二自由度陀螺的解耦控制
摘要
本文以直升机飞控系统中陀螺地平仪的主要部件——二自由度陀螺仪为例,从实际使用和反复检修后再重新使用的角度出发,将二自由度陀螺仪的耦合和由于部分不确定的干扰引起的陀螺漂移问题作为主要的研究问题。首先推导了理想状态和存在质量偏心状态下二自由度陀螺仪的动力学方程;其次,对于陀螺的几何耦合问题提出了交叉耦合控制(CCC)的解耦控制方法。最后,针对二自由度陀螺仪动力学方程的耦合问题,应用前馈控制的原理,并将非线性微分跟踪器(TD)和交叉耦合控制结合对其进行控制,达到对其几何耦合和动力耦合进行解耦的目的。然而,理论分析和实际之间存在一定的差别,本文在分析基于TD的交叉耦合控制器对陀螺控制精度低的原因的基础上,增加扩张状态观测器(ESO)对不确定的扰动进行估计,得出了基于自抗扰控制(ADRC)的解耦器。与传统PID控制结合交叉耦合控制组成的基于PID解耦器的仿真结果进行比较,基于自抗扰控制(ADRC)的解耦器对二自由陀螺仪的控制精度大大提高,使运载体和相关系统的高精度和稳定性得以保证。
Two-degrees-of-freedom gyroscope, which is the main component of gyroscope horizon indicator in flight control system of helicopter, is considered as the controlled plant in this paper. In order to meet the requirement of both actual usage and afresh usage via repetitious examination and repair, this paper focuses on the drift problem of gyroscope that due to some uncertain factors and the coupling problem of two-degrees-of-freedom gyroscope. Firstly, dynamic formulas of gyroscope under the ideal condition and the actual condition are derived. Sencondly, the Cross-Coupling Control (CCC) is put forward to solve the geometric coupling problem of two-degrees-of-freedom gyroscope. Finally, aiming at the dynamic coupling of two-degrees-of-freedom gyroscope, the theory of the forward feedback is applied. Meanwhile, Tracking Diffrentia (TD) is added to decouple the dynamics coupling and the geometric coupling of two-degrees-of-freedom gyroscope. However, there is some difference in result between theory and practice. The reason that the control accuracy can not reach request is given in this paper. The Active Disturbance Rejection Control (ADRC) technique is proposed by increasing the Extension-State-Observe (ESO). Comparing with the tradition PID, the ADRC based on CCC consumedly improves the control accuracy of two-degrees-of-freedom gyroscope. It assures the stability and high accuracy of its carrier and related system.
Two-degrees-of-freedom gyroscope, which is the main component of gyroscope horizon indicator in flight control system of helicopter, is considered as the controlled plant in this paper. In order to meet the requirement of both actual usage and afresh usage via repetitious examination and repair, this paper focuses on the drift problem of gyroscope that due to some uncertain factors and the coupling problem of two-degrees-of-freedom gyroscope. Firstly, dynamic formulas of gyroscope under the ideal condition and the actual condition are derived. Sencondly, the Cross-Coupling Control (CCC) is put forward to solve the geometric coupling problem of two-degrees-of-freedom gyroscope. Finally, aiming at the dynamic coupling of two-degrees-of-freedom gyroscope, the theory of the forward feedback is applied. Meanwhile, Tracking Diffrentia (TD) is added to decouple the dynamics coupling and the geometric coupling of two-degrees-of-freedom gyroscope. However, there is some difference in result between theory and practice. The reason that the control accuracy can not reach request is given in this paper. The Active Disturbance Rejection Control (ADRC) technique is proposed by increasing the Extension-State-Observe (ESO). Comparing with the tradition PID, the ADRC based on CCC consumedly improves the control accuracy of two-degrees-of-freedom gyroscope. It assures the stability and high accuracy of its carrier and related system.
引文
[1]郭索云.陀螺仪原理及应用.哈尔滨:哈尔滨工业大学出版社,1985,10.
[2]王承瑶.陀螺稳定系统.北京:国防工业出版社,1985,6.
[3]王利强,宋菲君,等.陀螺的分类,原理及应用现状.电子测量与仪器学报,2004年增:857-863.
[4]沈廷祥.惯性陀螺仪设计特点及其关键技术.中国兵工学会火箭导弹学会交流,1995,4:317-320.
[5]王洪兰.陀螺仪在工程测量中的应用.北京:国防工业出版社,1995.
[6]曹锦业.某型直升机自动驾驶仪控制律设计及实现.硕士论文.西北工业大学,2005.3.
[7]徐丽娜,邓正隆.神经网络用于陀螺仪启动漂移误差补偿的研究.Proceedings of the 3rd World Congress on Intelligent Control and Automation,June 28-July 2,2000, Hefei,P.R.China:1156-1158.
[8] Herbert T. Califano.Minitact Gyroscope—The Low Cost Alternative. IEEE AES Systems Magazine, 1994,8: 12-16.
[9] Jong-Woo Kim, Roberto Cristi , Brij N. Agrawal. Attitude Determinate for NPS Three-Axis Spacecraft Simulator. Astrodynamics Specialist Conference and Exhibit, 2004,8:5386-5397.
[10] Oh H.-S, Vadali S.-R. Feedback Control and Steering Laws for Spacecraft Using Single Gimbal Control Moment Gyros. Journal of the Astronautical Sciences, vol. 39, no. 2, 1991: 183-203.
[11] Warren K. Soh, Norhizam Hamzah. Attitude Determination and Control Subsystem Hardware in the Loop Test on Air Bearing Trolley. Guidance, Navigation, and Control Conference and Exhibit, 2006,8,21-14:1-11.
[12] Billur Barshan, Hugh F. Durrant-Whyte. Evaluation of a Solid-state Gyroscope for Robotics Applications. IEEE Transaction on Instrumentation and Measurement, 1991,1(44):61 -67.
[13]冯璐,周建国.用于刚体姿态控制的一种非线性反馈控制器.中国控制会议论文集,1998,9,16-22:249-253.
[14]高坚,佟明安.刚体转动渐进跟踪控制的逆系统方法.电子科技大学学报,2002,4,2(31):141-144.
[15]张锦江,李季苏等.用单框架控制力矩陀螺的大型航天器姿态控制系统实物仿真研究. 2005全国仿真技术学术会议论文集, 2005,4: 198-203.
[16] Tiejun Qu, Xudong Yang, Ziyun Tian.A Self-compensation Algorithm for Drift of Platform Inertial Navigation System. IEEE Xplore. Restrictions apply, 2008,8: 101-104.
[17] Jingyang Zhou,di Zhou.Spacecraft Attitude Control with Double- Gimbaled Control Moment Gyroscopes. Proceedings of the 2007 IEEE International Conference on Robotics and Biomimetics, 2007,11,15-18: 1557-1563.
[18]和兴锁.理论力学.西安:西北工业大学出版社,2005,6.
[19]肖亚伦.飞行器运动方程.北京:航空工业出版社,1987,12.
[20]彭建华,刘延柱.带偏心转子陀螺体的混沌运动.力学季刊,2000,21(2):162 -167.
[21]胡刚,刘永清,李远清.不确定性控制系统的成因、分类与控制策略.工业工程,2001,3,4(1):49-53.
[22]谢蓉.鲁棒控制在某型直升机飞控系统设计中的应用.硕士论文.西北工业大学,2007.3.
[23]陶利明.转子高精度动平衡测试与自动平衡技术研究.博士论文.国防科技大学,2006.6.
[24]白方周,庞国仲等.多变量频域理论与设计技术.北京:中国科学技术大学国防工业出版社,1988,2.
[25]杨亚辉,苏玉鑫等.机器人系统同步协调自适应控制.系统仿真学报, 2008,20(1):117-120.
[26] Y. Xiao, K. Y. Zhu. A Cross-coupling Refenence Model Control Algorithm. International Journal of Adaptive Control and Signal Processing, 2005 (19): 623-638.
[27] Syh-Shiuh Yeh, Pau-Lo Hsu. Estimation of the Contouring Error Vector for the Cross-Coupled Control Design. IEEE/ASME Transaction on Mechatronics, 2002, 7 (1): 44-51.
[28]Ρ.Η.萨维特.陀螺仪理论和设计.北京:科学出版社,1977,2.
[29]张平等.MATLAB基础与应用.北京:北京航空航天大学出版社,2007,11.
[30] Han,J. Q.,N onlinear Design Methods for Control System,The Proc.of the 14th IFAC World Congress, 1999.
[31]韩京清.控制理论一模型论还是控制论.系统科学与数学,1989, 9(4):328-335.
[32]韩京清.非线性控制系统中状态反馈的实现.控制与决策,1991, 6(3):161一167.
[33]韩京清.一类不确定系统的控制与滤波.系统仿真学报,1992增刊:1-7.
[34]韩京清,王伟.非线性跟踪微分器.系统科学与数学,1994,14(2): 177-183.
[35]韩京清.一类不确定对象的扩张状态观测器.控制与决策,1995, 10(1):85-88.
[36]韩京清.非线性状态误差反馈控制律一NLSEF.控制与决策,1995, 10(3):221-225.
[37]韩京清.自抗扰控制器及其应用.控制与决策,1998,13(1): 283-287.
[38]韩京清,王伟.非线性跟踪微分器.系统科学与数学,1994,14(2): 177-183.
[39]张文革,韩京清.跟踪微分器用于零点配置.自动化学报,2001,9(27): 724-727.
[40]刘金琨.先进PID控制及其MATLAB仿真.北京:电子工业出版社,2003,1.
[41]陶永华.新型PID控制及其应用.北京:机械工业出版社,1998,11.
[42]韩京清.自抗扰控制技术.前沿科学, 2007,1(1):24-32.
[2]王承瑶.陀螺稳定系统.北京:国防工业出版社,1985,6.
[3]王利强,宋菲君,等.陀螺的分类,原理及应用现状.电子测量与仪器学报,2004年增:857-863.
[4]沈廷祥.惯性陀螺仪设计特点及其关键技术.中国兵工学会火箭导弹学会交流,1995,4:317-320.
[5]王洪兰.陀螺仪在工程测量中的应用.北京:国防工业出版社,1995.
[6]曹锦业.某型直升机自动驾驶仪控制律设计及实现.硕士论文.西北工业大学,2005.3.
[7]徐丽娜,邓正隆.神经网络用于陀螺仪启动漂移误差补偿的研究.Proceedings of the 3rd World Congress on Intelligent Control and Automation,June 28-July 2,2000, Hefei,P.R.China:1156-1158.
[8] Herbert T. Califano.Minitact Gyroscope—The Low Cost Alternative. IEEE AES Systems Magazine, 1994,8: 12-16.
[9] Jong-Woo Kim, Roberto Cristi , Brij N. Agrawal. Attitude Determinate for NPS Three-Axis Spacecraft Simulator. Astrodynamics Specialist Conference and Exhibit, 2004,8:5386-5397.
[10] Oh H.-S, Vadali S.-R. Feedback Control and Steering Laws for Spacecraft Using Single Gimbal Control Moment Gyros. Journal of the Astronautical Sciences, vol. 39, no. 2, 1991: 183-203.
[11] Warren K. Soh, Norhizam Hamzah. Attitude Determination and Control Subsystem Hardware in the Loop Test on Air Bearing Trolley. Guidance, Navigation, and Control Conference and Exhibit, 2006,8,21-14:1-11.
[12] Billur Barshan, Hugh F. Durrant-Whyte. Evaluation of a Solid-state Gyroscope for Robotics Applications. IEEE Transaction on Instrumentation and Measurement, 1991,1(44):61 -67.
[13]冯璐,周建国.用于刚体姿态控制的一种非线性反馈控制器.中国控制会议论文集,1998,9,16-22:249-253.
[14]高坚,佟明安.刚体转动渐进跟踪控制的逆系统方法.电子科技大学学报,2002,4,2(31):141-144.
[15]张锦江,李季苏等.用单框架控制力矩陀螺的大型航天器姿态控制系统实物仿真研究. 2005全国仿真技术学术会议论文集, 2005,4: 198-203.
[16] Tiejun Qu, Xudong Yang, Ziyun Tian.A Self-compensation Algorithm for Drift of Platform Inertial Navigation System. IEEE Xplore. Restrictions apply, 2008,8: 101-104.
[17] Jingyang Zhou,di Zhou.Spacecraft Attitude Control with Double- Gimbaled Control Moment Gyroscopes. Proceedings of the 2007 IEEE International Conference on Robotics and Biomimetics, 2007,11,15-18: 1557-1563.
[18]和兴锁.理论力学.西安:西北工业大学出版社,2005,6.
[19]肖亚伦.飞行器运动方程.北京:航空工业出版社,1987,12.
[20]彭建华,刘延柱.带偏心转子陀螺体的混沌运动.力学季刊,2000,21(2):162 -167.
[21]胡刚,刘永清,李远清.不确定性控制系统的成因、分类与控制策略.工业工程,2001,3,4(1):49-53.
[22]谢蓉.鲁棒控制在某型直升机飞控系统设计中的应用.硕士论文.西北工业大学,2007.3.
[23]陶利明.转子高精度动平衡测试与自动平衡技术研究.博士论文.国防科技大学,2006.6.
[24]白方周,庞国仲等.多变量频域理论与设计技术.北京:中国科学技术大学国防工业出版社,1988,2.
[25]杨亚辉,苏玉鑫等.机器人系统同步协调自适应控制.系统仿真学报, 2008,20(1):117-120.
[26] Y. Xiao, K. Y. Zhu. A Cross-coupling Refenence Model Control Algorithm. International Journal of Adaptive Control and Signal Processing, 2005 (19): 623-638.
[27] Syh-Shiuh Yeh, Pau-Lo Hsu. Estimation of the Contouring Error Vector for the Cross-Coupled Control Design. IEEE/ASME Transaction on Mechatronics, 2002, 7 (1): 44-51.
[28]Ρ.Η.萨维特.陀螺仪理论和设计.北京:科学出版社,1977,2.
[29]张平等.MATLAB基础与应用.北京:北京航空航天大学出版社,2007,11.
[30] Han,J. Q.,N onlinear Design Methods for Control System,The Proc.of the 14th IFAC World Congress, 1999.
[31]韩京清.控制理论一模型论还是控制论.系统科学与数学,1989, 9(4):328-335.
[32]韩京清.非线性控制系统中状态反馈的实现.控制与决策,1991, 6(3):161一167.
[33]韩京清.一类不确定系统的控制与滤波.系统仿真学报,1992增刊:1-7.
[34]韩京清,王伟.非线性跟踪微分器.系统科学与数学,1994,14(2): 177-183.
[35]韩京清.一类不确定对象的扩张状态观测器.控制与决策,1995, 10(1):85-88.
[36]韩京清.非线性状态误差反馈控制律一NLSEF.控制与决策,1995, 10(3):221-225.
[37]韩京清.自抗扰控制器及其应用.控制与决策,1998,13(1): 283-287.
[38]韩京清,王伟.非线性跟踪微分器.系统科学与数学,1994,14(2): 177-183.
[39]张文革,韩京清.跟踪微分器用于零点配置.自动化学报,2001,9(27): 724-727.
[40]刘金琨.先进PID控制及其MATLAB仿真.北京:电子工业出版社,2003,1.
[41]陶永华.新型PID控制及其应用.北京:机械工业出版社,1998,11.
[42]韩京清.自抗扰控制技术.前沿科学, 2007,1(1):24-32.