetics,2007,27(6): 371-385
[13]熊万里,侯志泉,吕浪.气体悬浮电主轴动态特性研究进展[J].机械工程学报,2011,47(5)：40-58
[14]邓自刚,王家素,王素玉.高温超导磁悬浮轴承研发现状[J].电工技术学报,2009,9(24)：1-8.
[15]李松生,杨柳欣,吴梅英.数控机床用高速电主轴技术的现状与发展趋势[J].世界制造技术与装备市场,2003,(5)：13-15
[16]孙巍.高速电主轴系统设计与动静态性能分析[D].沈阳：沈阳工业大学,2007
[17]张丹,陈闽杰.电主轴在数控机床中的发展及其应用方向[J].制造技术与机床,2006,(8)：1-3
[18]周延佑,李中行.第一讲电主轴概述[J].制造技术与机床,2003,(15)：61-63
[19]严道发.电主轴技术综述[J].机械研究与应用.2006,(12)：5-7
[20]P. E. Allaire, R. R. Humphris, R. D. Kelm. Dynamics of a flexible rotor in magnetic bearings[M]. New York:NASA Conference Publication,1986
[21]Keith, F., R. Williams. Digital control of magnetic bearings supporting a multimass flexible rotor[M]. Hampton:Suspension Technology Workshop,1988
[22]Hartavi, A. E., O. Ustun. A Comparative approach on PD and fuzzy control of AMB using RCP[C]//IEEE International Symposium on Electric Machines and Drives, Madison, Wisconsin, 2003.
[23]M. Petrov, I. Ganchev. Fuzzy PID Control of Nonlinear Plants[C]//IEEE International Symposium on Intelligent Systems,2002
[24]H. Masujiro, I. Yoshio, M. Junichi. Development of digitally controlled magnetic bearing[J]. Nippon Kikai Gakkai Ronbunshu,1985,465(51):1095-1100
[25]I. Takakazu, S. Takashi, T. Nobuyoshi. Active vibration control of flexible rotor using electromagnetic damper[C]//IECON Proceedings of Industrial Electronics,1991:437-442
[26]T. Sato, Y. Tanno. Magnetic bearing having PID controller and discontinuous controller[C]//Proc. Int. Electronics, Control, and Instrumention,1993
[27]D. Ronald, E. Williams, F. Joseph. Digital control of active magnetic bearings[J]. IEEE Transaction on Industrial Electronics,1990,31(1):19-27
[28]S. Tokat, I. Eksin. A new PI+D type hierarchical fuzzy logic controller[C]//EEEE Conference on Control Applications,2003:570-575.
[29]M. Habib, J. I. Hussain. Control of dual acting magnetic bearing actuator system using fuzzy logic[C]//IEEE International Symposium on Computational Intelligence in Robortics and Automation, Kobe, Japan,2003
[30]A.M.Mohamed, F.P.Emad.Conical magnetic bearing with radical and thrust control [J]. IEEE Transactions on Automatic Control,1992,37(12):1895-1868
[31]A. M. Mohamed, I. Busch-Vishniac. Imbalance compensation and automation balancing in magnetic bearing systems using the Q-parameterization theory[J]. IEEE Transactions on Control System Technology,1995,3(2):202-211
[32]D. C. McFarlane, K. Glover. A loop shaping design procedure using H-infinity synthesis[J]. IEEE Transactions on Automatic Control,2010:59-769
[33]K. Glover, J.A. Sefton, D.C. McFarlane. A tutorial on loop shaping using H-infinity robust stabilisation[J]. Transactions of the Institute of Measurement and Control,1992,14(3):157-168
[34]M. Fujita, H. Hatake, F. Matsumura. Loop shaping based robust control of a magnetic bearing[J], IEEE Control Systems Magazine,1993,13(4):57-65
[35]韩璞,周世梁,刘玉燕,等.基于H∞环路成形和自适应神经模糊推理系统的模糊控制器设计[J].控制理论与应用,2004,21(5)：693-698
[36]孙涛,喻凡,柳江.基于混合不确定建模的主动悬架鲁棒综合控制分析[J].上海交通大学学报,2006,40(6)：936-941.
[37]K. Nonami, T. Ito.μ Synthesis of flexible rotor-magnetic bearing systems[J]. IEEE Transactions on Control System Technology,1996,4(5):503-512.
[38]M.Fujita, T.Namerikawa, F.Matsumura, K.Uchida. μ-synthesis of an electromagnetic suspension systems[J]. IEEE Transactions on Automatic Control,1995,40(3):530-536
[39]Losch, F.Gahler, C. Herzog. Low-order u-synthesis controller design for a large boiler feed Pump equipped with active magnetic bearings[C]//IEEE International Conference on Control Applications, Hawaii, USA,1999:22-27
[40]郑世强,房建成,魏彤,丁力.MSCMG磁轴承μ综合控制方法与实验研究[J1.仪器仪表学报,2010.6(31)：1375-1380
[41]H. Tian, K. Nonami, Tans. Robust control of flexible rotor-magnetic bearing systems using discrete time sliding mode control[C]//Proceedings of the 4th International Symposium on Magnetic Bearings, Zurich, Switzerland,1996
[42]A. E. Rundell, S. V. Drakunov. A sliding mode observer and controller for stabilization of rotational motion of a vertical shaft magnetic bearing[J]. IEEE Transactions on Control System Technology,1996,4(5):598-608.
[43]S.Sivrioglu, K.Nonami. Sliding Mode control with time-varying hyperplane for AMB systems[J]. IEEE Trans.Mechatronics,1998,3(1):51-59
[44]Sinha,A, Mease,K.L,Wang,K.W. Sliding Mode Control of a Rigid Rotor via Magnetic Bearings. ASME Journal of Model Analysis.vol.38,pp.209-217,1991.
[45]楼晓春,吴国庆.主动磁轴承系统的自适应滑模控制[J].电工技术学报,2012,27(1)：142-147
[46]毛承雄,何金平,王丹.全控器件励磁系统的多变量反馈线性化控制[J].中国电机工程学报,2013,33(22)：53-60
[47]D. L. Trumper, S. M. Olson. Linearizing Control of Magnetic Suspension Systems[J]. IEEE Transaction on Control System Technology,1997,5(4):427-437.
[48]L. C. Lin, T. B. Gau. Feedback Linearization and Fuzzy Control for Conical Magnetic Bearings." IEEE Trans[J]. Control System Technology,1997,5(4):417-426.
[49]A. Ishidori,.Nonlinear control systems:an introduction[M]. New York:Springer-Verlag.1987
[50]M. Krstic, I. Kanellakopoulos. Nonlinear and adaptive control design[M]. New York:Wiley,1995
[51]李俊,徐德民,黄心汉.主动磁悬浮轴承的非线性反演变结构控制[J].华中理工大学学报,1999,24(5)：63-66.
[52]M.S. Queiroz, D.M. Dawson. Nonlinear control of active magnetic bearings:a backstepping approach[J]. IEEE Transaction on Control Systems Technology (special issue on Magnetic Bearing Control),1996,4(5):545-552
[53]S. Sivrioglu. Adaptive backstepping for switching control active magnetic bearing system with vibrating base[J]. IET Control Theory Application,2007,4(1):1054-1059.
[54]H. Bleuler, C. Gahler. Application of digital signal processors for industrial magnetic bearings[J]. IEEE Transaction Control System Technology,1994,2(4):280-289.
[55]于灵慧,房建成.基于主动磁轴承的高速飞轮转子系统的非线性控制研究[J].宇航学报,2005,26(3)：302-305.
[56]J.T. Jeng, T.T. Lee. Control of magnetic bearing systems via the chebyshev polynomial-based unified model neural network[J]. IEEE Transaction on System Man and Cybern, Part B, 2000,30(1):85-92
[57]王喜莲,葛宝明,伍召莉.基于柔性神经网络自适应PID的磁轴承径向力控制[J].北京交通大学学报,2012,23(2)：125-132
[58]K. Liu, F. L. Lewis. Some issues about fuzzy logic control[C]//The 32nd Conference on Decision and Control, San Antonio, Texas,1993
[59]L. Reznik. Fuzzy controllers[M]. Oxford:Copyright Leonid Reznik,1997
[60]J. Y. Hung. Magnetic bearing control using fuzzy logic[J]. IEEE Transactions on Industry Applications,1995,31 (6):1492-1497
[61]S.Jee, Y. Koren. Adaptive fuzzy logic controller for feed drives of a CNC machine tool[J]. Mechatroniccs,2004,14(3):299-326
[62]L. C. Lin, C. P. Jou. GA-based fuzzy enforcement learning for control of a magnetic bearing system[J]. IEEE Transaction Control System Technology,2000,30(2):276-189
[63]Sung-Kyung Hong, R. Langari. Robust fuzzy control of a magnetic bearing system subject to harmonic disturbances[J]. IEEE Transactions on Control Systems Technology,2003,8(2):366-371
[64]S. J. Huang, L.C. Lin. Fuzzy modeling and control for conical magnetic bearings using linear matrix inequality [J]. Journal of Intelligent and Robotic Systems:Theory and Applications, 2003,37(2):209-232
[65]K. P. Nair, T M.Abraham.3-D analysis of radial type electromagnetic bearing using the finite element method[C]//7th International Symposium on Megnetic Bearings, ETH Zurich,Swiss,2000, 29-32
[66]孙首群,耿海鹏,虞烈.实心磁铁推力磁轴承热分析[J].电工技术学报,2002,17(5)：16-20
[67]孙首群,朱卫光,赵玉香.推力磁轴承转子系统温度场[J].上海理工大学学报,2008,30(2)：179-184
[68]K.S. Khoo, S.D. Garvey, K. Kalita. The specific load capacity of radial-flux radial magnetic bearings[J]. IEEE Transaction on Magnetics,2007,43(7):3293-3300
[69]李新生,杨作兴,赵雷,等.轴向电磁轴承发热问题研究[J].清华大学学报(自然科学版),2002,42(8)：1015-1018
[70]A. Chiba, T. Fukao, O. Ichikawa, et al. Magnetic bearings and bearingless drives [M]. London: Newnes,2005:239-249.
[71]靳廷船,李伟力,李守法.感应电机定子温度场的数值计算[J].电机与控制学报,2006,10(5)：492-497
[72]M. Ahrens, L. Kucera. Analatical calculation of fields, forces and losses of a radial magnetic bearing with a totaling rotor considering eddy currents[C]//5th International Symposium on Magnetic Bearings, kanazawa, Japan,1996
[73]Shyh-Leh Chen, Chan Tang Hsu. Optimal design of a three-pole active magnetic bearing[J]. IEEE Transaction on Magnetics,2002,38(5):1292-1297
[74]F. Kreith. Convection heat transfer in rotating systems[J]. Advances in Heat Transfer, Academic Press Inc,1968,5:129-251
[75]Yanhua Sun, Lie Yu. Analytical Method for Eddy Current Loss in Laminated Rotors with magnetic bearings[J]. IEEE TRANSACTIONS ON MAGNETICS,2002,38(2):1341-1347.
[76]G Schweitzer著.徐旸译.磁悬浮轴承——理论、设计及旋转机械应用[M].北京：机械工业出版社,2012
[77]A. Chiba, T. Fukao, O. Ichikawa, et al. Magnetic bearings and bearingless drives[M]. Tokyo: Newnes,2005.
[78]H. Kanzaki, K. Sato, M. Kumagai. A study of an estimation method for predicting the equivalent thermal conductivity of an electric coil[J].Heat Transfer Japanese Research,1998,21(5):429-433.
[79]K.S. Ball, B. Farouk, V.C. Dixit. An experimental study of heat transfer in a vertical annulus with a rotating cylinder[J]. International Journal of Heat Mass Transfer,1989,32:1517-1527
[80]J. Xypteras, V, Hatziathanassiou.Thermal analysis of an electrical machine taking into account the iron losses and the deep-bar effect[J]. IEEE Transactions on Energy Conversion, 1999,14(4):996-1003
[81]邹继斌,张洪亮,江善林,等.电磁稳态条件下的力矩电机三维暂态温度场分析[J].中国电机工程学报,2007,27(21)：66-70
[82]杨虎,刘惊荪,钟波.数理统计[M].北京：高等教育出版社,2004：168-178
[83]嵇尚华,朱烧秋.交流主动磁轴承参数设计与优化[J].中国电机工程学报,2011,31(21)：150-157
[84]Nan-Chyuan Tsai, Chien-Hsien Kuo. Regulation on radial position deviation for vertical AMB systems[J]. Mechanical Systems and Signal Processing,2007,21:2777-2793
[85]S. Sivrioglu, K. Nonami, M. Saigo. Low power consumption nonlinear control with H-infinity compensator for a zero-bias flywheel AMB system[J]. Journal of Vibration and Control,2004, 10(8):1151-1166
[86]P. Schroder, B. Green, N. Grum, P.J Fleming. On-line evolution of robust control systems:an industrial active magnetic bearing application[J]. Control Engineering Practice,2001,9(1):37-49.
[87]K.Y. Zhu, Y. Xiao, U. Rajendra. Optimal control of the magnetic bearings for a flywheel energy storage system[J]. Mechatronics,2009,19(8):1221-1235
[88]Jr-Yi Shen, C.Brian, Fabien. Optimal control of a flywheel energy storage system with a radial flux hybrid magnetic bearing[J]. Journal of the Franklin Institute,2002,339(2):189-210
[89]D. D. Moerder, A. J. Calise. Convergence of a numerical algorithm for calculating optimal output feedback gains[J]. IEEE Transactions on Automatic Control,1985,30 (9):900-903
[90]V. Syrmos, C. Abdallah, P. Dorato. Static output feedback:A survey[C]//IEEE Conference on Decision and Control, Piscataway, NJ,1994:837-842
[91]J. Gadewadikar, F. L. Lewis, L. Xie. Parameterization of all stabilizing H∞ static state-feedback gains:application to output-feedback design[J]. Automatica,2007,43:1597-1604
[92]Sae Kyu Nam, Ho Shik Kang, Seop Song. Fuzzy H∞ output feedback control for rotor magnetic bearing system[C]//IEEE International Conference on Fuzzy Systems,2002:455-459
[93]M. Davoodi, P.K. Sedgh, R. Amirifar. H2 and H∞ dynamic output feedback control of a magnetic bearing system via LMIs[C]//American Control Conference,2008:2522-2527
[94]F. Jamshidi, M.G. Moghadam, M.T.H. Beheshti. An LMI approach to mixed H2/H∞ synthesis via dynamic output-feedback for active magnetic bearing[C]//International Conference on Advanced Computer Control,2009:225-230
[95]Shi-Jing Huang, Lih-Chang Lin. Fuzzy dynamic output feedback control with adaptive rotor imbalance compensation for magnetic bearing systems[J]. IEEE Transactions on Systems, Man, and Cybernetics,2004,34(4):1854-1864
[96]K. Zhou, J. C. Doyle. Essentials of robust control[M]. New Jersey:Prentice Hall,1998
[97]T. Bauar, P. Bernard. H∞ optimal control and related minimax design problems[M]. Swiss: Birkhauser,1995
[98]A. Azemi, E. E. Yaz. Using MATLAB in a graduate electrical engineering optimal control course[C]//Proc.27th Frontier in Educ. Conf.,1997,1:13-17
[99]F. L. Lewis, V. L. Syrmos. Optimal Control,3nd ed[M]. New York:Wiley-Interscience,2012
[100]M T. Ho. Synthesis of H∞ PID controllers:A parametric approach[J]. Automatica,2003,39(6): 1069-1075
[101]M. Saeki. Properties of Stabilizing PID Gain Set in Parameter Space[J]. IEEE Transactions on Automatic Control,2007,52(9):1710-1715
[102]L. H. Keel, S. P. Bhattacharyya. Controller synthesis free of analytical models:three term controllers[J]. IEEE Transactions on Automatic Control,2008,53(6):367-372
[103]Silva G J, Datta A, Bhattacharyya S P. On the stability and controller robustness of some popular PID tuning rules[J]. IEEE Transactions on Automatic Control,2003,48(9):1638-1641
[104]方斌.时滞系统PID控制器参数稳定域的实现[J].电子科技大学学报,2011,3：150-157
[105]林示麟,欧林林,俞立.无模型SISO时滞系统的PID参数稳定域研究[J].控制理论与应用,2009,26(4)：443-445
[106]方斌.基于稳定裕量的二阶时滞系统PID控制器参数稳定域[J].信息与控制,2011(02)：255-273
[107]P. Bhattacharyya, H. Chapeliat, L.H. Keel.Robust control:the parametric approach[M]. Upper Saddle River, NJ:Prentice Hall PTR,1995
[108]Neimark,Yu.I. Structure of the D-partition of a space of polynomials and the diagrams of Visnegradskii and Nyquist[J]. IEEE Transactions on Automatic Control,1948,59:853-856.
[109]Proter,B.,1989,Stability criteria for linear dynamical systems, Academic Press:New York
[110]S. Ruan, J. Wei. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays[J]. Dynamics of Continuous, Discrete and Impulsive Systems, Series A:Mathematical Analysis,2003,10(6):863-874
[111]K. Walton, J. E. Marshall. Direct method for TDS stability analysis[C]//International Conference on Control,2004,70(34):101-107
[112]J. Ackermann, A. Bartlett, D. Kaesbauer, et al. Robust control systems with uncertain physical parameters[M]. Berlin:Springer-Verlag Press,1993
[113]G. H. Lii, C.H. Chang, K.W. Han, Analysis of robust control systems using stability equations[J]. Journal of Control Systems and Technology,1993,1:83-89
[114]H. Kwakernaak. Robust control and H∞ optimization tutorial paper[J]. Automatica, 1993,29(2):255-273
[115]欧林林,顾诞英,张卫东.线性时滞系统的P和PI控制器稳定参数集算法[J].上海交通大学学报,2006,7：148-152
[116]李德广,刘淑琴.磁悬浮轴承数字控制的稳定性分析及预补偿算法[J].电工技术学报,2011,26(6)：108-112
[117]陈国呈.PWM变频调速及软开关电力技术[M],北京：机械工业出版社,2001
[118]孙首群.电磁轴承转子系统的温度场、动态响应及系统设计研究[D].西安：西安交通大学,2003
[2]孙传余.新型低功耗永磁偏置混合磁轴承的研究[D].济南：山东大学,2010
[3]戴大海.磁悬浮轴承数字控制器的研究与设计[D].南京：南京航空航天大学,2006
[4]K. Jiro, S. Tadahiko, L. Lichuan, S. Akira. Miniaturization of a one-Axis-controlled magnetic bearing[J]. Precision Engineering,2005,29(2):208-218
[5]A. M. Mohamed, F. P. Emad. Conical Magnetic Bearings with Radial and Thrust Control[C]// Proceedings of the IEEE Conference on Decision and Control Including the Symposium on Adaptive Processes,1989:554-561
[6]A. C. Lee, F. Z. Hsiao, D. Ko. Analysis and testing of magnetic bearing wish permanent magnets for bias[J]. JSME International Journal,1994,37(4):774-782
[7]Y. H. Fan, A. C. Lee. Design of a permanent/electromagnetic magnetic bearing-controlled rotor system[J]. Journal of the Franklin Institute,1997,334(3):337-359
[8]Schweitzer G, Traxler A, Bleuler H. Magnetlager [M]. Berlin:Springer-Verlag Berlin Heidelberg, 1993.
[9]S. Fukata, S. Matsuoka. Control system and dynamics of cone shaped magnetic bearings actuated by five electromagnets[C]//Fourth International Symposium on Magnetic Bearings, Zurich,Sweitzland,1994:245-250
[10]S. L. Chen, C. T. Hsu. Optimal design of a three-pole active magnetic bearing[J]. IEEE Transactions on Magnetics,2002,38(5):3458-3466
[11]C.T. Hsu, S. L. Chen. Exact linearization of a voltage-controlled three-pole active magnetic bearing system[J]. IEEE Transactions on Control Systems Technology,2002,10(5):618-625
[12]N. C. Tsai, S. L. Hsu. On sandwiched magnetic bearing design[J]. Electromegnetics,2007,27(6): 371-385
[13]熊万里,侯志泉,吕浪.气体悬浮电主轴动态特性研究进展[J].机械工程学报,2011,47(5)：40-58
[14]邓自刚,王家素,王素玉.高温超导磁悬浮轴承研发现状[J].电工技术学报,2009,9(24)：1-8.
[15]李松生,杨柳欣,吴梅英.数控机床用高速电主轴技术的现状与发展趋势[J].世界制造技术与装备市场,2003,(5)：13-15
[16]孙巍.高速电主轴系统设计与动静态性能分析[D].沈阳：沈阳工业大学,2007
[17]张丹,陈闽杰.电主轴在数控机床中的发展及其应用方向[J].制造技术与机床,2006,(8)：1-3
[18]周延佑,李中行.第一讲电主轴概述[J].制造技术与机床,2003,(15)：61-63
[19]严道发.电主轴技术综述[J].机械研究与应用.2006,(12)：5-7
[20]P. E. Allaire, R. R. Humphris, R. D. Kelm. Dynamics of a flexible rotor in magnetic bearings[M]. New York:NASA Conference Publication,1986
[21]Keith, F., R. Williams. Digital control of magnetic bearings supporting a multimass flexible rotor[M]. Hampton:Suspension Technology Workshop,1988
[22]Hartavi, A. E., O. Ustun. A Comparative approach on PD and fuzzy control of AMB using RCP[C]//IEEE International Symposium on Electric Machines and Drives, Madison, Wisconsin, 2003.
[23]M. Petrov, I. Ganchev. Fuzzy PID Control of Nonlinear Plants[C]//IEEE International Symposium on Intelligent Systems,2002
[24]H. Masujiro, I. Yoshio, M. Junichi. Development of digitally controlled magnetic bearing[J]. Nippon Kikai Gakkai Ronbunshu,1985,465(51):1095-1100
[25]I. Takakazu, S. Takashi, T. Nobuyoshi. Active vibration control of flexible rotor using electromagnetic damper[C]//IECON Proceedings of Industrial Electronics,1991:437-442
[26]T. Sato, Y. Tanno. Magnetic bearing having PID controller and discontinuous controller[C]//Proc. Int. Electronics, Control, and Instrumention,1993
[27]D. Ronald, E. Williams, F. Joseph. Digital control of active magnetic bearings[J]. IEEE Transaction on Industrial Electronics,1990,31(1):19-27
[28]S. Tokat, I. Eksin. A new PI+D type hierarchical fuzzy logic controller[C]//EEEE Conference on Control Applications,2003:570-575.
[29]M. Habib, J. I. Hussain. Control of dual acting magnetic bearing actuator system using fuzzy logic[C]//IEEE International Symposium on Computational Intelligence in Robortics and Automation, Kobe, Japan,2003
[30]A.M.Mohamed, F.P.Emad.Conical magnetic bearing with radical and thrust control [J]. IEEE Transactions on Automatic Control,1992,37(12):1895-1868
[31]A. M. Mohamed, I. Busch-Vishniac. Imbalance compensation and automation balancing in magnetic bearing systems using the Q-parameterization theory[J]. IEEE Transactions on Control System Technology,1995,3(2):202-211
[32]D. C. McFarlane, K. Glover. A loop shaping design procedure using H-infinity synthesis[J]. IEEE Transactions on Automatic Control,2010:59-769
[33]K. Glover, J.A. Sefton, D.C. McFarlane. A tutorial on loop shaping using H-infinity robust stabilisation[J]. Transactions of the Institute of Measurement and Control,1992,14(3):157-168
[34]M. Fujita, H. Hatake, F. Matsumura. Loop shaping based robust control of a magnetic bearing[J], IEEE Control Systems Magazine,1993,13(4):57-65
[35]韩璞,周世梁,刘玉燕,等.基于H∞环路成形和自适应神经模糊推理系统的模糊控制器设计[J].控制理论与应用,2004,21(5)：693-698
[36]孙涛,喻凡,柳江.基于混合不确定建模的主动悬架鲁棒综合控制分析[J].上海交通大学学报,2006,40(6)：936-941.
[37]K. Nonami, T. Ito.μ Synthesis of flexible rotor-magnetic bearing systems[J]. IEEE Transactions on Control System Technology,1996,4(5):503-512.
[38]M.Fujita, T.Namerikawa, F.Matsumura, K.Uchida. μ-synthesis of an electromagnetic suspension systems[J]. IEEE Transactions on Automatic Control,1995,40(3):530-536
[39]Losch, F.Gahler, C. Herzog. Low-order u-synthesis controller design for a large boiler feed Pump equipped with active magnetic bearings[C]//IEEE International Conference on Control Applications, Hawaii, USA,1999:22-27
[40]郑世强,房建成,魏彤,丁力.MSCMG磁轴承μ综合控制方法与实验研究[J1.仪器仪表学报,2010.6(31)：1375-1380
[41]H. Tian, K. Nonami, Tans. Robust control of flexible rotor-magnetic bearing systems using discrete time sliding mode control[C]//Proceedings of the 4th International Symposium on Magnetic Bearings, Zurich, Switzerland,1996
[42]A. E. Rundell, S. V. Drakunov. A sliding mode observer and controller for stabilization of rotational motion of a vertical shaft magnetic bearing[J]. IEEE Transactions on Control System Technology,1996,4(5):598-608.
[43]S.Sivrioglu, K.Nonami. Sliding Mode control with time-varying hyperplane for AMB systems[J]. IEEE Trans.Mechatronics,1998,3(1):51-59
[44]Sinha,A, Mease,K.L,Wang,K.W. Sliding Mode Control of a Rigid Rotor via Magnetic Bearings. ASME Journal of Model Analysis.vol.38,pp.209-217,1991.
[45]楼晓春,吴国庆.主动磁轴承系统的自适应滑模控制[J].电工技术学报,2012,27(1)：142-147
[46]毛承雄,何金平,王丹.全控器件励磁系统的多变量反馈线性化控制[J].中国电机工程学报,2013,33(22)：53-60
[47]D. L. Trumper, S. M. Olson. Linearizing Control of Magnetic Suspension Systems[J]. IEEE Transaction on Control System Technology,1997,5(4):427-437.
[48]L. C. Lin, T. B. Gau. Feedback Linearization and Fuzzy Control for Conical Magnetic Bearings." IEEE Trans[J]. Control System Technology,1997,5(4):417-426.
[49]A. Ishidori,.Nonlinear control systems:an introduction[M]. New York:Springer-Verlag.1987
[50]M. Krstic, I. Kanellakopoulos. Nonlinear and adaptive control design[M]. New York:Wiley,1995
[51]李俊,徐德民,黄心汉.主动磁悬浮轴承的非线性反演变结构控制[J].华中理工大学学报,1999,24(5)：63-66.
[52]M.S. Queiroz, D.M. Dawson. Nonlinear control of active magnetic bearings:a backstepping approach[J]. IEEE Transaction on Control Systems Technology (special issue on Magnetic Bearing Control),1996,4(5):545-552
[53]S. Sivrioglu. Adaptive backstepping for switching control active magnetic bearing system with vibrating base[J]. IET Control Theory Application,2007,4(1):1054-1059.
[54]H. Bleuler, C. Gahler. Application of digital signal processors for industrial magnetic bearings[J]. IEEE Transaction Control System Technology,1994,2(4):280-289.
[55]于灵慧,房建成.基于主动磁轴承的高速飞轮转子系统的非线性控制研究[J].宇航学报,2005,26(3)：302-305.
[56]J.T. Jeng, T.T. Lee. Control of magnetic bearing systems via the chebyshev polynomial-based unified model neural network[J]. IEEE Transaction on System Man and Cybern, Part B, 2000,30(1):85-92
[57]王喜莲,葛宝明,伍召莉.基于柔性神经网络自适应PID的磁轴承径向力控制[J].北京交通大学学报,2012,23(2)：125-132
[58]K. Liu, F. L. Lewis. Some issues about fuzzy logic control[C]//The 32nd Conference on Decision and Control, San Antonio, Texas,1993
[59]L. Reznik. Fuzzy controllers[M]. Oxford:Copyright Leonid Reznik,1997
[60]J. Y. Hung. Magnetic bearing control using fuzzy logic[J]. IEEE Transactions on Industry Applications,1995,31 (6):1492-1497
[61]S.Jee, Y. Koren. Adaptive fuzzy logic controller for feed drives of a CNC machine tool[J]. Mechatroniccs,2004,14(3):299-326
[62]L. C. Lin, C. P. Jou. GA-based fuzzy enforcement learning for control of a magnetic bearing system[J]. IEEE Transaction Control System Technology,2000,30(2):276-189
[63]Sung-Kyung Hong, R. Langari. Robust fuzzy control of a magnetic bearing system subject to harmonic disturbances[J]. IEEE Transactions on Control Systems Technology,2003,8(2):366-371
[64]S. J. Huang, L.C. Lin. Fuzzy modeling and control for conical magnetic bearings using linear matrix inequality [J]. Journal of Intelligent and Robotic Systems:Theory and Applications, 2003,37(2):209-232
[65]K. P. Nair, T M.Abraham.3-D analysis of radial type electromagnetic bearing using the finite element method[C]//7th International Symposium on Megnetic Bearings, ETH Zurich,Swiss,2000, 29-32
[66]孙首群,耿海鹏,虞烈.实心磁铁推力磁轴承热分析[J].电工技术学报,2002,17(5)：16-20
[67]孙首群,朱卫光,赵玉香.推力磁轴承转子系统温度场[J].上海理工大学学报,2008,30(2)：179-184
[68]K.S. Khoo, S.D. Garvey, K. Kalita. The specific load capacity of radial-flux radial magnetic bearings[J]. IEEE Transaction on Magnetics,2007,43(7):3293-3300
[69]李新生,杨作兴,赵雷,等.轴向电磁轴承发热问题研究[J].清华大学学报(自然科学版),2002,42(8)：1015-1018
[70]A. Chiba, T. Fukao, O. Ichikawa, et al. Magnetic bearings and bearingless drives [M]. London: Newnes,2005:239-249.
[71]靳廷船,李伟力,李守法.感应电机定子温度场的数值计算[J].电机与控制学报,2006,10(5)：492-497
[72]M. Ahrens, L. Kucera. Analatical calculation of fields, forces and losses of a radial magnetic bearing with a totaling rotor considering eddy currents[C]//5th International Symposium on Magnetic Bearings, kanazawa, Japan,1996
[73]Shyh-Leh Chen, Chan Tang Hsu. Optimal design of a three-pole active magnetic bearing[J]. IEEE Transaction on Magnetics,2002,38(5):1292-1297
[74]F. Kreith. Convection heat transfer in rotating systems[J]. Advances in Heat Transfer, Academic Press Inc,1968,5:129-251
[75]Yanhua Sun, Lie Yu. Analytical Method for Eddy Current Loss in Laminated Rotors with magnetic bearings[J]. IEEE TRANSACTIONS ON MAGNETICS,2002,38(2):1341-1347.
[76]G Schweitzer著.徐旸译.磁悬浮轴承——理论、设计及旋转机械应用[M].北京：机械工业出版社,2012
[77]A. Chiba, T. Fukao, O. Ichikawa, et al. Magnetic bearings and bearingless drives[M]. Tokyo: Newnes,2005.
[78]H. Kanzaki, K. Sato, M. Kumagai. A study of an estimation method for predicting the equivalent thermal conductivity of an electric coil[J].Heat Transfer Japanese Research,1998,21(5):429-433.
[79]K.S. Ball, B. Farouk, V.C. Dixit. An experimental study of heat transfer in a vertical annulus with a rotating cylinder[J]. International Journal of Heat Mass Transfer,1989,32:1517-1527
[80]J. Xypteras, V, Hatziathanassiou.Thermal analysis of an electrical machine taking into account the iron losses and the deep-bar effect[J]. IEEE Transactions on Energy Conversion, 1999,14(4):996-1003
[81]邹继斌,张洪亮,江善林,等.电磁稳态条件下的力矩电机三维暂态温度场分析[J].中国电机工程学报,2007,27(21)：66-70
[82]杨虎,刘惊荪,钟波.数理统计[M].北京：高等教育出版社,2004：168-178
[83]嵇尚华,朱烧秋.交流主动磁轴承参数设计与优化[J].中国电机工程学报,2011,31(21)：150-157
[84]Nan-Chyuan Tsai, Chien-Hsien Kuo. Regulation on radial position deviation for vertical AMB systems[J]. Mechanical Systems and Signal Processing,2007,21:2777-2793
[85]S. Sivrioglu, K. Nonami, M. Saigo. Low power consumption nonlinear control with H-infinity compensator for a zero-bias flywheel AMB system[J]. Journal of Vibration and Control,2004, 10(8):1151-1166
[86]P. Schroder, B. Green, N. Grum, P.J Fleming. On-line evolution of robust control systems:an industrial active magnetic bearing application[J]. Control Engineering Practice,2001,9(1):37-49.
[87]K.Y. Zhu, Y. Xiao, U. Rajendra. Optimal control of the magnetic bearings for a flywheel energy storage system[J]. Mechatronics,2009,19(8):1221-1235
[88]Jr-Yi Shen, C.Brian, Fabien. Optimal control of a flywheel energy storage system with a radial flux hybrid magnetic bearing[J]. Journal of the Franklin Institute,2002,339(2):189-210
[89]D. D. Moerder, A. J. Calise. Convergence of a numerical algorithm for calculating optimal output feedback gains[J]. IEEE Transactions on Automatic Control,1985,30 (9):900-903
[90]V. Syrmos, C. Abdallah, P. Dorato. Static output feedback:A survey[C]//IEEE Conference on Decision and Control, Piscataway, NJ,1994:837-842
[91]J. Gadewadikar, F. L. Lewis, L. Xie. Parameterization of all stabilizing H∞ static state-feedback gains:application to output-feedback design[J]. Automatica,2007,43:1597-1604
[92]Sae Kyu Nam, Ho Shik Kang, Seop Song. Fuzzy H∞ output feedback control for rotor magnetic bearing system[C]//IEEE International Conference on Fuzzy Systems,2002:455-459
[93]M. Davoodi, P.K. Sedgh, R. Amirifar. H2 and H∞ dynamic output feedback control of a magnetic bearing system via LMIs[C]//American Control Conference,2008:2522-2527
[94]F. Jamshidi, M.G. Moghadam, M.T.H. Beheshti. An LMI approach to mixed H2/H∞ synthesis via dynamic output-feedback for active magnetic bearing[C]//International Conference on Advanced Computer Control,2009:225-230
[95]Shi-Jing Huang, Lih-Chang Lin. Fuzzy dynamic output feedback control with adaptive rotor imbalance compensation for magnetic bearing systems[J]. IEEE Transactions on Systems, Man, and Cybernetics,2004,34(4):1854-1864
[96]K. Zhou, J. C. Doyle. Essentials of robust control[M]. New Jersey:Prentice Hall,1998
[97]T. Bauar, P. Bernard. H∞ optimal control and related minimax design problems[M]. Swiss: Birkhauser,1995
[98]A. Azemi, E. E. Yaz. Using MATLAB in a graduate electrical engineering optimal control course[C]//Proc.27th Frontier in Educ. Conf.,1997,1:13-17
[99]F. L. Lewis, V. L. Syrmos. Optimal Control,3nd ed[M]. New York:Wiley-Interscience,2012
[100]M T. Ho. Synthesis of H∞ PID controllers:A parametric approach[J]. Automatica,2003,39(6): 1069-1075
[101]M. Saeki. Properties of Stabilizing PID Gain Set in Parameter Space[J]. IEEE Transactions on Automatic Control,2007,52(9):1710-1715
[102]L. H. Keel, S. P. Bhattacharyya. Controller synthesis free of analytical models:three term controllers[J]. IEEE Transactions on Automatic Control,2008,53(6):367-372
[103]Silva G J, Datta A, Bhattacharyya S P. On the stability and controller robustness of some popular PID tuning rules[J]. IEEE Transactions on Automatic Control,2003,48(9):1638-1641
[104]方斌.时滞系统PID控制器参数稳定域的实现[J].电子科技大学学报,2011,3：150-157
[105]林示麟,欧林林,俞立.无模型SISO时滞系统的PID参数稳定域研究[J].控制理论与应用,2009,26(4)：443-445
[106]方斌.基于稳定裕量的二阶时滞系统PID控制器参数稳定域[J].信息与控制,2011(02)：255-273
[107]P. Bhattacharyya, H. Chapeliat, L.H. Keel.Robust control:the parametric approach[M]. Upper Saddle River, NJ:Prentice Hall PTR,1995
[108]Neimark,Yu.I. Structure of the D-partition of a space of polynomials and the diagrams of Visnegradskii and Nyquist[J]. IEEE Transactions on Automatic Control,1948,59:853-856.
[109]Proter,B.,1989,Stability criteria for linear dynamical systems, Academic Press:New York
[110]S. Ruan, J. Wei. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays[J]. Dynamics of Continuous, Discrete and Impulsive Systems, Series A:Mathematical Analysis,2003,10(6):863-874
[111]K. Walton, J. E. Marshall. Direct method for TDS stability analysis[C]//International Conference on Control,2004,70(34):101-107
[112]J. Ackermann, A. Bartlett, D. Kaesbauer, et al. Robust control systems with uncertain physical parameters[M]. Berlin:Springer-Verlag Press,1993
[113]G. H. Lii, C.H. Chang, K.W. Han, Analysis of robust control systems using stability equations[J]. Journal of Control Systems and Technology,1993,1:83-89
[114]H. Kwakernaak. Robust control and H∞ optimization tutorial paper[J]. Automatica, 1993,29(2):255-273
[115]欧林林,顾诞英,张卫东.线性时滞系统的P和PI控制器稳定参数集算法[J].上海交通大学学报,2006,7：148-152
[116]李德广,刘淑琴.磁悬浮轴承数字控制的稳定性分析及预补偿算法[J].电工技术学报,2011,26(6)：108-112
[117]陈国呈.PWM变频调速及软开关电力技术[M],北京：机械工业出版社,2001
[118]孙首群.电磁轴承转子系统的温度场、动态响应及系统设计研究[D].西安：西安交通大学,2003
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