激光制导炸弹控制方法的研究
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摘要
制导炸弹作为精确打击武器,在现代战争中发挥的作用越来越重要,激光制导炸弹作为制导炸弹的一种,受到世界各国的重视。本文给出了比例导引激光制导炸弹自动驾驶仪的设计方法。
建立了激光制导炸弹的动力学方程和运动学方程。在弹体轴对称且不滚转假设条件下,把炸弹运动方程解耦成俯仰、偏航和滚转三个独立通道,经过线性化处理,得到系统线性化模型。
详细讨论了H∞/混合灵敏度设计中加权函数的选取方法。基于H∞/混合灵敏度设计方法,对某比例导引激光制导炸弹的俯仰和偏航通道自动驾驶仪分别进行了设计,以俯仰通道数值仿真验证了所设计的控制系统对系统参数摄动的鲁棒性和跟踪过载指令的性能。用古典控制理论进行了滚转通道设计。
把基于H∞/混合灵敏度方法设计的飞行控制系统与基于古典控制理论设计的飞行控制系统进行鲁棒性和指令跟踪性能比较,得出的结论是H∞/混合灵敏度方法设计的系统效果较好。
将三个通道结合在一起,进行了六自由度全弹道仿真,检验H∞/混合灵敏度自动驾驶仪的控制效果。仿真结果证明, H∞/混合灵敏度自动驾驶仪对于参数摄动具有强鲁棒性,能够抑制干扰和噪声,并且能够快速跟踪过载指令。
在MATLAB环境下,编写了三维动画程序将全弹道仿真数据复现在三维空间,演示了激光制导炸弹在整个飞行过程中飞行轨迹和姿态信息。
As a precision strike weapon, the guided bomb more and more plays an important role in a modern war. The laser guided bomb with Proportional Navigation guidance law is a main kind of guided bomb, and has been developed in many countries. In this paper, the autopilot of this guided bomb is designed.
Dynamic equations and kinematic equations are established for the design. Assuming that the body of the bomb is symmetrical and non-rolling, we decouple the motion equations into pitch, yaw and roll channels. Each channel is represented by a linearized model.
A crucial technique in H-infinity mixed sensitivity design is how to properly choose the weighting functions that reflect both stability and performance requirements. This technique is carefully discussed. With the mixed sensitivity tool, the autopilots of pitch and yaw channels are designed, respectively. To test the control systems’robustness against the bomb system uncertainties and the command tracking performance of the designed systems, single channel simulation results are provided. The controller of the roll channel is designed with classical control tool.
Comparing the mixed sensitivity design with a design based on the classical control tool, we conclude that the mixed sensitivity design achieves better robustness and command tracking performance. To verify the effectiveness of the H-infinity mixed sensitivity autopilot, we combine the three channels to simulate the six-degree of freedom motion of the guided bomb in a whole flight path. This simulation also proves that the H-infinity mixed sensitivity autopilot has better robustness against parameters’uncertainties, and it effectively attenuates disturbances and noises, and tracks an overload command rapidly.
In order to intuitively show the variations of the guided bomb in a whole flight course, a three dimensional animation program is written in Matlab environment.
建立了激光制导炸弹的动力学方程和运动学方程。在弹体轴对称且不滚转假设条件下,把炸弹运动方程解耦成俯仰、偏航和滚转三个独立通道,经过线性化处理,得到系统线性化模型。
详细讨论了H∞/混合灵敏度设计中加权函数的选取方法。基于H∞/混合灵敏度设计方法,对某比例导引激光制导炸弹的俯仰和偏航通道自动驾驶仪分别进行了设计,以俯仰通道数值仿真验证了所设计的控制系统对系统参数摄动的鲁棒性和跟踪过载指令的性能。用古典控制理论进行了滚转通道设计。
把基于H∞/混合灵敏度方法设计的飞行控制系统与基于古典控制理论设计的飞行控制系统进行鲁棒性和指令跟踪性能比较,得出的结论是H∞/混合灵敏度方法设计的系统效果较好。
将三个通道结合在一起,进行了六自由度全弹道仿真,检验H∞/混合灵敏度自动驾驶仪的控制效果。仿真结果证明, H∞/混合灵敏度自动驾驶仪对于参数摄动具有强鲁棒性,能够抑制干扰和噪声,并且能够快速跟踪过载指令。
在MATLAB环境下,编写了三维动画程序将全弹道仿真数据复现在三维空间,演示了激光制导炸弹在整个飞行过程中飞行轨迹和姿态信息。
As a precision strike weapon, the guided bomb more and more plays an important role in a modern war. The laser guided bomb with Proportional Navigation guidance law is a main kind of guided bomb, and has been developed in many countries. In this paper, the autopilot of this guided bomb is designed.
Dynamic equations and kinematic equations are established for the design. Assuming that the body of the bomb is symmetrical and non-rolling, we decouple the motion equations into pitch, yaw and roll channels. Each channel is represented by a linearized model.
A crucial technique in H-infinity mixed sensitivity design is how to properly choose the weighting functions that reflect both stability and performance requirements. This technique is carefully discussed. With the mixed sensitivity tool, the autopilots of pitch and yaw channels are designed, respectively. To test the control systems’robustness against the bomb system uncertainties and the command tracking performance of the designed systems, single channel simulation results are provided. The controller of the roll channel is designed with classical control tool.
Comparing the mixed sensitivity design with a design based on the classical control tool, we conclude that the mixed sensitivity design achieves better robustness and command tracking performance. To verify the effectiveness of the H-infinity mixed sensitivity autopilot, we combine the three channels to simulate the six-degree of freedom motion of the guided bomb in a whole flight path. This simulation also proves that the H-infinity mixed sensitivity autopilot has better robustness against parameters’uncertainties, and it effectively attenuates disturbances and noises, and tracks an overload command rapidly.
In order to intuitively show the variations of the guided bomb in a whole flight course, a three dimensional animation program is written in Matlab environment.
引文
1范金荣.制导炸弹的发展综述.现代防御技术. 2004, 32 (3):27~31
2谢建华.未来战场的明星武器.现代防御技术. 2001, 29(1):33~36
3李保平.航空制导炸弹的发展技术途径与关键技术.弹箭与制导学报.2006:101~102
4范保虎,赵长明,马国强.激光制导技术在现代武器中的应用与发展.飞航导弹. 2006, (5): 47~50
5张求知,李克己,姜长生.激光制导炸弹的火控原理及应用.火力与指挥控制. 2001, 26(1):18~22
6 G. Zames. Input-output Feedback Stability and Robustness 1959-85. IEEE Control Systems. 1996:61~66
7 B. A. Francis, J. C. Doyle. Linear Control Theory with an H∞Optional Criterion. SIAM Control Opt. 1987, (25):815~844
8 J. C. Doyle, K. Glover, P. Khargonegar, B. A. Francis. State-Space Solution to Standard H 2 and H∞Control Problem. IEEE Trans Ac,1989, 34(8):381~347
9 K. Zhou, P. Khargonegar. An Algebraic Riccati Equation Approach to H∞Optimization. Systems Control Letter. 1988, (11):85~92
10 K. Glover, J. C. Doyle. State-Space Formulae for all Stabilizing Controllers that Satisfy and H∞Norm Bound and Relations Risk Sensitivity. Systems and Control Letters. 1988, (11):167~172
11 S. J. Williams, R. A. Hyde. A Comparison of Different H∞Methods in VSTOL Flight Control System Design. AIAA Conference on G. N. &C, 1992: 2508~2513
12 R. Y. Chiang and M. G. Safonov. Robust Control Toolbox. Natick, MA: The MathWorks, 1992:23~42
13 G. J. Balas, J. C. Doyle, K. Glover, A. Packard, R. Smith.μ-Analysis and Synthesis Toolbox. Natick, MA: The MathWorks, 1991:34~56
14郑建华,杨涤.鲁棒控制理论在倾斜转弯导弹中的应用.国防工业出版社, 2001:10~12
15郑建华,杨涤. BTT导弹H∞/加权混合灵敏度自动驾驶仪设计方法.宇航学报. 1998, 19(1):103~108
16陶涛,阉文博.航空发动机H∞/混合灵敏度控制中加权阵的选取.推进技术. 1999, 20(4):66~70
17宋斌,马广富.基于H∞鲁棒控制的挠性卫星姿态控制.系统仿真学报. 2005, 17(4):968~985
18姚郁,懂锡军.飞行仿真转台混合灵敏度设计.航天控制. 1999, (3): 65~70
19赵慧,姜洪洲. H∞混合灵敏度控制在液压伺服系统中的应用.中国机械工程. 2002, 13(3):195~197
20郑载满,游林儒. H∞在伺服系统中的应用.黑龙江自动化技术与应用. 1992, (2):7~10
21李友年,贾晓红,王海波. H∞控制理论在空空导弹自动驾驶仪设计中的应用.航空兵器. 2004, (6):12~14
22杨军,李江.基于H∞控制理论的某型导弹自动驾驶仪设计与仿真.军械工程学院学报. 2005, 17(6):11~17
23贺有智,张晓宇.基于混合灵敏度下H∞控制在三滑块质量矩导弹上的应用.宇航学报. 2006, 27(6):1254~1260
24吴建刚,周冉辉. H∞控制理论在飞航导弹姿态控制中的应用.湖北航天科技. 2005, (6):22~27
25高云霞,田沛.基于H∞混合灵敏度的主汽温控制系统的研究.华北电力大学学报. 2006, 33(1):76~79
26陶宏刚,蔡元虎.综合飞行/推进系统H∞控制设计.飞行力学. 2006, 24(3):80~83
27 F. Dale, Enns. Rocket Stabilization as a Structured Singular Value Synthesis Design Example. IEEE Control Systems. 1999, (6):67~73
28 H. Oloomi, B. Shafai. Weight Selection in Mixed Sensitivity Robust Control for Improving the Sinusoidal Tracking. Conference on Design and Control, Maui, Hawaii USA, 2003, (12):300~305
29 R. Galindo. Mixed Sensitivity H∞Control of a Three-Tank-System. American Control Conference , Portland, OR, USA, 2005:1764~1769
30 K. Okajima, K. Z. Liu. Improvement of the Transient Response of the Automatic Transmission of a Car by H∞Control. Trans of SICE, 1999, 35(1):147~149
31 S. Duchi, K. Z. Liu, et al. Mine Train Control System by H∞Control. Trans of SICE, 1998, 34(3):225~231
32 S. Mei, J. Chen, et al. Nonlinear Multi-target Controller for Thyristor-Controlled Series Compensation. IEEP Roc, Gener, Transm, Distrib, 2001, 148(6): 557~561
33梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用.清华大学出版社, 2003:219~242
34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: 28~60
35 G. Zames. Feedback and Optimal Sensitivity: Model Reference Transformations Multiplicative Seminars and Approxirpate Inverses. IEEE Transaction on Automatic Control. 1981, (26):301~320
36 D. S. Flamm, H. Yang. Optimal Mixed Sensitivity for SISO-distributed Plants.IEEE Transactions on Automatic Control. 1994, 39(6):1150~1165
37 F. Ruth. Curtain, Y. Zhou. A Weighted Mixed-Sensitivity H∞-Control Design for Irrational Transfer Matrices. IEEE Transactions on Automatic Control. 1996, 41(9):1312~1321
38 C. Foias, A. Tannenbaum, D. Enns. On the Nonlinear Mixed Sensitivity Problem. Proceeding of the 28th Conference on Decision and Control, Tampa, Florida, 1989:986~989
39 V. Kneppova, U. Kiffineier, H. Unbehauen. Weighting Function Selection in H∞-Optimal Control with Application to a Thyristor-driven DC-motor. Proceedings of the American Control Conference, Seattle Washington, 1995:3002~3008
40 V. Besson, A. Shenton. An Interactive Space Method for Robust Performance in Mixed Sensitivity Problems. IEEE Transactions on automatic Control, 1999, 44(6):1272~1276
41 I. Postlethwaite, T. Miching, D. Gu. Weighting Function Selection in H∞Design. 11th IFAC, Tallinn, 1990:104~109
42吴旭东,解学书. H∞鲁棒控制中的加权阵选择.清华大学学报(自然科学版). 1997, (37):27~30
43郑建华,张立荣,杨涤.大范围模型参数变化系统的H∞加权混合灵敏度设计方法研究.自动化学报. 1998, 24(5):707~710
44王曦,曾庆福.频域不确定性系统加权混合灵敏度函数频域整形.航空学报. 1999, 20(4):358~361
2谢建华.未来战场的明星武器.现代防御技术. 2001, 29(1):33~36
3李保平.航空制导炸弹的发展技术途径与关键技术.弹箭与制导学报.2006:101~102
4范保虎,赵长明,马国强.激光制导技术在现代武器中的应用与发展.飞航导弹. 2006, (5): 47~50
5张求知,李克己,姜长生.激光制导炸弹的火控原理及应用.火力与指挥控制. 2001, 26(1):18~22
6 G. Zames. Input-output Feedback Stability and Robustness 1959-85. IEEE Control Systems. 1996:61~66
7 B. A. Francis, J. C. Doyle. Linear Control Theory with an H∞Optional Criterion. SIAM Control Opt. 1987, (25):815~844
8 J. C. Doyle, K. Glover, P. Khargonegar, B. A. Francis. State-Space Solution to Standard H 2 and H∞Control Problem. IEEE Trans Ac,1989, 34(8):381~347
9 K. Zhou, P. Khargonegar. An Algebraic Riccati Equation Approach to H∞Optimization. Systems Control Letter. 1988, (11):85~92
10 K. Glover, J. C. Doyle. State-Space Formulae for all Stabilizing Controllers that Satisfy and H∞Norm Bound and Relations Risk Sensitivity. Systems and Control Letters. 1988, (11):167~172
11 S. J. Williams, R. A. Hyde. A Comparison of Different H∞Methods in VSTOL Flight Control System Design. AIAA Conference on G. N. &C, 1992: 2508~2513
12 R. Y. Chiang and M. G. Safonov. Robust Control Toolbox. Natick, MA: The MathWorks, 1992:23~42
13 G. J. Balas, J. C. Doyle, K. Glover, A. Packard, R. Smith.μ-Analysis and Synthesis Toolbox. Natick, MA: The MathWorks, 1991:34~56
14郑建华,杨涤.鲁棒控制理论在倾斜转弯导弹中的应用.国防工业出版社, 2001:10~12
15郑建华,杨涤. BTT导弹H∞/加权混合灵敏度自动驾驶仪设计方法.宇航学报. 1998, 19(1):103~108
16陶涛,阉文博.航空发动机H∞/混合灵敏度控制中加权阵的选取.推进技术. 1999, 20(4):66~70
17宋斌,马广富.基于H∞鲁棒控制的挠性卫星姿态控制.系统仿真学报. 2005, 17(4):968~985
18姚郁,懂锡军.飞行仿真转台混合灵敏度设计.航天控制. 1999, (3): 65~70
19赵慧,姜洪洲. H∞混合灵敏度控制在液压伺服系统中的应用.中国机械工程. 2002, 13(3):195~197
20郑载满,游林儒. H∞在伺服系统中的应用.黑龙江自动化技术与应用. 1992, (2):7~10
21李友年,贾晓红,王海波. H∞控制理论在空空导弹自动驾驶仪设计中的应用.航空兵器. 2004, (6):12~14
22杨军,李江.基于H∞控制理论的某型导弹自动驾驶仪设计与仿真.军械工程学院学报. 2005, 17(6):11~17
23贺有智,张晓宇.基于混合灵敏度下H∞控制在三滑块质量矩导弹上的应用.宇航学报. 2006, 27(6):1254~1260
24吴建刚,周冉辉. H∞控制理论在飞航导弹姿态控制中的应用.湖北航天科技. 2005, (6):22~27
25高云霞,田沛.基于H∞混合灵敏度的主汽温控制系统的研究.华北电力大学学报. 2006, 33(1):76~79
26陶宏刚,蔡元虎.综合飞行/推进系统H∞控制设计.飞行力学. 2006, 24(3):80~83
27 F. Dale, Enns. Rocket Stabilization as a Structured Singular Value Synthesis Design Example. IEEE Control Systems. 1999, (6):67~73
28 H. Oloomi, B. Shafai. Weight Selection in Mixed Sensitivity Robust Control for Improving the Sinusoidal Tracking. Conference on Design and Control, Maui, Hawaii USA, 2003, (12):300~305
29 R. Galindo. Mixed Sensitivity H∞Control of a Three-Tank-System. American Control Conference , Portland, OR, USA, 2005:1764~1769
30 K. Okajima, K. Z. Liu. Improvement of the Transient Response of the Automatic Transmission of a Car by H∞Control. Trans of SICE, 1999, 35(1):147~149
31 S. Duchi, K. Z. Liu, et al. Mine Train Control System by H∞Control. Trans of SICE, 1998, 34(3):225~231
32 S. Mei, J. Chen, et al. Nonlinear Multi-target Controller for Thyristor-Controlled Series Compensation. IEEP Roc, Gener, Transm, Distrib, 2001, 148(6): 557~561
33梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用.清华大学出版社, 2003:219~242
34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: 28~60
35 G. Zames. Feedback and Optimal Sensitivity: Model Reference Transformations Multiplicative Seminars and Approxirpate Inverses. IEEE Transaction on Automatic Control. 1981, (26):301~320
36 D. S. Flamm, H. Yang. Optimal Mixed Sensitivity for SISO-distributed Plants.IEEE Transactions on Automatic Control. 1994, 39(6):1150~1165
37 F. Ruth. Curtain, Y. Zhou. A Weighted Mixed-Sensitivity H∞-Control Design for Irrational Transfer Matrices. IEEE Transactions on Automatic Control. 1996, 41(9):1312~1321
38 C. Foias, A. Tannenbaum, D. Enns. On the Nonlinear Mixed Sensitivity Problem. Proceeding of the 28th Conference on Decision and Control, Tampa, Florida, 1989:986~989
39 V. Kneppova, U. Kiffineier, H. Unbehauen. Weighting Function Selection in H∞-Optimal Control with Application to a Thyristor-driven DC-motor. Proceedings of the American Control Conference, Seattle Washington, 1995:3002~3008
40 V. Besson, A. Shenton. An Interactive Space Method for Robust Performance in Mixed Sensitivity Problems. IEEE Transactions on automatic Control, 1999, 44(6):1272~1276
41 I. Postlethwaite, T. Miching, D. Gu. Weighting Function Selection in H∞Design. 11th IFAC, Tallinn, 1990:104~109
42吴旭东,解学书. H∞鲁棒控制中的加权阵选择.清华大学学报(自然科学版). 1997, (37):27~30
43郑建华,张立荣,杨涤.大范围模型参数变化系统的H∞加权混合灵敏度设计方法研究.自动化学报. 1998, 24(5):707~710
44王曦,曾庆福.频域不确定性系统加权混合灵敏度函数频域整形.航空学报. 1999, 20(4):358~361