基于奇异摄动的三轴稳定挠性卫星姿态控制系统研究
|
摘要
随着空间任务需求的不断增长,越来越多的卫星采用大尺寸挠性附件,并且要求高精度姿态控制。然而,挠性卫星的刚体运动与挠性附件的振动存在耦合,影响卫星本体运动。本文以“空间智能控制技术国家重点实验室项目”为依托,对带挠性帆板的三轴稳定卫星进行了姿态控制和帆板抑振研究。
本文首先对某型号三轴稳定挠性卫星的模型进行分析,表明了挠性帆板对卫星的姿态控制影响较大,进行帆板抑振的必要性。其次针对挠性卫星高阶、非线性、非定常的特性,将其当作一个含小摄动参数的多时标系统,应用奇异摄动理论,对挠性卫星数学模型进行降阶分解,得到了代表挠性卫星刚性本体运动的慢变子系统和描述挠性帆板振动的快变子系统。
利用奇异摄动模型,根据快慢子系统不同特性和控制要求,设计了基于PID和线性二次最优(LQR)的复合控制器,以及基于滑模变结构和LQR的复合控制器。仿真结果表明,两种复合控制器都能够在较好地进行姿态控制的同时,抑制了帆板的弹性振动,但在PID-LQR复合控制下系统的姿态角具有一定的超调量,利用滑模变结构控制对这一点进行了改进,兼顾了系统的快速性和稳定性,具有较强的鲁棒性,表明了奇异摄动理论应用于三轴稳定挠性卫星姿态控制的可行性。
With the development of aerospace mission, more and more satellite adopts large scale flexible structure. However, rigid body motion of flexible spacecraft in orbit is strongly coupled with elastic vibration of flexible body. The dissertation, supported by a grant from National laboratory of space intelligent control, studies the design and realization of attitude control and vibration suppression for the three-axe stabilized satellite with flexible solar-array appendages.
By model analyzing of a specific satellite with flexible solar-array appendages, it proved the importance of vibration suppression in attitude control of flexible satellite. Then, taking the flexible satellite as a singular perturbation system, a singular perturbation model is developed to reduce the order of dynamics model. The slow subsystem represents the rigid body motion while the fast subsystem describes the elastic vibrations.
Based on the singular perturbation model, two composite controllers are adopted:one is PID and LQR composite controller and the other is SMC and LQR composite controller. The simulation results show that both of the two methods can approve the attitude control precise requirement and suppress the vibration of flexible solar-array appendages efficiently. However, there is small overshoot exists under the control of PID and LQR composite controller. The composite SMC and LQR controller improves it and has good robustness. The feasibility of singular perturbation method used in three-axe stabilized satellite attitude control is proved.
本文首先对某型号三轴稳定挠性卫星的模型进行分析,表明了挠性帆板对卫星的姿态控制影响较大,进行帆板抑振的必要性。其次针对挠性卫星高阶、非线性、非定常的特性,将其当作一个含小摄动参数的多时标系统,应用奇异摄动理论,对挠性卫星数学模型进行降阶分解,得到了代表挠性卫星刚性本体运动的慢变子系统和描述挠性帆板振动的快变子系统。
利用奇异摄动模型,根据快慢子系统不同特性和控制要求,设计了基于PID和线性二次最优(LQR)的复合控制器,以及基于滑模变结构和LQR的复合控制器。仿真结果表明,两种复合控制器都能够在较好地进行姿态控制的同时,抑制了帆板的弹性振动,但在PID-LQR复合控制下系统的姿态角具有一定的超调量,利用滑模变结构控制对这一点进行了改进,兼顾了系统的快速性和稳定性,具有较强的鲁棒性,表明了奇异摄动理论应用于三轴稳定挠性卫星姿态控制的可行性。
With the development of aerospace mission, more and more satellite adopts large scale flexible structure. However, rigid body motion of flexible spacecraft in orbit is strongly coupled with elastic vibration of flexible body. The dissertation, supported by a grant from National laboratory of space intelligent control, studies the design and realization of attitude control and vibration suppression for the three-axe stabilized satellite with flexible solar-array appendages.
By model analyzing of a specific satellite with flexible solar-array appendages, it proved the importance of vibration suppression in attitude control of flexible satellite. Then, taking the flexible satellite as a singular perturbation system, a singular perturbation model is developed to reduce the order of dynamics model. The slow subsystem represents the rigid body motion while the fast subsystem describes the elastic vibrations.
Based on the singular perturbation model, two composite controllers are adopted:one is PID and LQR composite controller and the other is SMC and LQR composite controller. The simulation results show that both of the two methods can approve the attitude control precise requirement and suppress the vibration of flexible solar-array appendages efficiently. However, there is small overshoot exists under the control of PID and LQR composite controller. The composite SMC and LQR controller improves it and has good robustness. The feasibility of singular perturbation method used in three-axe stabilized satellite attitude control is proved.
引文
[1]W.C.Schneider, A. A. Garman. Tracking and data relay satellite system:NASA's new space craft data acquisition system, Acta Astronautica,1981,8:179-194.
[2]P.S. Aubert, et al. Centralized vs Decentralized Options for a European Data Relay Satellite System, Acta Astronautica,1986,13:387-401.
[3]H. Dodel, et al. Antenna System Alternatives for Data Relay Satellites with Multiple Steer able Beams, Acta Astronautica,1988,17:553-560.
[4]魏晨曦.跟踪与数据中继卫星系统的发展[J].中国航天,2001,11：14-18.
[5]中国新闻网.中国风云3号卫星将于5月择机发射[EB／OL].http://news.21 cn.com/domestic/yaowen/2008/01/24/4277461.shtml,2008.
[6]王祥,王存恩.日本“准天顶卫星”系统及其应用计划[J].国际太空,2010,3：7-12.
[7]钱勇.高精度三轴稳定卫星姿态确定和控制系统研究[D].西北工业大学,2002.
[8]李果,刘良栋.航天控制器若干技术问题的新进展[J].空间控制技术与应用,2008,2(34)： 14-19.
[9]A. Grewal, V. J. Modi. Multibody Dynamic and Robust Control of Flexible Spacecraft, IEEE Trans. Aerospace and Electronic System,2000,36 (2):491-499.
[10]曲广吉.航天器动力学工程[M].北京：中国科学技术出版社,2000.
[11]屠善澄,陈义庆等.卫星姿态动力学与控制[M].北京：中国宇航出版社,2005.
[12]张育林,吴建军.航天器[M].北京：国防工业出版社,2006.
[13]Toshiaki Yamashita, Naoto Ogurb. Improved satellite attitude control using a disturbance compensator[J]. Acta Astronautica,2004,55:15-25.
[14]耿云海,崔祜涛,孙兆伟,杨涤.小卫星主动磁控制地球捕获姿态控制系统设计[J].航空学报,2000,21(2)：142-145.
[15]刘新建,雷勇军,唐乾刚.大挠性太阳能帆板航天器的姿态控制[J].国防科技大学学报,2003,25(5)：6-8.
[16]Jianhua Zheng, Stephen P. Banks, Hugo Alleyne. Optimal attitude control for three-axis stabilized flexible spacecraft[J]. Acta Astronautica,2005,56:519-528.
[17]Joseph, M.Fulton. LQG/LTR optimal attitude control of small flexible spacecraft using free-free boundary conditions[D]. Colorado:University of Colorado,2006.
[18]韩曾晋.自适应控制[M].北京：清华大学出版社,1995.
[19]吴宏鑫.自适应控制技术的应用和发展[J].控制理论与应用,1992,9(2)：105-114.
[20]张国琪,丁建钊.柔性航天器姿态快速机动的自适应控制方法[J].空间控制技术与 应用,2008,34(4)：23-27.
[21]Bong-Jun Yang, Anthony J.Calise, James I. Craig. Adaptive control of Truss Structures for Gossamer Spacecraft[R]. AIAA NSFC-042,2007.
[22]褚健,俞立,苏宏业.鲁棒控制理论及应用[M].杭州：浙江大学出版社,2000.
[23]C Scherer, P Gahnite, M Chilali. Multi-objective Output-feedback Control via LMI Optimization[J]. IEEE Trans. on Autom. Contr,1997,42 (7):896-911.
[24]宋斌,马广富,李传江,谌颖.基于H∞鲁棒控制的挠性卫星姿态控制[J].系统仿真学报,2005,17(4)：968-970.
[25]兰维瑶,陈亚陵.新型卫星姿态运动的鲁棒控制器设计[J].厦门大学学报,1999,38(2)： 193-198.
[26]王广雄,张静,朱井泉.挠性系统的鲁棒控制设计[J].控制与决策,2003,18(3)：281-284.
[27]孙增圻.智能控制理论与技术[M].清华大学出版社,1997.
[28]S Thongchet, S Kuntanapreeda. A fuzzy neural bang-bang controller for satellite attitude control[C]. Proceedings of SPIE-The International Society for Optical Engineering, 2001,4390:97-104.
[29]刘军,韩潮.基于单神经元的卫星姿态自适应PID控制[J].计算机仿真,2006,23(3)：45-48.
[30]张云,王培垣.一种用于挠性卫星姿态控制的改进模糊控制器[J].上海航天,2004,6(6)：42-46.
[31]孙庆,吴宏鑫.挠性结构卫星单轴气浮台的模糊控制[J].航天控制,1997,2：29-36.
[32]高为炳.变结构控制理论基础[M].北京：中国科学技术出版社,1990.
[33]姜野.挠性卫星姿态机动的时变滑模变结构主动振动控制研究[D].哈尔滨工业大学,2007.
[34]周军,李季苏,牟小刚.挠性卫星振动抑振的变结构主动控制方案及实验研究[J].航天控制,1996,4：1-6.
[35]李勇,吴宏鑫.一类挠性航天器的变结构控制[J].宇航学报,1998,19(1)：13-20.
[36]王庆超,岑小锋,马兴瑞.挠性航天器旋转机动的输入成形变结构控制[J].系统工程与电子技术,2006,28(5)：727-730.
[37]Y. Zeng, A.D. Araujo, and S.N. Singh. Output Feedback Variable Structure Adaptive Control of a Flexible Spacecraft[J]. Acta Astronautica,1999,44 (1):1-22.
[38]周连文,周军.挠性航天器大角度机动的变结构控制[J].航天控制,2003(3)：48-52.
[39]唐超颖,沈春林,李丽荣.航天器姿态滑模变结构控制系统的设计[J].南京航空航天大学学报,2003,35(4)：361-365.
[40]管萍,陈家斌.挠性卫星的自适应模糊滑膜控制[J].航天控制,2004,22(4)：62-67.
[41]杨大智.智能材料与智能系统[M].天津：天津大学出版社,2000.2-5.
[42]T. Bailey, and J.E. Hubbard, Distributed Piezoelectric-polymer Active Vibration Control of a Cantilever Beam[J]. Journal of Guidance Control,1985,8 (5):605-611.
[43]Q.L. Hu, G.F. Ma. Spacecraft Vibration Suppression Using Variable Structure Output Feedback Control and Smart Materials [J]. ASME Journal of Vibration and Acoustics, 2006,128 (2):221-230.
[44]仝西岳.挠性卫星动力学建模与控制系统研究[D].国防科学技术大学,2001.
[45]李英波.挠性充液卫星动力学分析与姿态控制研究[D].上海交通大学,2001.
[46]袁家军.卫星结构与设计与分析[D].北京：宇航出版社,2004.
[47]许可康.控制系统中的奇异摄动[M].北京：科学出版社,1986.
[48]P.V. Kokotovic, R.E. O'Malley, Jr. and P. Sannuti. Singular perturbation and order reduction in control theory-an overview[C]. Automatica,1976,12:123-132.
[49]Hassan K.Khalil.非线性系统(第三版)[M].北京：电子工业出版社,2005.
[50]蔡晨晓.奇异摄动系统的稳定反馈控制[D].南京理工大学,2004.
[51]刘华平,孙富春,何克忠,孙增圻.奇异摄动控制系统：理论与应用[J].控制理论与应用,2003,20(1)：1-7.
[52]F.L. Lewis, M.W. Vandergrift. Flexible robot arm control by a feedback linearization/singular perturbation approach[C]. Proc. IEEE Conf. On Robo. Autom, 1993,729-736.
[53]M.W. Vandergrift, F.L. Lewis. Flexible-link robot arm control by a feedback linearization/singular perturbation approach[J]. Journal of Robotic Systems,1994,11(7): 591-603.
[54]S.Q. Zhu, S. Commuri and F.L. Lewis. A singular perturbation approach to stabilization of the internal dynamics of multilink flexible robots[C]. Proc. IEEE Conf. On Robo. Autom,1994,1386-1390.
[55]J. Lin, F.L. Lewis. Two-time scale fuzzy logic controller of flexible link robot arm[J]. Fuzzy Sets and Systems,2003(139):125-149.
[56]Zhang Yu. Neuro-Sliding-Mode control of flexible-link manipulators based on singularly perturbed model[J]. Tsinghua Science and Technology,2009,14(4):444-451.
[57]张友安,吕凤琳,孙富春.基于奇异摄动的双连杆柔性臂模糊控制[J].计算机仿真,2004,21(4)：109-112.
[58]Singh H, Naidu D S, Nagurka M L. Unified H∞ approach for a singularly perturbed aircraft model [C]. IEEE, Proceedings of American Control Conference.2000, 1847-1851.
[59]程雪梅,李言俊.一类非线性奇异摄动系统的轨道激动控制[J].航天控制,2001(4),41-47.
[60]唐志国.基于奇异摄动机械臂协调操作柔性负载系统控制研究[D].吉林大学,2008.
[61]陶永华,尹怡欣,葛芦生.新型PID控制及其应用[M].北京：机械工业出版社.1998.
[62]黄友锐,曲立国.PID控制器参数整定与实现[M].北京：科学出版社,2010.
[63]胡寿松,王执铨,胡维礼.最优控制理论与系统[M].北京：科学出版社,2005.
[64]刘金琨.滑模变结构控制MATLAB仿真[M].北京：清华大学出版社,2005.
[65]王丰饶.滑膜变结构控制[M].北京：机械工业出版社,1995.
[66]高为炳.变结构控制的理论及设计方法[M].北京：科学出版社,1996.
[2]P.S. Aubert, et al. Centralized vs Decentralized Options for a European Data Relay Satellite System, Acta Astronautica,1986,13:387-401.
[3]H. Dodel, et al. Antenna System Alternatives for Data Relay Satellites with Multiple Steer able Beams, Acta Astronautica,1988,17:553-560.
[4]魏晨曦.跟踪与数据中继卫星系统的发展[J].中国航天,2001,11：14-18.
[5]中国新闻网.中国风云3号卫星将于5月择机发射[EB／OL].http://news.21 cn.com/domestic/yaowen/2008/01/24/4277461.shtml,2008.
[6]王祥,王存恩.日本“准天顶卫星”系统及其应用计划[J].国际太空,2010,3：7-12.
[7]钱勇.高精度三轴稳定卫星姿态确定和控制系统研究[D].西北工业大学,2002.
[8]李果,刘良栋.航天控制器若干技术问题的新进展[J].空间控制技术与应用,2008,2(34)： 14-19.
[9]A. Grewal, V. J. Modi. Multibody Dynamic and Robust Control of Flexible Spacecraft, IEEE Trans. Aerospace and Electronic System,2000,36 (2):491-499.
[10]曲广吉.航天器动力学工程[M].北京：中国科学技术出版社,2000.
[11]屠善澄,陈义庆等.卫星姿态动力学与控制[M].北京：中国宇航出版社,2005.
[12]张育林,吴建军.航天器[M].北京：国防工业出版社,2006.
[13]Toshiaki Yamashita, Naoto Ogurb. Improved satellite attitude control using a disturbance compensator[J]. Acta Astronautica,2004,55:15-25.
[14]耿云海,崔祜涛,孙兆伟,杨涤.小卫星主动磁控制地球捕获姿态控制系统设计[J].航空学报,2000,21(2)：142-145.
[15]刘新建,雷勇军,唐乾刚.大挠性太阳能帆板航天器的姿态控制[J].国防科技大学学报,2003,25(5)：6-8.
[16]Jianhua Zheng, Stephen P. Banks, Hugo Alleyne. Optimal attitude control for three-axis stabilized flexible spacecraft[J]. Acta Astronautica,2005,56:519-528.
[17]Joseph, M.Fulton. LQG/LTR optimal attitude control of small flexible spacecraft using free-free boundary conditions[D]. Colorado:University of Colorado,2006.
[18]韩曾晋.自适应控制[M].北京：清华大学出版社,1995.
[19]吴宏鑫.自适应控制技术的应用和发展[J].控制理论与应用,1992,9(2)：105-114.
[20]张国琪,丁建钊.柔性航天器姿态快速机动的自适应控制方法[J].空间控制技术与 应用,2008,34(4)：23-27.
[21]Bong-Jun Yang, Anthony J.Calise, James I. Craig. Adaptive control of Truss Structures for Gossamer Spacecraft[R]. AIAA NSFC-042,2007.
[22]褚健,俞立,苏宏业.鲁棒控制理论及应用[M].杭州：浙江大学出版社,2000.
[23]C Scherer, P Gahnite, M Chilali. Multi-objective Output-feedback Control via LMI Optimization[J]. IEEE Trans. on Autom. Contr,1997,42 (7):896-911.
[24]宋斌,马广富,李传江,谌颖.基于H∞鲁棒控制的挠性卫星姿态控制[J].系统仿真学报,2005,17(4)：968-970.
[25]兰维瑶,陈亚陵.新型卫星姿态运动的鲁棒控制器设计[J].厦门大学学报,1999,38(2)： 193-198.
[26]王广雄,张静,朱井泉.挠性系统的鲁棒控制设计[J].控制与决策,2003,18(3)：281-284.
[27]孙增圻.智能控制理论与技术[M].清华大学出版社,1997.
[28]S Thongchet, S Kuntanapreeda. A fuzzy neural bang-bang controller for satellite attitude control[C]. Proceedings of SPIE-The International Society for Optical Engineering, 2001,4390:97-104.
[29]刘军,韩潮.基于单神经元的卫星姿态自适应PID控制[J].计算机仿真,2006,23(3)：45-48.
[30]张云,王培垣.一种用于挠性卫星姿态控制的改进模糊控制器[J].上海航天,2004,6(6)：42-46.
[31]孙庆,吴宏鑫.挠性结构卫星单轴气浮台的模糊控制[J].航天控制,1997,2：29-36.
[32]高为炳.变结构控制理论基础[M].北京：中国科学技术出版社,1990.
[33]姜野.挠性卫星姿态机动的时变滑模变结构主动振动控制研究[D].哈尔滨工业大学,2007.
[34]周军,李季苏,牟小刚.挠性卫星振动抑振的变结构主动控制方案及实验研究[J].航天控制,1996,4：1-6.
[35]李勇,吴宏鑫.一类挠性航天器的变结构控制[J].宇航学报,1998,19(1)：13-20.
[36]王庆超,岑小锋,马兴瑞.挠性航天器旋转机动的输入成形变结构控制[J].系统工程与电子技术,2006,28(5)：727-730.
[37]Y. Zeng, A.D. Araujo, and S.N. Singh. Output Feedback Variable Structure Adaptive Control of a Flexible Spacecraft[J]. Acta Astronautica,1999,44 (1):1-22.
[38]周连文,周军.挠性航天器大角度机动的变结构控制[J].航天控制,2003(3)：48-52.
[39]唐超颖,沈春林,李丽荣.航天器姿态滑模变结构控制系统的设计[J].南京航空航天大学学报,2003,35(4)：361-365.
[40]管萍,陈家斌.挠性卫星的自适应模糊滑膜控制[J].航天控制,2004,22(4)：62-67.
[41]杨大智.智能材料与智能系统[M].天津：天津大学出版社,2000.2-5.
[42]T. Bailey, and J.E. Hubbard, Distributed Piezoelectric-polymer Active Vibration Control of a Cantilever Beam[J]. Journal of Guidance Control,1985,8 (5):605-611.
[43]Q.L. Hu, G.F. Ma. Spacecraft Vibration Suppression Using Variable Structure Output Feedback Control and Smart Materials [J]. ASME Journal of Vibration and Acoustics, 2006,128 (2):221-230.
[44]仝西岳.挠性卫星动力学建模与控制系统研究[D].国防科学技术大学,2001.
[45]李英波.挠性充液卫星动力学分析与姿态控制研究[D].上海交通大学,2001.
[46]袁家军.卫星结构与设计与分析[D].北京：宇航出版社,2004.
[47]许可康.控制系统中的奇异摄动[M].北京：科学出版社,1986.
[48]P.V. Kokotovic, R.E. O'Malley, Jr. and P. Sannuti. Singular perturbation and order reduction in control theory-an overview[C]. Automatica,1976,12:123-132.
[49]Hassan K.Khalil.非线性系统(第三版)[M].北京：电子工业出版社,2005.
[50]蔡晨晓.奇异摄动系统的稳定反馈控制[D].南京理工大学,2004.
[51]刘华平,孙富春,何克忠,孙增圻.奇异摄动控制系统：理论与应用[J].控制理论与应用,2003,20(1)：1-7.
[52]F.L. Lewis, M.W. Vandergrift. Flexible robot arm control by a feedback linearization/singular perturbation approach[C]. Proc. IEEE Conf. On Robo. Autom, 1993,729-736.
[53]M.W. Vandergrift, F.L. Lewis. Flexible-link robot arm control by a feedback linearization/singular perturbation approach[J]. Journal of Robotic Systems,1994,11(7): 591-603.
[54]S.Q. Zhu, S. Commuri and F.L. Lewis. A singular perturbation approach to stabilization of the internal dynamics of multilink flexible robots[C]. Proc. IEEE Conf. On Robo. Autom,1994,1386-1390.
[55]J. Lin, F.L. Lewis. Two-time scale fuzzy logic controller of flexible link robot arm[J]. Fuzzy Sets and Systems,2003(139):125-149.
[56]Zhang Yu. Neuro-Sliding-Mode control of flexible-link manipulators based on singularly perturbed model[J]. Tsinghua Science and Technology,2009,14(4):444-451.
[57]张友安,吕凤琳,孙富春.基于奇异摄动的双连杆柔性臂模糊控制[J].计算机仿真,2004,21(4)：109-112.
[58]Singh H, Naidu D S, Nagurka M L. Unified H∞ approach for a singularly perturbed aircraft model [C]. IEEE, Proceedings of American Control Conference.2000, 1847-1851.
[59]程雪梅,李言俊.一类非线性奇异摄动系统的轨道激动控制[J].航天控制,2001(4),41-47.
[60]唐志国.基于奇异摄动机械臂协调操作柔性负载系统控制研究[D].吉林大学,2008.
[61]陶永华,尹怡欣,葛芦生.新型PID控制及其应用[M].北京：机械工业出版社.1998.
[62]黄友锐,曲立国.PID控制器参数整定与实现[M].北京：科学出版社,2010.
[63]胡寿松,王执铨,胡维礼.最优控制理论与系统[M].北京：科学出版社,2005.
[64]刘金琨.滑模变结构控制MATLAB仿真[M].北京：清华大学出版社,2005.
[65]王丰饶.滑膜变结构控制[M].北京：机械工业出版社,1995.
[66]高为炳.变结构控制的理论及设计方法[M].北京：科学出版社,1996.