磁悬浮轴承系统的鲁棒H_∞控制研究
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摘要
本文的主要工作是将鲁棒H∞控制理论应用到主动磁悬浮轴承实验平台中。首先对系统的各个环节进行了分析,包括转子动力学、传感器、功率放大器和控制器结构分析,建立了五自由度磁悬浮轴承-转子数学模型,并将其进行了强制解耦,得到了分散控制需要的数学模型。
考虑到磁悬浮轴承系统中的参数不确定性,本文采用参数不确定H∞控制理论,利用结构化设计和分散控制策略,通过求解2-Riccati方程,设计了单自由度上的H∞控制器,并采用仿真实验,探讨了该控制器对参数摄动的抑制性能。针对磁悬浮轴承-转子结构中存在的未建模动态等不确定性,本文采用H∞混合灵敏度法设计了分散H∞控制器,设计过程中,提出了加权函数与控制器之间的部分内在联系。针对径向和轴向的H∞控制器,本文在Matlab/Simulink环境中还分别进行了磁悬浮轴承系统的仿真实验,从理论上验证了所求H∞控制器良好的信号跟踪和干扰抑制性能。
最后,通过对H∞控制器进行双线性变换,本文编写了C语言H∞控制程序,并将其应用到基于PC机实时控制系统的磁悬浮轴承实验平台中,在DOS操作系统下,实现了转子在空间五个自由度上的稳定的静态悬浮和在悬浮状态下的30000转/分钟的高速运转。本文针对该平台设计的H∞控制器的控制精度在静态悬浮时径向为±0.5μm,轴向为±3.6μm,高速运转时径向为±15μm,轴向为±3.6μm。实验结果直接证明了本文所设计的控制器在参数摄动和动态摄动范围内具有很好的鲁棒稳定性和鲁棒性能。
The primary focus of this dissertation is the practical application of robust H-infinity control theory on the Active Magnetic Bearings (AMB) experimental platform. Initially every segment of the AMB experimental platform including rotor dynamics, sensors, amplifiers and controller structure is analyzed, then an accurate five-axes AMB mathematical modeling is obtained as a result which would be great useful for centralized control. And a mathematical modeling for decentralized control is gained by imperative decoupling.
For the parameter uncertainties in AMB system, H-infinity controller of single axes is worked out by solving two-Riccati equations based on parameter uncertainty H-infinity control theory using system structure design method and decentralized control strategy. What’s more, in order to restrain the unmodelled dynamical uncertainties in AMB system, H-infinity controllers in thrust and radial axes are further designed base on H-infinity mixed-sensitivity control theory, during which terms of inner connections between weighting function and subsequent controller are put forward, and these rules contribute to an effective way on how to select weighting functions according to closed-loop performance. Then both of the methods are qualified by system simulation on MATLAB/SIMULINK, of which the stimulant levitation results prove that H-infinity controller performs well in signal track and noise rejection theoretically.
After bilinear transformation, H-infinity controllers are made up into C program in AMB experiment platform based on PC real-time control system. Finally, the laboratory rotor is suspended successfully both in static and high rotation speed state with its displacement error restrained within±0.5μm in radial,±3.6μm in thrust axes when static and±15μm in radial,±3.6μm in thrust axes when the rotation speed is 30000 r/min. This very experiment result indicates that the controllers designed have a good robust stability and robust performance upon system’s parameter uncertainties and dynamic uncertainties.
考虑到磁悬浮轴承系统中的参数不确定性,本文采用参数不确定H∞控制理论,利用结构化设计和分散控制策略,通过求解2-Riccati方程,设计了单自由度上的H∞控制器,并采用仿真实验,探讨了该控制器对参数摄动的抑制性能。针对磁悬浮轴承-转子结构中存在的未建模动态等不确定性,本文采用H∞混合灵敏度法设计了分散H∞控制器,设计过程中,提出了加权函数与控制器之间的部分内在联系。针对径向和轴向的H∞控制器,本文在Matlab/Simulink环境中还分别进行了磁悬浮轴承系统的仿真实验,从理论上验证了所求H∞控制器良好的信号跟踪和干扰抑制性能。
最后,通过对H∞控制器进行双线性变换,本文编写了C语言H∞控制程序,并将其应用到基于PC机实时控制系统的磁悬浮轴承实验平台中,在DOS操作系统下,实现了转子在空间五个自由度上的稳定的静态悬浮和在悬浮状态下的30000转/分钟的高速运转。本文针对该平台设计的H∞控制器的控制精度在静态悬浮时径向为±0.5μm,轴向为±3.6μm,高速运转时径向为±15μm,轴向为±3.6μm。实验结果直接证明了本文所设计的控制器在参数摄动和动态摄动范围内具有很好的鲁棒稳定性和鲁棒性能。
The primary focus of this dissertation is the practical application of robust H-infinity control theory on the Active Magnetic Bearings (AMB) experimental platform. Initially every segment of the AMB experimental platform including rotor dynamics, sensors, amplifiers and controller structure is analyzed, then an accurate five-axes AMB mathematical modeling is obtained as a result which would be great useful for centralized control. And a mathematical modeling for decentralized control is gained by imperative decoupling.
For the parameter uncertainties in AMB system, H-infinity controller of single axes is worked out by solving two-Riccati equations based on parameter uncertainty H-infinity control theory using system structure design method and decentralized control strategy. What’s more, in order to restrain the unmodelled dynamical uncertainties in AMB system, H-infinity controllers in thrust and radial axes are further designed base on H-infinity mixed-sensitivity control theory, during which terms of inner connections between weighting function and subsequent controller are put forward, and these rules contribute to an effective way on how to select weighting functions according to closed-loop performance. Then both of the methods are qualified by system simulation on MATLAB/SIMULINK, of which the stimulant levitation results prove that H-infinity controller performs well in signal track and noise rejection theoretically.
After bilinear transformation, H-infinity controllers are made up into C program in AMB experiment platform based on PC real-time control system. Finally, the laboratory rotor is suspended successfully both in static and high rotation speed state with its displacement error restrained within±0.5μm in radial,±3.6μm in thrust axes when static and±15μm in radial,±3.6μm in thrust axes when the rotation speed is 30000 r/min. This very experiment result indicates that the controllers designed have a good robust stability and robust performance upon system’s parameter uncertainties and dynamic uncertainties.
引文
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[2] 汪通悦,陈辽军,周峰,康志军,等,磁浮轴承的技术发展,现状趋势战略,2002,40卷(第 455 期):21~23。
[3] 虞烈,袁崇军 译,主动磁轴承,北京,新时代出版社,1997。
[4] Michael Scharfe, Karl Meizer, Ralf Zimmermann, Development of a Magnetic-Bearing Momentum Wheel for the AMSAT Phase 3-D Small Satellite。
[5] 古良东,磁悬浮轴承研究报告,阶段性总结,广州机床研究所,1989.11。
[6] 丛华,磁悬浮轴承电涡流传感器研究与设计,[博士学位论文],清华大学,1999。
[7] 杨作兴,赵雷,赵鸿宾,磁轴承 MPW 开关功率放大器的研究,电力电子技术,2000,5:23~25。
[8] 张德魁,赵雷,赵鸿滨,等,磁悬浮轴承内圆磨床电主轴及其控制,轴承,2000,11:11~13。
[9] 张德魁,赵雷,赵鸿宾,电流响应速度及力响应速度对磁轴承系统性能的影响,清华大学学报(自然科学版),2001,6:23~26。
[10] 赵艾萍,凌卫青,谢友柏,支承飞轮的推力磁轴承设计,航空学报,2001,04:355~358。
[11] 汪希平,张直明,于良,等,电磁轴承在透平膨胀机中的应用研究进展,中国机械工程,2000,4:379~381。
[12] 胡业发,郭顺生,盛步云,等,磁力轴承系统的虚拟设计,中国机械工程,2000,9:1033~1034。
[13] 陈钢,胡业发,磁力轴承高速磨削主轴结构设计,湖北工学院学报,1997,4:36~41。
[14] 李根博,黎文勇,张先彤,等,磁悬浮轴承控制系统调节器设计与仿真,机械工艺师,1996,1:9~11。
[15] 黄晓蔚,唐钟麟,电磁轴承系统实现自动平衡的一种新方法,机械工程学报,2001,7:96~99。
[16] 龙志强,王水泉,杨泉林,径向磁轴承电磁参数的计算,磁性材料及器件,2000,5:14~17。
[17] 曾励,朱熀秋，曾学明，等，基于 DSP 的混和磁悬浮轴承数字控制器的设计与实现,数据采集与处理,2000,2: 213~216。
[18] 曾励,朱熀秋，曾学明，等，单自由度混合磁悬浮轴承控制系统腜偷难芯浚暇┖娇?航天大学学报,1998,6: 685~690。
[19] An-Chen Lee et al.,Decentralized PID Control of Magnetic Bearings in a Rotor system,5th Int. Symp. on Magnetic Bearings,Kanazawa,Japan,1996,13~18。
[20] 汪希平,电磁轴承系统的参数设计与应用研究,[博士学位论文],西安交通大学,1994。
[21] S. M. Yang,G. J. Sheu,C. D. Yang,Vibration Control of Rotor Systems with Noncollocated Sensor/Actuator by Experimental Design,Trans. ASME,Journal of Vibration and Acoustics, 1997,420~427。
[22] 蔡中,有源磁悬浮轴承数字控制系统的研究与实现,[博士学位论文],清华大学 1991。
[23] P.Wurmsdobler,et al.,State Space Adaptive Control for a Rigid Rotor Suspended in Active Magnetic Bearings,5th Int. Symp. on Magnetic Bearings,Kanazawa, Japan,1996,185~190。
[24] Betschon F,et al.,On-Line-Adapted Vibration Control,6thInt.Symp.on Magnetic Bearings,Virginia,USA,1998,362~370。
[25] Chong-Won Lee,Young-Ho Ha,Frequency-Shaped Optimal Control of Unbalance Response in Active Magnetic Bearing System,5th Int. Symp. on Magnetic Bearings,Kanazawa,Japan,1996,165~170。
[26] Weirong Xiao,Bernd Weidemann,Fuzzy modelling and its application to magnetic bearing systems,Fuzzy sets and systems,73 1995,201~217。
[27] W.Cui and K.Nonami,H∞ Control of Flexible Rotor-Magnetic Bearing Systems,Proc.of the 3rd Int. Sym. On Magnetic Bearings,505~512,1992。
[28] F.Carrère,S.Font and G.Duc,H∞ Control Design of Flexible Rotor Magnetic Bearing System,4th Int. Symp. on Magnetic Bearings,August 1994,ETH Zurich,65~71。
[29] Hirata M et al.,Robust Control of a Magnetic Bearing System Using Constantly Scaled H∞ Control 6thInt.Symp.on Magnetic Bearings,Virginia,USA,1998,713~722。
[30] M.Fujita et. al.,μ Analysis and Synthesis of a Flexible Beam Magnetic Suspension Systems,Proc.of the 3rd Int. Sym. On Magnetic Bearings1992,495~504。
[31] Kenzo Nonami and Takayuki Ito,μ Synthesis of Flexible Rotor Magnetic Bearing Systems,4th Int. Symp.on Magnetic Bearings,August 1994,ETH Zurich,73~78。
[32] L.Scott Stephens and C R.Knospe,μ Synthesis Base,Robust Controller Design for AMB Machining Spindles,5th Int. Symp. on Magnetic Bearings,Kanazawa,Japan,1996,153~158
[33] 李永盼,磁悬浮轴承滑动模态控制的研究,[博士学位论文],清华大学,1994。
[34] Kenzo Nonami and Kenichi Nishina,Discrete Time Sliding Mode Control with Simple VSS Observer of Zero-Power Magnetic Bearing Systems,5th Int. Symp. on Magnetic Bearings,Kanazawa,Japan,1996,221~226。
[35] Jiang Y H,et al.,Neural Networks Control of Magnetic Bearings for Low Speed Rotor Systems,4th Int. Symp. on Magnetic Bearings,August 1994,ETH Zurich,197~202。
[36] Yoichi KANEMITSU,Masaru OHSAWA and Eishi MARUI,Comparison of Control Laws for Magnetic Levitation,4th Int. Symp. on Magnetic Bearings,August 1994,ETH Zurich,13~18。
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