高精度转台速率平稳性问题研究
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摘要
高精度测试转台是惯导系统和惯性仪表测试和标定的主要设备,其性能的优劣直接关联到惯导系统和惯性仪表的精度和可靠性。转台的速率特性(包括速率精度和速率平稳性)是衡量转台性能的重要指标,然而其速率平稳性的提高受到电磁力矩波动、摩擦、中断信号等因素的影响。因此,从控制的角度出发,克服这些因素的影响从而达到提高转台性能的目的具有很重要的理论意义和工程价值。
本文首先介绍了国内外转台发展现状,着重分析了关于影响转台速率平稳性两个主要因素,即电磁力矩波动和摩擦,并研究了关于电磁力矩波动抑制和摩擦补偿的许多方法。
针对电磁力矩波动,深入分析了其成因及对转台速率平稳性的影响。基于内模原理能有效抑制周期性扰动的特点,采用了改进型离散重复控制的抑制方法,与转台PID控制组成复合控制。结合控制系统极点分布理论,给出了重复控制增益最优值选取方法,提升系统性能。
针对摩擦扰动,在深入分析其机理的基础上,基于库伦和LuGre两种摩擦模型,分别采用了模型参考自适应和自校正两种摩擦补偿方案。加入摩擦补偿的转台控制系统能在线辨识摩擦模型参数来进行实时补偿,并由李雅普诺夫稳定性理论证明了系统的稳定性。
由转台控制系统的实时性要求可知,RTX中断的精确程度会对转台的速率特性产生影响。首先从中断信号的偏差和波动两个角度展开研究,在理论上推导论证了中断信号的偏差和波动对转台速率性能的影响程度,并通过实际系统的数据进行了定量分析。
最后以实验室现有转台为研究对象,从工程角度出发,针对电磁力矩波动和摩擦扰动这两个因素,分别采用了巴特沃斯数字陷波滤波器和高频震颤的设计方案来提高转台的性能,并基于Windows+RTX平台来完成控制软件的实现和实验。
High precision testing tables are the main testing and calibration equipments for inertial navigation systems and the instruments, and the quality performance of the high precision turn tables can directly have influence on the reliability and confidence level of the test experiments. The rate smoothness is an important performance index for turntables, which need run precisely and smoothly to satisfy the test experiments. However, the rate performances are influenced by the electromagnetic torque fluctuation and friction, so it has important theoretical and practical value to overcome the impact of these factors by control methods.
Firstly, the present domestic and overseas development situation of turntables is introduced. The electromagnetic torque fluctuation and friction, which are the main two factors that influence the rate smoothness are analyzed, and the compensation methods are studied sequentially
The mechanism and the influence on tables of the electromagnetic torque fluctuations are analyzed deeply. A method of modified PTRC eliminating torque fluctuation is proposed which is composed with the traditional PID controllers based on the characteristic of the internal model principle that can effectively restrain the periodical disturbance. The method of optimal seletion of the repetitive control gain is proposed to improve the performance according to the pole distribution principle of control systems.
According to the friction disturbance, the mechanism is analyzed. According to the Coulomb model and the LuGre model, two adaptive compensation control methods which called Model reference adaptive and self correction are proposed, that can identify the friction model parameters on-line and make a real-time compensation. Finally, the stability of the control method is proved by Lyapunov theory.
According to the requirement for real time, it is known that the precision degree of RTX interruption is connected to rate characteristics of turntable. Firstly, demonstrating the point in theory that either the deviation or fluctuation would influence the rate characteristics of turntable. And then the level of influence by the deviation and fluctuation is analysed through the data of actual system.
Based on researching of turntable which the laboratory has, Butterworth digital trapped filter and dither are porposed from the aspect of engineering. At last, the realization and experiment of control software based on the Windows+RTX is completed.
本文首先介绍了国内外转台发展现状,着重分析了关于影响转台速率平稳性两个主要因素,即电磁力矩波动和摩擦,并研究了关于电磁力矩波动抑制和摩擦补偿的许多方法。
针对电磁力矩波动,深入分析了其成因及对转台速率平稳性的影响。基于内模原理能有效抑制周期性扰动的特点,采用了改进型离散重复控制的抑制方法,与转台PID控制组成复合控制。结合控制系统极点分布理论,给出了重复控制增益最优值选取方法,提升系统性能。
针对摩擦扰动,在深入分析其机理的基础上,基于库伦和LuGre两种摩擦模型,分别采用了模型参考自适应和自校正两种摩擦补偿方案。加入摩擦补偿的转台控制系统能在线辨识摩擦模型参数来进行实时补偿,并由李雅普诺夫稳定性理论证明了系统的稳定性。
由转台控制系统的实时性要求可知,RTX中断的精确程度会对转台的速率特性产生影响。首先从中断信号的偏差和波动两个角度展开研究,在理论上推导论证了中断信号的偏差和波动对转台速率性能的影响程度,并通过实际系统的数据进行了定量分析。
最后以实验室现有转台为研究对象,从工程角度出发,针对电磁力矩波动和摩擦扰动这两个因素,分别采用了巴特沃斯数字陷波滤波器和高频震颤的设计方案来提高转台的性能,并基于Windows+RTX平台来完成控制软件的实现和实验。
High precision testing tables are the main testing and calibration equipments for inertial navigation systems and the instruments, and the quality performance of the high precision turn tables can directly have influence on the reliability and confidence level of the test experiments. The rate smoothness is an important performance index for turntables, which need run precisely and smoothly to satisfy the test experiments. However, the rate performances are influenced by the electromagnetic torque fluctuation and friction, so it has important theoretical and practical value to overcome the impact of these factors by control methods.
Firstly, the present domestic and overseas development situation of turntables is introduced. The electromagnetic torque fluctuation and friction, which are the main two factors that influence the rate smoothness are analyzed, and the compensation methods are studied sequentially
The mechanism and the influence on tables of the electromagnetic torque fluctuations are analyzed deeply. A method of modified PTRC eliminating torque fluctuation is proposed which is composed with the traditional PID controllers based on the characteristic of the internal model principle that can effectively restrain the periodical disturbance. The method of optimal seletion of the repetitive control gain is proposed to improve the performance according to the pole distribution principle of control systems.
According to the friction disturbance, the mechanism is analyzed. According to the Coulomb model and the LuGre model, two adaptive compensation control methods which called Model reference adaptive and self correction are proposed, that can identify the friction model parameters on-line and make a real-time compensation. Finally, the stability of the control method is proved by Lyapunov theory.
According to the requirement for real time, it is known that the precision degree of RTX interruption is connected to rate characteristics of turntable. Firstly, demonstrating the point in theory that either the deviation or fluctuation would influence the rate characteristics of turntable. And then the level of influence by the deviation and fluctuation is analysed through the data of actual system.
Based on researching of turntable which the laboratory has, Butterworth digital trapped filter and dither are porposed from the aspect of engineering. At last, the realization and experiment of control software based on the Windows+RTX is completed.
引文
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[2]姜复兴,庞志成.惯导测试设备原理与设计[M].哈尔滨：哈尔滨工业大学出版社,1998：3-5
[3]曾庆双,秦嘉川.转台伺服系统低速性能分析[J].中国惯性技术学报,2001,9(2)：65-69
[4]Louis A, Demore. Design Study for a High Aeeuraey Three-Axis Test[C]//AIAA Guidance and Control Conference,1985
[5]王常虹,曾庆双,任顺清.惯导测试设备的最新进展[C]//惯性技术发展动态发展方向研讨会文集,2003:112-116
[6]徐国柱,刘樾,张元生.转台速率波动原因及其对转台速率性能影响的分析[C]//2003年中国惯性技术学会测试专业委员会第八次学术交流会论文集,2003：67-76
[7]曾庆双,孙群学,张廷录.电机齿槽力矩对转台速率平稳性的影响分析[J].黑龙江自动化技术与应用,1995(4)：59-62
[8]汤蕴璆.电机内的电磁场[M].北京：科学出版社,1998:348-352
[9]R.P.Deodhar, D.A.Staton, T.J.E.Miller. Modelling of skew using the flux-MMF diagram[J]. IEEE Transactions on Industry Applications,1996,32(6):1339-1347
[10]Z.Q.Zhu, D.Howe. Analytical prediction of the cogging torque in radial-field permanent magnet brushless motors[J]. IEEE Transactions on Magnetics,1992, 28(2):1371-1374
[11]T.Li, G.Slemon. Reduction of cogging torque in permanent magnet motors[J]. IEEE Transactions on Magnetics,1988,24(6):2901-2903
[12]T.Ishikawa, G.R.Slemon. A method of reducing ripple torque in permanent magnet motors without skewing[J]. IEEE Transactions on Magnetics,1993, 29(2):2028-2031
[13]K.C.Seop, Y.H.Soo, N.K.Woong, edc. Magnetic pole shape optimization of permanent motor for reduction of cogging torque[J]. IEEE Transactions of Magnetics,1997,33(2):1822-1827
[14]K.K.Tan, S.Zhao. Adaptive force ripple suppression in iron-core permanent magnet linear motors[J]. IEEE International Symposium on Intelligent Control, 2002:266-269
[15]Y.Liu, D.Q.Chen. Adaptive rejection of velocity-ripple from position transducer in a motion control system[C]//Proceedings of the IEEE Conference on Decision and Control,1994:690-695
[16]N.Bodika, R.J.Cruise, C.F.Landy. Design of a PI controller to counteract the effect of cogging forces in a permanent magnet synchronous linear motor[C]//IEEE AFRICON Conference,1999:893-896
[17]L.Bascetta, GMagnani, P.Rocco. Force ripple compensation in linear motors with application to a parallel kinematic machine[C]//IEEE/ASME International Conference on Advanced Intelligent Mechatronics,2007
[18]C.C.Tsai, S.C.Lin, T.S.Cheng. Adaptive integral position control using RBF neural networks for brushless DC linear motor drive[C]//Proceeding of the IEEE International Conference on Control Applications,2006:3188-3193
[19]J.Kabzinski. Fuzzy modeling of disturbance torques/forces in rotational/linear interior permanent magnet synchronous motors[C]//2005 European Conference on Power Electronics and Applications,2005
[20]K.M.Tao, R.L.Kosut, G.Aral. Learning feedforward control[C]//Proceedings of the American Control Conference,1994,3:2575-2579
[21]A.P.Hu, A.Register, N.Sadegh. Using a learning controller to achieve accurate linear motor motion control[C]//Proceeding of the 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics,1999:611-616
[22]B.A.Francis, W.M.Wonham. The internal model principle of control theory[J]. Automatica,1976,12(5):457-465
[23]王旭永.三轴台外框电液位置伺服系统低速运动的研究[D].哈尔滨：哈尔滨工业大学博士学位论文,1993：6-10
[24]PE.Dupont, E.P.Dunlap. Friction modeling and PD compensation at very low velocities[J]. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME,1995,117(1):8-14
[25]E.D.Tung, Y.Urushisaki, M.Tomizuka. Low velocity friction compensation formachine tool feed drives[C]//American Control Conference,1993:1932-1936
[26]B.H.Armstrong, P.Dupont, C.D.W.Canudas. Survey of models, analysis tools and compensation methods for the control of machines with friction[J]. Automatica, 1994,30(7):1083-1138
[27]黄进.含摩擦环节伺服系统的分析及控制补偿研究[D].西安：西安电子科技大学博士论文,1998：6-8
[28]C.L.Tsai, T.C.Lee, S.K.Lin. Friction compensation of a mini voice coil motor by sliding mode control[J]. IEEE International Symposium on Industrial Electronics, 2009:609-614
[29]T.L.Liao, T.I.Chi en. Exponentially stable adaptive friction compensator[J]. IEEE Transactions on Automatic Control,2000,45(5):977-980
[30]L.Marton, B.Lantos. Modeling,identification,and compensation of stick-slip friction[J]. IEEE Transactions on Industrial Electronics,2007,54(1):511-521
[31]X.Z.Kong, Y.Wang, S.Y.Jiang. Friction chatter-compensation based on stribeck model [J]. Journal of Mechanical Engineering,2010,46(5):68-73
[32]R.Kelly, V.Santibanez, E.Gonazalez. Adaptive friction compensation in mechanisms using the Dahl model[J]. Proceedings of the Institution of Mechanical Engineers,2004,218(1):53-57
[33]J.Moreno, R.Kelly, R.Campa. ON velocity control using friction compensation[C]//Proceedings of the IEEE Conference on Decision and Control, 2002,1:95-100
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