三轴稳定质量矩控制导弹的建模、分析及仿真
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摘要
本文主要对三轴稳定质量矩控制导弹的模型建立和模型简化问题进行了分析与研究。根据牛顿运动定律建立质心运动和绕质心转动动力学方程,由于模型的非线性、强耦合等特点,为方便控制系统的设计,对模型进行了必要的简化。
质心运动方程的简化相对比较简单。绕质心转动动力学方程的简化由于导弹内部质量块的运动而变得相对比较复杂。本文对导弹内部各质量块的位置参数采用正弦输入信号,通过改变正弦输入信号的角频率进行仿真实验,进而分析各质量块运动速度及加速度对系统的影响,仿真结果表明当质量块运动速度及加速度在一定范围内变化时,可以对绕质心转动方程进行简化。
在质量矩控制导弹简化模型基础上,利用Lyapunov理论对质量矩控制导弹进行了稳定性分析。应用时标分离方法将系统分成快、慢两个子系统,采用动态逆控制方法对控制导弹的非线性系统进行了设计,仿真结果验证了此方法的可行性。
在不同的初始条件下,根据视线坐标系、惯性坐标系及弹体坐标系的转换关系,采用修正的比例导引律对导弹拦截目标进行了空间全弹道仿真,对所给出的简化模型做了进一步的验证,使质量矩控制导弹的工程实现成为可能。
The main research contents of this paper are the modeling and model simplification analysis of three-axis stabilized mass moment control missile.Establishing the center of mass movement and rotation around the center of mass kinetic equation according to Newton's laws of motion.The model is nonlinear, strong coupling and so on, in order to facilitate the design of control system, the model was necessary to be simplified.
The simplification of equation of motion of mass is relatively simple. While the simplification of rotating around the center of mass kinetic equations is relatively more complex because the movement of mass within the missile. It is inputted sine signal to the position parameters of the mass moment within the missile, simulation experiment is conducted by changing the angular frequency of sinusoidal, and then analyzes the effect of velocity and acceleration of mass moment on the system. Simulation results demonstrate that when the velocity and mass acceleration changes in a certain range, we can accomplish the simplification of equation around the center of mass.
According to the simplified model of the missile, the stability analysis of three-axis stabilized mass moment control missile is done on the support of Lyapunov theory. The system is departed into a fast and a slow subsystem with the application of separation of time scale.The nonlinear system of the control of the missile is designed with the dynamic inversion method, this method is proved feasible by the simulation experiment.
In different initial conditions, according to the transformation of vision coordinate system, inertial coordinate system and the body coordinate system,adopt modified proportional guidance law to intercept the missile target in space the whole trajectory simulation on the simplified model given to do further verification, it made the engineering realization of mass moment control missile become possible.
质心运动方程的简化相对比较简单。绕质心转动动力学方程的简化由于导弹内部质量块的运动而变得相对比较复杂。本文对导弹内部各质量块的位置参数采用正弦输入信号,通过改变正弦输入信号的角频率进行仿真实验,进而分析各质量块运动速度及加速度对系统的影响,仿真结果表明当质量块运动速度及加速度在一定范围内变化时,可以对绕质心转动方程进行简化。
在质量矩控制导弹简化模型基础上,利用Lyapunov理论对质量矩控制导弹进行了稳定性分析。应用时标分离方法将系统分成快、慢两个子系统,采用动态逆控制方法对控制导弹的非线性系统进行了设计,仿真结果验证了此方法的可行性。
在不同的初始条件下,根据视线坐标系、惯性坐标系及弹体坐标系的转换关系,采用修正的比例导引律对导弹拦截目标进行了空间全弹道仿真,对所给出的简化模型做了进一步的验证,使质量矩控制导弹的工程实现成为可能。
The main research contents of this paper are the modeling and model simplification analysis of three-axis stabilized mass moment control missile.Establishing the center of mass movement and rotation around the center of mass kinetic equation according to Newton's laws of motion.The model is nonlinear, strong coupling and so on, in order to facilitate the design of control system, the model was necessary to be simplified.
The simplification of equation of motion of mass is relatively simple. While the simplification of rotating around the center of mass kinetic equations is relatively more complex because the movement of mass within the missile. It is inputted sine signal to the position parameters of the mass moment within the missile, simulation experiment is conducted by changing the angular frequency of sinusoidal, and then analyzes the effect of velocity and acceleration of mass moment on the system. Simulation results demonstrate that when the velocity and mass acceleration changes in a certain range, we can accomplish the simplification of equation around the center of mass.
According to the simplified model of the missile, the stability analysis of three-axis stabilized mass moment control missile is done on the support of Lyapunov theory. The system is departed into a fast and a slow subsystem with the application of separation of time scale.The nonlinear system of the control of the missile is designed with the dynamic inversion method, this method is proved feasible by the simulation experiment.
In different initial conditions, according to the transformation of vision coordinate system, inertial coordinate system and the body coordinate system,adopt modified proportional guidance law to intercept the missile target in space the whole trajectory simulation on the simplified model given to do further verification, it made the engineering realization of mass moment control missile become possible.
引文
1.于本水.防空导弹总体设计.宇航出版社, 1995年11月
2.戈罗别夫,斯维特洛夫编.防空导弹设计.张志鸿等译
3.高长生.导弹质量矩控制技术发展综述.宇航学报, 2010(02): 17-21
4. T. Petsopoulos, F. J. Regan. A Moving-mass roll control system for fixed-trim reentry vehicle
5. T. Petsopoulos, F. J. Regan, and J. Barlow. Moving-mass roll control system for fixed-trim reentry vehicle. Journal of Spacecraft and Rockets, 1996, 33(1): 54-60
6. Raymond H. Byrne, R.R. Sturgis ,R. D. Robinett. A Moving Mass Trim Control System For Reentry Vehicle Guidance. AIAA-96-3438-CP
7. D. M. Halsmer, D. L. Mingori. The passive control attenuator(PCA);Internal mass motion and axial thrust combine to produce asymptotic nutational stability. AIAA-92-4544-CP
8. D. M. Halsmer, Nutational Stability and Passive Control of Symmetric Spinning Bodies with axial Forcing and Internal Mass Motion
9. T. Petsopoulos. A Moving-mass roll control system for a fixed-trim reentry vehicle. M.S. Thesis, Univ. of Maryland. College Park
10. John E.White, R. D. Robinett III. Principal Axis Misalignment Control for Deconing of Spinning Spacecraft. Journal of Guidance, Control, and Dynamics, July-August 2004, Vol.17, No.4: 823-830
11. Dr. P. K. Menon. Integrated Guidance and Control of Moving Mass Actuated Kinetic Energy Kill Vehicles. Optimal Synthesis Inc
12. Kevin A. Wise, David J. Broy. Agile Missile Dynamics and Control. Journal of Guidance, Control, and Dynamics, ,1998, Vol(21): 441-449
13. Craig A. Phillips, James M. Chisholm. Missile guidance and control challenges for short range anti-air warfare . AIAA-95-3283-CP
14. P.K.Menon, G.d.Sweriduk, E.J.Ohlmeyer, D.S.Malyevac. Integrated Guidance and Control of Moving Mass Actuated Kinetic Warheads
15. Zarchan,P., Tactical and Strategic Missile Guidance, 2nd Edition, 1994, AIAA Press
16. Raymond H. Byrne , R. D. Robinett III, R.R. Sturgis. Moving Mass Trim Control System Design. AIAA-96-3826
17. C. A. Woolsey, N. E. Leonard. Moving Mass Control for Underwater Vehicles. Proceedings of the American Control Conference Anchorage, 2002, May 8-10
18. A. Malmgren. Modeling and Analysis of Rolling Missiles with a Single Control Surface Plane. AIAA-99-3977
19. Kerry Gildea. Services Eye New Design For Future Dual-Role Missile. Defence Daily
20. Menon, P.K., Iragavarapu, V.R., Ohlmeyer, E.J. , Integrated Design of Agile Missile Guidance and Control System, AIAA Missile sciences Conference, November 17-19, 1998, Monterey, CA
21. Chadwick, W.R., Malyevac, D.S., Considerations on the Design of Kinetic Kill Interceptor with Moving Mass Control, Draft Report
22. NSWCDD TR00/87, Naval Surface Warfare Center, Dahlgren, VA, August, 2000
23. Menon, P.K., Iragavarapu, V.R., Integrated Design of Agile Missile Guidance and Control Systems, Final Report Submitted under Nary Contract No. N00178-97-C-1028, Optimal Synthesis Inc., Palo Alto, CA, October 1998
24. C. A. Woolsey, N. E. Leonard. Stabilizing underwater vehicle motion using internal rotors. To appear in Automatica
25. R.D.Robinett, B.Rainwater, S.A.Kerr, Moving mass trim control for aerospace vehicles, in Proc. Of the Annual AIAA. Missile Sciences Conference, 1994
26. Mick L. Blackledge, Mass Moment Missile, Navy PEO Theater Surface Combatants
27.周凤岐等.弹道式导弹弹头变质心机动控制.宇航学报, Vol.21增刊, 2000年11月:
28-30
28.廖国宾.质量矩导弹的神经网络及自适应非线性控制(英文).宇航学报, 2004(05): 19-20
29.廖国宾.质量矩控制技术的机理分析及方程简化研究.系统工程与电子技术, 2004(11): 23-26
30.廖国宾.质量矩控制导弹制导控制系统的仿真研究.战术导弹技术, 2004(05): 36-37
31.贺有智.基于混合灵敏度下H_∞控制在三质量块质量矩导弹上的应用.宇航学报, 2006(06): 21-23
32.贺有智.模糊变结构在三质量块质量矩导弹系统上的应用.系统工程与电子技术, 2005(02): 11-12
33.贺有智.神经网络在质量矩导弹控制系统上的应用.系统工程与电子技术, 2005(01): 30-32
34.张有济.战术导弹飞行力学设计(上、下).宇航出版社, 1998年8月
35.钱杏芳,林瑞雄,赵亚男.导弹飞行力学.北京理工大学出版社, 2000
36.曾颖超,陆毓敏.战术导弹与姿态动力学.西北工业大学出版社
37.西北工业大学主编.理论力学(上、下册)
38.袁子怀.有控飞行力学与计算机仿真.国防工业出版社, 2001年4月
39.张景绘.动力学系统建模.国防工业出版社, 2002年2月
40.郝丽杰.质量矩控制导弹的建模与仿真研究,系统仿真学报, 2005(09): 27-30
41.徐明友.弹箭飞行动力学.国防工业出版社, 2003年1月
42.周韬.导弹质量矩控制技术建模与静态性能分析.宇航学报, 2006(05): 5-8
43. Isidori Alberto. Nonlinear Control Systems (2nd Edition). Springer Verlag,1989
44. Sadhukhan D., Feteih S. F8 Neurocontroller Based on Dynamics Inversion. J. Guid.Contr.Dyn.,1996,19(1):150-156
45. Botrots S.M., Caglayan A.K., Zacharias G.L. Learning the Nonlinear Inverse Flight Dynamics Using Radial Basis Functions. Proc.of the ACC, Washington. 2005:3510-3514
46. Michael B.McFarland, Shaheen M.Hoque, Robustness of A Nonlinear Missile Autopilot Design Using Dynamic Inversion. AIAA-2000-3970
47. Commuri S., Lewis F.L. CMAC Neural Networks for Nonlinear Dynamical Systems: Structure, Stability and Passivity, Automatica. 2007, 33 (4):635-431
48. Michael B.McFarland, Anthony J.Calise. Multilayer Neural Networks and adaptive Nonlinear Control of Agile Anti-air Missiles
49.胡正东.基于质量矩技术的机动弹头再入仿真研究.飞行力学, 2007(02): 13-15
50.姜宇.一种质量矩飞行器配置方案及其控制问题分析.系统工程与电子技术, 2008(02): 30-34
51.易彦等.基于变质心控制导弹的运动分析.航天控制, 2010年第3期: 40-43
52.崔利明.弹头变质心机动控制系统的设计与仿真.西北工业大学硕士论文. 1999年
53.崔利明.弹头变质心机动控制系统的设计与仿真.西北工业大学博士论文. 2001年
54.绪方胜彦著,卢伯英等译.现代控制工程.科学出版社, 1981
55.徐明友.用李亚普诺夫直接法建立弹箭飞行动稳定条件.南京理工大学学报, 2007(1): 3-5
56.王忠俊.非线性飞行控制方法研究概述.飞行力学, Vol.13, No.3, 1995.9
57.冯纯伯,费树氓.非线性控制系统分析与设计.电子工业出版社, 1998
58.高长生.质量矩导弹构型及自适应控制律设计.航空学报, 2010(08): 9-11
59.张友安,胡云安.导弹控制和制导的非线性设计方法.国防工业出版社, 2003.7:79-92
60.李琳琳,赵光恒,赵长安.不确定性非线性系统鲁棒控制研究.宇航学报, 2008, Vol.24 , No.4
61.彭冠一.防空导弹武器制导控制系统设计(上).宇航出版社, 1996年2月
62. Hodapp.A.E.,Jr., Clark,E.,L.,Jr. A Technique for Determining Approximate Roll RateHistories for Ballistic Reentry Vehicles Having Mass, Inertia, and Aerodynamic Asymmetries. Sandia National Labs.,Rept. SC-CR-69-804, Albuquerque, NM
63. Mc Dowell, D.M., Irwin.C.W., McConnell. Online Neural Control Applied to a Bank-to-Turn Missile Autopilot. Proceedings of the AIAA Guidance, Navigation, and Control Conference, baltimore, MD, 1995:1280-1294
64. Jagannathan S., Commuri S., Lewis F.L. Feedback Linearization Using CMAC Neural Networks. Automatica. 2008, 34(5):547-557
65.文仲辉.导弹系统分析与设计.北京理工大学出版社, 1989年10月
66. P.Garnell. Guided Weapon Control Systems. Revised by Prof.Qi Zai-kang and Xia Qun-li Flying Vehicle Engineering Department. Beijing Institute of Technology
67.李春文,冯元昆.多变量非线性控制的逆系统方法.清华大学出版社, 1991年
2.戈罗别夫,斯维特洛夫编.防空导弹设计.张志鸿等译
3.高长生.导弹质量矩控制技术发展综述.宇航学报, 2010(02): 17-21
4. T. Petsopoulos, F. J. Regan. A Moving-mass roll control system for fixed-trim reentry vehicle
5. T. Petsopoulos, F. J. Regan, and J. Barlow. Moving-mass roll control system for fixed-trim reentry vehicle. Journal of Spacecraft and Rockets, 1996, 33(1): 54-60
6. Raymond H. Byrne, R.R. Sturgis ,R. D. Robinett. A Moving Mass Trim Control System For Reentry Vehicle Guidance. AIAA-96-3438-CP
7. D. M. Halsmer, D. L. Mingori. The passive control attenuator(PCA);Internal mass motion and axial thrust combine to produce asymptotic nutational stability. AIAA-92-4544-CP
8. D. M. Halsmer, Nutational Stability and Passive Control of Symmetric Spinning Bodies with axial Forcing and Internal Mass Motion
9. T. Petsopoulos. A Moving-mass roll control system for a fixed-trim reentry vehicle. M.S. Thesis, Univ. of Maryland. College Park
10. John E.White, R. D. Robinett III. Principal Axis Misalignment Control for Deconing of Spinning Spacecraft. Journal of Guidance, Control, and Dynamics, July-August 2004, Vol.17, No.4: 823-830
11. Dr. P. K. Menon. Integrated Guidance and Control of Moving Mass Actuated Kinetic Energy Kill Vehicles. Optimal Synthesis Inc
12. Kevin A. Wise, David J. Broy. Agile Missile Dynamics and Control. Journal of Guidance, Control, and Dynamics, ,1998, Vol(21): 441-449
13. Craig A. Phillips, James M. Chisholm. Missile guidance and control challenges for short range anti-air warfare . AIAA-95-3283-CP
14. P.K.Menon, G.d.Sweriduk, E.J.Ohlmeyer, D.S.Malyevac. Integrated Guidance and Control of Moving Mass Actuated Kinetic Warheads
15. Zarchan,P., Tactical and Strategic Missile Guidance, 2nd Edition, 1994, AIAA Press
16. Raymond H. Byrne , R. D. Robinett III, R.R. Sturgis. Moving Mass Trim Control System Design. AIAA-96-3826
17. C. A. Woolsey, N. E. Leonard. Moving Mass Control for Underwater Vehicles. Proceedings of the American Control Conference Anchorage, 2002, May 8-10
18. A. Malmgren. Modeling and Analysis of Rolling Missiles with a Single Control Surface Plane. AIAA-99-3977
19. Kerry Gildea. Services Eye New Design For Future Dual-Role Missile. Defence Daily
20. Menon, P.K., Iragavarapu, V.R., Ohlmeyer, E.J. , Integrated Design of Agile Missile Guidance and Control System, AIAA Missile sciences Conference, November 17-19, 1998, Monterey, CA
21. Chadwick, W.R., Malyevac, D.S., Considerations on the Design of Kinetic Kill Interceptor with Moving Mass Control, Draft Report
22. NSWCDD TR00/87, Naval Surface Warfare Center, Dahlgren, VA, August, 2000
23. Menon, P.K., Iragavarapu, V.R., Integrated Design of Agile Missile Guidance and Control Systems, Final Report Submitted under Nary Contract No. N00178-97-C-1028, Optimal Synthesis Inc., Palo Alto, CA, October 1998
24. C. A. Woolsey, N. E. Leonard. Stabilizing underwater vehicle motion using internal rotors. To appear in Automatica
25. R.D.Robinett, B.Rainwater, S.A.Kerr, Moving mass trim control for aerospace vehicles, in Proc. Of the Annual AIAA. Missile Sciences Conference, 1994
26. Mick L. Blackledge, Mass Moment Missile, Navy PEO Theater Surface Combatants
27.周凤岐等.弹道式导弹弹头变质心机动控制.宇航学报, Vol.21增刊, 2000年11月:
28-30
28.廖国宾.质量矩导弹的神经网络及自适应非线性控制(英文).宇航学报, 2004(05): 19-20
29.廖国宾.质量矩控制技术的机理分析及方程简化研究.系统工程与电子技术, 2004(11): 23-26
30.廖国宾.质量矩控制导弹制导控制系统的仿真研究.战术导弹技术, 2004(05): 36-37
31.贺有智.基于混合灵敏度下H_∞控制在三质量块质量矩导弹上的应用.宇航学报, 2006(06): 21-23
32.贺有智.模糊变结构在三质量块质量矩导弹系统上的应用.系统工程与电子技术, 2005(02): 11-12
33.贺有智.神经网络在质量矩导弹控制系统上的应用.系统工程与电子技术, 2005(01): 30-32
34.张有济.战术导弹飞行力学设计(上、下).宇航出版社, 1998年8月
35.钱杏芳,林瑞雄,赵亚男.导弹飞行力学.北京理工大学出版社, 2000
36.曾颖超,陆毓敏.战术导弹与姿态动力学.西北工业大学出版社
37.西北工业大学主编.理论力学(上、下册)
38.袁子怀.有控飞行力学与计算机仿真.国防工业出版社, 2001年4月
39.张景绘.动力学系统建模.国防工业出版社, 2002年2月
40.郝丽杰.质量矩控制导弹的建模与仿真研究,系统仿真学报, 2005(09): 27-30
41.徐明友.弹箭飞行动力学.国防工业出版社, 2003年1月
42.周韬.导弹质量矩控制技术建模与静态性能分析.宇航学报, 2006(05): 5-8
43. Isidori Alberto. Nonlinear Control Systems (2nd Edition). Springer Verlag,1989
44. Sadhukhan D., Feteih S. F8 Neurocontroller Based on Dynamics Inversion. J. Guid.Contr.Dyn.,1996,19(1):150-156
45. Botrots S.M., Caglayan A.K., Zacharias G.L. Learning the Nonlinear Inverse Flight Dynamics Using Radial Basis Functions. Proc.of the ACC, Washington. 2005:3510-3514
46. Michael B.McFarland, Shaheen M.Hoque, Robustness of A Nonlinear Missile Autopilot Design Using Dynamic Inversion. AIAA-2000-3970
47. Commuri S., Lewis F.L. CMAC Neural Networks for Nonlinear Dynamical Systems: Structure, Stability and Passivity, Automatica. 2007, 33 (4):635-431
48. Michael B.McFarland, Anthony J.Calise. Multilayer Neural Networks and adaptive Nonlinear Control of Agile Anti-air Missiles
49.胡正东.基于质量矩技术的机动弹头再入仿真研究.飞行力学, 2007(02): 13-15
50.姜宇.一种质量矩飞行器配置方案及其控制问题分析.系统工程与电子技术, 2008(02): 30-34
51.易彦等.基于变质心控制导弹的运动分析.航天控制, 2010年第3期: 40-43
52.崔利明.弹头变质心机动控制系统的设计与仿真.西北工业大学硕士论文. 1999年
53.崔利明.弹头变质心机动控制系统的设计与仿真.西北工业大学博士论文. 2001年
54.绪方胜彦著,卢伯英等译.现代控制工程.科学出版社, 1981
55.徐明友.用李亚普诺夫直接法建立弹箭飞行动稳定条件.南京理工大学学报, 2007(1): 3-5
56.王忠俊.非线性飞行控制方法研究概述.飞行力学, Vol.13, No.3, 1995.9
57.冯纯伯,费树氓.非线性控制系统分析与设计.电子工业出版社, 1998
58.高长生.质量矩导弹构型及自适应控制律设计.航空学报, 2010(08): 9-11
59.张友安,胡云安.导弹控制和制导的非线性设计方法.国防工业出版社, 2003.7:79-92
60.李琳琳,赵光恒,赵长安.不确定性非线性系统鲁棒控制研究.宇航学报, 2008, Vol.24 , No.4
61.彭冠一.防空导弹武器制导控制系统设计(上).宇航出版社, 1996年2月
62. Hodapp.A.E.,Jr., Clark,E.,L.,Jr. A Technique for Determining Approximate Roll RateHistories for Ballistic Reentry Vehicles Having Mass, Inertia, and Aerodynamic Asymmetries. Sandia National Labs.,Rept. SC-CR-69-804, Albuquerque, NM
63. Mc Dowell, D.M., Irwin.C.W., McConnell. Online Neural Control Applied to a Bank-to-Turn Missile Autopilot. Proceedings of the AIAA Guidance, Navigation, and Control Conference, baltimore, MD, 1995:1280-1294
64. Jagannathan S., Commuri S., Lewis F.L. Feedback Linearization Using CMAC Neural Networks. Automatica. 2008, 34(5):547-557
65.文仲辉.导弹系统分析与设计.北京理工大学出版社, 1989年10月
66. P.Garnell. Guided Weapon Control Systems. Revised by Prof.Qi Zai-kang and Xia Qun-li Flying Vehicle Engineering Department. Beijing Institute of Technology
67.李春文,冯元昆.多变量非线性控制的逆系统方法.清华大学出版社, 1991年