卫星姿态的磁控制方法研究
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摘要
由于具备了“更快、更好、更省”等优点,近年来小卫星的研究受到了世界各国的高度重视,成为航天发展的一个重要方向。另一方面,由于磁力矩器具有结构简单、质量轻、功耗低、成本低等特性,直接使用磁力矩器对小卫星进行姿态控制也成为当前的研究热点。本文就对三轴稳定小卫星的姿态磁控制方法进行了研究。
与传统控制器不同的是,磁控制力矩受地磁场限制,只能在与地磁场正交平面内产生,即系统在任意时刻都是不完全可控的,致使姿态磁控制没能在实际中得到广泛应用。本文则考虑了磁控制力矩产生的方向性约束和所受到的空间干扰力矩,建立了磁控小卫星的系统模型,分别针对不同飞行任务设计了四种磁控制律,并对它们进行了数学仿真验证和结果分析对比。
首先,本文在研究了周期线性系统特性的基础上,针对卫星的周期线性系统模型,基于LQR方法设计了周期时变控制律并通过数学仿真验证了其控制性能;接着为了减少计算量,同样基于LQR方法设计了定常增益反馈控制器,并利用周期系统的Floquet定理对其稳定性进行了分析,仿真结果同样表明了该控制器的有效性和实用性。
为了增强系统的鲁棒性,本文结合预测控制中的在线滚动优化原理,针对卫星的离散系统模型,设计了控制力矩受地磁场线性约束时的预测控制律,并分析了其稳定性。数学仿真表明了该控制算法有着稳态精度高,干扰抑制能力强等优点。
考虑卫星在完成姿态机动任务时的强非线性,本文最后研究了滑模控制在卫星姿态磁控制中的应用。通过研究滑模控制原理和周期非线性系统稳定性定理,针对卫星的非线性系统模型设计了工程实用的滑模控制律,并结合磁力矩产生的方向性约束对其进行了修正。仿真结果表明,该控制律具有较强的鲁棒性和快速性。
In recent years, research on small satellites has been paid great attention, and has become an important research area of space technology due to some“Faster Better Cheaper”characteristics for small satellites. Magnetic control system is attractive for small satellites, since the magnetorquers are relatively simple and lightweight, require low power and are inexpensive. The primary purpose of the work is to develop control laws for three axis stabilization of small satellites.
The magnetic control torques are different from the traditional controller, which can only be generated perpendicular to the local geomagnetic field vector, and hence the satellite is instantaneously under-actuated. So far, this has prevented the application in practice using magenetorquers only. However, this paper presents the satellite model of a small magnetic actuated satellite with the constrainted control torques and environment model. Four magnetic controller designs are implemented for different missions, and their pros and cons are discussed via simulation.
After provided the introduction to periodic linear system and the periodic linear model of satellite, a periodic time varying controller is presented based on LQR method and then examined its performance via simulation; At the same time a constant gain LQR controller is designed in order to reduce the computer burden on satellite, the stability of which can be checked by means of Floquet theory. The controller is also effective and with certain utility according to simulation results.
Online receding horizon optimal strategy in Model Predictive Control is applied to magnetic attitude control problems in this paper to enhance the robustness of the system, a predictive control algorithm is designed with constraints on the control torque based on the discrete model of satellite, afterwards its stability is also analyzed. The simulation results showed that the control law designed has high steady precision and strong ability to mitigate interference.
The last approach to the attitude control for a magnetic actuated satellite is based on sliding mode control considering the strong nonlinear in attitude maneuver missions. A stable controller is applied which can be easily used in practical based on the nonlinear model of satellite, and then a modification has been done on it combined with the constraints of magnetic control torque. The analysis of simulation results showed that the control law designed has fast dynamic response and strong robustness.
与传统控制器不同的是,磁控制力矩受地磁场限制,只能在与地磁场正交平面内产生,即系统在任意时刻都是不完全可控的,致使姿态磁控制没能在实际中得到广泛应用。本文则考虑了磁控制力矩产生的方向性约束和所受到的空间干扰力矩,建立了磁控小卫星的系统模型,分别针对不同飞行任务设计了四种磁控制律,并对它们进行了数学仿真验证和结果分析对比。
首先,本文在研究了周期线性系统特性的基础上,针对卫星的周期线性系统模型,基于LQR方法设计了周期时变控制律并通过数学仿真验证了其控制性能;接着为了减少计算量,同样基于LQR方法设计了定常增益反馈控制器,并利用周期系统的Floquet定理对其稳定性进行了分析,仿真结果同样表明了该控制器的有效性和实用性。
为了增强系统的鲁棒性,本文结合预测控制中的在线滚动优化原理,针对卫星的离散系统模型,设计了控制力矩受地磁场线性约束时的预测控制律,并分析了其稳定性。数学仿真表明了该控制算法有着稳态精度高,干扰抑制能力强等优点。
考虑卫星在完成姿态机动任务时的强非线性,本文最后研究了滑模控制在卫星姿态磁控制中的应用。通过研究滑模控制原理和周期非线性系统稳定性定理,针对卫星的非线性系统模型设计了工程实用的滑模控制律,并结合磁力矩产生的方向性约束对其进行了修正。仿真结果表明,该控制律具有较强的鲁棒性和快速性。
In recent years, research on small satellites has been paid great attention, and has become an important research area of space technology due to some“Faster Better Cheaper”characteristics for small satellites. Magnetic control system is attractive for small satellites, since the magnetorquers are relatively simple and lightweight, require low power and are inexpensive. The primary purpose of the work is to develop control laws for three axis stabilization of small satellites.
The magnetic control torques are different from the traditional controller, which can only be generated perpendicular to the local geomagnetic field vector, and hence the satellite is instantaneously under-actuated. So far, this has prevented the application in practice using magenetorquers only. However, this paper presents the satellite model of a small magnetic actuated satellite with the constrainted control torques and environment model. Four magnetic controller designs are implemented for different missions, and their pros and cons are discussed via simulation.
After provided the introduction to periodic linear system and the periodic linear model of satellite, a periodic time varying controller is presented based on LQR method and then examined its performance via simulation; At the same time a constant gain LQR controller is designed in order to reduce the computer burden on satellite, the stability of which can be checked by means of Floquet theory. The controller is also effective and with certain utility according to simulation results.
Online receding horizon optimal strategy in Model Predictive Control is applied to magnetic attitude control problems in this paper to enhance the robustness of the system, a predictive control algorithm is designed with constraints on the control torque based on the discrete model of satellite, afterwards its stability is also analyzed. The simulation results showed that the control law designed has high steady precision and strong ability to mitigate interference.
The last approach to the attitude control for a magnetic actuated satellite is based on sliding mode control considering the strong nonlinear in attitude maneuver missions. A stable controller is applied which can be easily used in practical based on the nonlinear model of satellite, and then a modification has been done on it combined with the constraints of magnetic control torque. The analysis of simulation results showed that the control law designed has fast dynamic response and strong robustness.
引文
1林来兴.小卫星将引起卫星应用和卫星技术的重大变革.现代小卫星技术(一).1995: 1~33
2林来兴.小卫星技术的发展和应用前景.中国航天. 2006(11):43~47
3谢祥华.微小卫星姿态控制系统研究.南京航空航天大学硕士学位论文. 2007:1~6
4孔庆松.低轨小卫星高性能磁力矩器的设计与实现.中国科学院空间科学与应用研究中心硕士学位论文. 2006:1~6
5屠善澄.卫星姿态动力学与控制.宇航出版社,1999:49~73
6周军.航天器控制原理.西北工业大学出版社,2001:113~134
7胡恒章.航天器控制.宇航出版社,1997:141~179
8李太玉.微小卫星姿态磁控制及三轴被动稳定研究.国防科学技术大学博士学位论文.2002:1~12
9 M. Lovera. Spacecraft Attitude Control Using Magnetic Actuators. Automatica. 2004(40):1405~1414
10 R. Wisniewski, M. Blanke. Fully Magnetic Attitude Control for Spacecraft Subject to Gravity Gradient. Automatica. 1999,35(7):1201~1214
11 E. Silani, M. Lovera. Magnetic Spacecraft Attitude Control: a Survey and Some New Results. Control Engineering Practice, 2005, 13(3): 357~371
12 E.I. Ergin, P.C. Wheeler. Magnetic Control of a Spinning Satellite. Journal of Spacecraft and Rockets. 1965,2(6):846~850
13 M. L. Renard. Command Laws for Magnetic Attitude Control of Spin-Stabilized Earth Satellites. Journal of Spacecraft and Rockets. 1967:4(2):156~163
14 M. Psiaki. Magnetic Torquer Attitude Control via Asympotic Periodic Linear Quadratic Regulation. Journal of Guidance, Control, and Dynamics. 2001, 24(2): 386~394
15马广富,李传江.卫星姿态控制器周期时变磁控制器的设计.第五届全球智能控制与自动化大会.杭州,2004:5454~5457
16刘海颖,王惠南,程月华.主动磁控微卫星姿态控制.应用科学学报. 2007,25(4):377~381
17 F. Martel, P. K. Pal, M. Psiaki. Active magnetic control system for gravity gradient stabilized spacecraft. Proceedings of the 2nd Annual AIAA/USU Conference on Small Satellites. Logan, Utah,1988:1~19
18 K.L. Musser, W.L. Ebert. Autonomous Spacecraft Attitude Control using Magnetic Torquing Only. Proceedings of the Flight Mechanics/EstimationTheory Symposium. NASA Goddard Space Flight Center. Greenbelt, MD. 1989:23~38
19 A. Cavallo, G. D. Maria. A sliding manifold approach to satellite attitude control. 12th. World Congress IFAC. Sidney, 1993:177~184
20 P. Wang, Y. Shtessel. Satellite Attitude Control Using only Magnetorquers. Proceedings of the American Control Conference Philadelphia. Pennsylvania, 1998:500~504
21 Ch. Byrnes, A. Isidori. On the Attitude Stabilization of Rigid Spacecraft. Automatic.1991,27(1):87~95
22 J. Wen, K. Kreutz-Delgado. The Attitude Control Problem. IEEE Transactions on Automatic Control. 1991(36):1148~1162
23 F. Martel, K. Parimal P, M. Psiaki. Active Magnetic Control System for Gravity Gradient Stabilized Spacecraft. 2nd Annual AIAA/Utah State University Conference on Small Satellites. 1998: 1~19
24 R. Wisniewski. Satellite Atitude Cntrol Using Only Electromagnetic Actuation. Ph.D. thesis, Aalborg University, Denmark. 1996:24~44,71~86
25 R. Wisniewski, L. Markley. Optimal Magnetic Attitude Control. Proceedings of the 14th IFAC World Congress. Beijing,China,1999:285~291
26 M. Lovera. Global Attitude Regulation Using Magnetic Control. Proceedings of the 40th IEEE Conference on Decision and Control Orlando. Florida,USA, 2001:4604~4609
27 R. Wisniewski. Linear Time-varying Approach to Satellite Attitude Control Using Only Electromagnetic Actuation. Journal of Guidance, Control and Dynamics. 2000,23(4):640~646
28 L. Jinsong, R. Fullmer.Time-Optimal Magnetic Attitude Control for Small Spacecraft. 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas,2004:255~260
29 ?. Hegren?s. Attitude Control by Means of Explicit Model Predictive Control, via Multi-parametric Quadratic Programming. 2005 American Control Conference. Portland, OR, USA, 2005:901~906
30 T.R. Krogstad. Explicit Model Predictive Control of a Satellite with Magnetic Torquers. Proceedings of the 13th Mediterranean Conference on Control and Automation Limassol. Cyprus, 2005:491~496
31 M. Wood, C. Wen-Hua. Regulation of Magnetically Actuated Satellites using Model Predictive Control with Disturbance Modelling. IEEE InternationalConference on Networking, Sensing and Control. 2008:692~697
32 M. Wood. Model Predictive Control of Low Earth Orbiting Spacecraft with Magneto-torquers. Proceedings of the 2006 IEEE International Conference on Control Applications Munich. Germany, 2006:2908~2913
33 N. Sivaprakash, J. Shanmugam. Neural Network Based Three Axis Satellite Attitude Control Using Only Magnetic Torquers. Digital Avionics Systems Conference. 2005(2):6~12
34 S. P. Bhat. Controllability of Nonlinear Time-Varying Systems: Applications to Spacecraft Attitude Control Using Magnetic Actuation. IEEE Transactions on Automatic Control. 2005,50(11):1725~1735
35 J. H. McDuffie, Y. B. Shtessel. A De-coupled Sliding Mode Controller and Observer for Satellite Attitude Control. Proceedings of the American Control Conference. Albuquerque, New Mexico,1997:564~565
36 P. Guan, X.J. Liu. Flexible Satellite Attitude Control via Sliding Mode Technique. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference. Seville, Spain, 2005:1258~1263
37 R. Wisniewski. Sliding Mode Attitude Control for Magnetic Actuated Satellite. 14th IFAC Symposium on Automatic Control in Aerospace,1998
38姜雪原.卫星姿态确定及敏感器误差修正的滤波算法研究.哈尔滨工业大学博士学位论文.2006:17~25
39章仁为.卫星轨道姿态动力学与控制.北京航空航天大学, 1998:95~112
40 M. Lovera, E. D. Marci. Periodic Attitude Control Techniques for Small Satellites with Magnetic Actuators. IEEE Transactions on Control Systems Technology. 2002, 10(1): 90~95
41 S. Bittanti, P. Colaneri, G.D. Nicolao. The Difference Periodic Ricati Equation for the Periodic Prediction Problem. IEEE Transactions on Automatic Control. 1988,3(8):706~712
42 S. Bittanti, P. Colaneri. Lyapunov and Riccati Equations: Periodic Inertia Theorems. IEEE Transactions on Automatic Control. 1986,31(7):659~661
43胡跃明,胡终须,毛宗源.非线性控制系统的近似化方法.控制理论与应用. 2001,18 (2):160~165
44胡跃明.非线性控制系统理论与应用.国防工业出版社,第2版. 2005:36~53,154~164
45段广仁.线性系统.哈尔滨工业大学出版社,第2版. 2004:69~75,144~162
46胡寿松.最优控制理论.科学出版社,第3版.1994:620~622
47叶彪明.有限时间二次型最优调节器的数值解.南京师范大学学报(工程技术版).2003,3(1):30~33
48 S. Bittanti. The Riccati Equation. Springer Verlag. 1991.
49 C. Zhang, J. Zhang, K. Furuta. Performance analysis of periodically time varying controllers. Proc. of the 13th IFAC World Congress. San Francisco, USA,1996,D:207~212
50席裕庚.预测控制.国防工业出版社. 1993:5~42
51李书臣.预测控制最新算法综述.系统仿真学报. 2004, 16(6):1314~1319
52 D. Q. Mayne, J. B. Rawlings. Constrained model predictive control: Stability and optimality. Automatica. 2000(36):789~814
53李志军.约束模型预测控制的稳定性与鲁棒性研究.华北电力大学博士学位论文. 2005:1~42
54 J. Gravdahl. Magnetic attitude control for satellites. 43rd IEEE Conference on Decision and Control. 2004,8(2):261~266
55刘海颖,王惠南,程月华.纯磁控微小卫星姿态控制研究.空间科学学报. 2007,27(5):425~429
56 M. Lovera, A. Astolfi. Global Magenetic Attitude Control of Spacecraft. 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas 2004,8(3):268~272
2林来兴.小卫星技术的发展和应用前景.中国航天. 2006(11):43~47
3谢祥华.微小卫星姿态控制系统研究.南京航空航天大学硕士学位论文. 2007:1~6
4孔庆松.低轨小卫星高性能磁力矩器的设计与实现.中国科学院空间科学与应用研究中心硕士学位论文. 2006:1~6
5屠善澄.卫星姿态动力学与控制.宇航出版社,1999:49~73
6周军.航天器控制原理.西北工业大学出版社,2001:113~134
7胡恒章.航天器控制.宇航出版社,1997:141~179
8李太玉.微小卫星姿态磁控制及三轴被动稳定研究.国防科学技术大学博士学位论文.2002:1~12
9 M. Lovera. Spacecraft Attitude Control Using Magnetic Actuators. Automatica. 2004(40):1405~1414
10 R. Wisniewski, M. Blanke. Fully Magnetic Attitude Control for Spacecraft Subject to Gravity Gradient. Automatica. 1999,35(7):1201~1214
11 E. Silani, M. Lovera. Magnetic Spacecraft Attitude Control: a Survey and Some New Results. Control Engineering Practice, 2005, 13(3): 357~371
12 E.I. Ergin, P.C. Wheeler. Magnetic Control of a Spinning Satellite. Journal of Spacecraft and Rockets. 1965,2(6):846~850
13 M. L. Renard. Command Laws for Magnetic Attitude Control of Spin-Stabilized Earth Satellites. Journal of Spacecraft and Rockets. 1967:4(2):156~163
14 M. Psiaki. Magnetic Torquer Attitude Control via Asympotic Periodic Linear Quadratic Regulation. Journal of Guidance, Control, and Dynamics. 2001, 24(2): 386~394
15马广富,李传江.卫星姿态控制器周期时变磁控制器的设计.第五届全球智能控制与自动化大会.杭州,2004:5454~5457
16刘海颖,王惠南,程月华.主动磁控微卫星姿态控制.应用科学学报. 2007,25(4):377~381
17 F. Martel, P. K. Pal, M. Psiaki. Active magnetic control system for gravity gradient stabilized spacecraft. Proceedings of the 2nd Annual AIAA/USU Conference on Small Satellites. Logan, Utah,1988:1~19
18 K.L. Musser, W.L. Ebert. Autonomous Spacecraft Attitude Control using Magnetic Torquing Only. Proceedings of the Flight Mechanics/EstimationTheory Symposium. NASA Goddard Space Flight Center. Greenbelt, MD. 1989:23~38
19 A. Cavallo, G. D. Maria. A sliding manifold approach to satellite attitude control. 12th. World Congress IFAC. Sidney, 1993:177~184
20 P. Wang, Y. Shtessel. Satellite Attitude Control Using only Magnetorquers. Proceedings of the American Control Conference Philadelphia. Pennsylvania, 1998:500~504
21 Ch. Byrnes, A. Isidori. On the Attitude Stabilization of Rigid Spacecraft. Automatic.1991,27(1):87~95
22 J. Wen, K. Kreutz-Delgado. The Attitude Control Problem. IEEE Transactions on Automatic Control. 1991(36):1148~1162
23 F. Martel, K. Parimal P, M. Psiaki. Active Magnetic Control System for Gravity Gradient Stabilized Spacecraft. 2nd Annual AIAA/Utah State University Conference on Small Satellites. 1998: 1~19
24 R. Wisniewski. Satellite Atitude Cntrol Using Only Electromagnetic Actuation. Ph.D. thesis, Aalborg University, Denmark. 1996:24~44,71~86
25 R. Wisniewski, L. Markley. Optimal Magnetic Attitude Control. Proceedings of the 14th IFAC World Congress. Beijing,China,1999:285~291
26 M. Lovera. Global Attitude Regulation Using Magnetic Control. Proceedings of the 40th IEEE Conference on Decision and Control Orlando. Florida,USA, 2001:4604~4609
27 R. Wisniewski. Linear Time-varying Approach to Satellite Attitude Control Using Only Electromagnetic Actuation. Journal of Guidance, Control and Dynamics. 2000,23(4):640~646
28 L. Jinsong, R. Fullmer.Time-Optimal Magnetic Attitude Control for Small Spacecraft. 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas,2004:255~260
29 ?. Hegren?s. Attitude Control by Means of Explicit Model Predictive Control, via Multi-parametric Quadratic Programming. 2005 American Control Conference. Portland, OR, USA, 2005:901~906
30 T.R. Krogstad. Explicit Model Predictive Control of a Satellite with Magnetic Torquers. Proceedings of the 13th Mediterranean Conference on Control and Automation Limassol. Cyprus, 2005:491~496
31 M. Wood, C. Wen-Hua. Regulation of Magnetically Actuated Satellites using Model Predictive Control with Disturbance Modelling. IEEE InternationalConference on Networking, Sensing and Control. 2008:692~697
32 M. Wood. Model Predictive Control of Low Earth Orbiting Spacecraft with Magneto-torquers. Proceedings of the 2006 IEEE International Conference on Control Applications Munich. Germany, 2006:2908~2913
33 N. Sivaprakash, J. Shanmugam. Neural Network Based Three Axis Satellite Attitude Control Using Only Magnetic Torquers. Digital Avionics Systems Conference. 2005(2):6~12
34 S. P. Bhat. Controllability of Nonlinear Time-Varying Systems: Applications to Spacecraft Attitude Control Using Magnetic Actuation. IEEE Transactions on Automatic Control. 2005,50(11):1725~1735
35 J. H. McDuffie, Y. B. Shtessel. A De-coupled Sliding Mode Controller and Observer for Satellite Attitude Control. Proceedings of the American Control Conference. Albuquerque, New Mexico,1997:564~565
36 P. Guan, X.J. Liu. Flexible Satellite Attitude Control via Sliding Mode Technique. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference. Seville, Spain, 2005:1258~1263
37 R. Wisniewski. Sliding Mode Attitude Control for Magnetic Actuated Satellite. 14th IFAC Symposium on Automatic Control in Aerospace,1998
38姜雪原.卫星姿态确定及敏感器误差修正的滤波算法研究.哈尔滨工业大学博士学位论文.2006:17~25
39章仁为.卫星轨道姿态动力学与控制.北京航空航天大学, 1998:95~112
40 M. Lovera, E. D. Marci. Periodic Attitude Control Techniques for Small Satellites with Magnetic Actuators. IEEE Transactions on Control Systems Technology. 2002, 10(1): 90~95
41 S. Bittanti, P. Colaneri, G.D. Nicolao. The Difference Periodic Ricati Equation for the Periodic Prediction Problem. IEEE Transactions on Automatic Control. 1988,3(8):706~712
42 S. Bittanti, P. Colaneri. Lyapunov and Riccati Equations: Periodic Inertia Theorems. IEEE Transactions on Automatic Control. 1986,31(7):659~661
43胡跃明,胡终须,毛宗源.非线性控制系统的近似化方法.控制理论与应用. 2001,18 (2):160~165
44胡跃明.非线性控制系统理论与应用.国防工业出版社,第2版. 2005:36~53,154~164
45段广仁.线性系统.哈尔滨工业大学出版社,第2版. 2004:69~75,144~162
46胡寿松.最优控制理论.科学出版社,第3版.1994:620~622
47叶彪明.有限时间二次型最优调节器的数值解.南京师范大学学报(工程技术版).2003,3(1):30~33
48 S. Bittanti. The Riccati Equation. Springer Verlag. 1991.
49 C. Zhang, J. Zhang, K. Furuta. Performance analysis of periodically time varying controllers. Proc. of the 13th IFAC World Congress. San Francisco, USA,1996,D:207~212
50席裕庚.预测控制.国防工业出版社. 1993:5~42
51李书臣.预测控制最新算法综述.系统仿真学报. 2004, 16(6):1314~1319
52 D. Q. Mayne, J. B. Rawlings. Constrained model predictive control: Stability and optimality. Automatica. 2000(36):789~814
53李志军.约束模型预测控制的稳定性与鲁棒性研究.华北电力大学博士学位论文. 2005:1~42
54 J. Gravdahl. Magnetic attitude control for satellites. 43rd IEEE Conference on Decision and Control. 2004,8(2):261~266
55刘海颖,王惠南,程月华.纯磁控微小卫星姿态控制研究.空间科学学报. 2007,27(5):425~429
56 M. Lovera, A. Astolfi. Global Magenetic Attitude Control of Spacecraft. 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas 2004,8(3):268~272