Sensitivity Analysis of Design Bandwidth of Missile Three-loop Acceleration Control

doi:10.3969/j.issn.1000-1093.2014.12.014

Abstract

Abstract: Because the aerodynamic uncertainties of a missile are distributed in the coupling subsystems for the popularly used three-loop acceleration autopilot, the traditional stability margins are unable to illustrate the robust range of the closed-loop system in relative to the uncertain characteristic parameters.The acceleration control is parameterized by using a design bandwidth, and then the closed-loop sensitivity of the restoring and manipulation moment coefficients with regard to this bandwidth is investigated in a unified manner by means of the D-decomposition method. The robust stability of the closed-loop system is described. The numerical examples demonstrate that the proposed method can provide the accurate robust stability boundary of the closed-loop system to the primary uncertain factors, revealing the variation rule of the sensitivity of the bandwidth to statically unstable and stable missiles. The key factor in determining the crucial angular velocity gain is also specified as the manipulation moment coefficient.

Key words: control and navigation technology of aerocraft, three-loop autopilot, robustness, sensitivity, frequency bandwidth

CLC Number:

V448

SUN Ming-wei, ZHANG Li-min, CHEN Zeng-qiang. Sensitivity Analysis of Design Bandwidth of Missile Three-loop Acceleration Control[J]. Acta Armamentarii, 2014, 35(12): 2023-2029.

References

［1］刘代军. 主动控制技术在空空导弹中的应用[J]．战术导弹技术, 2001(5)：43-49.
LIU Dai-jun．The application of active control technology to air to air missiles[J]. Tactical Missile Technology, 2001(5):43-49.(in Chinese)
[2] Zarchan P. Tactical and strategic missile guidance[M]. 5rd ed.Virginia: AIAA Inc, 2007:483-539.
[3] Nesline F W，Nesline M L. How autopilot requirements constrain the aerodynamic design of homing missiles[C]∥American Control Conference. San Diego, CA:IEEE, 1984:716-730.
[4] Mracek C P，Ridgely D B. Missile longitudinal autopilot: comparison of multiple three loop topologies[C]∥AIAA Guidance, Navigation, and Control Conference．San Francisco, CA:AIAA, 2005:2005-6380.
[5] 王娟利，祁载康. 三回路自动驾驶仪特点分析[J]．北京理工大学学报, 2006, 26(3):239-243.
WANG Juan-li, QI Zai-kang. Analysis of a three-loop autopilot[J]. Transactions of Beijing Institute of Technology, 2006, 26(3):239-243. (in Chinese)
[6] 李友年，郑鹍鹏，陈星阳. 三回路过载驾驶仪的快速性极限分析[J]. 弹箭与制导学报, 2013, 33(3):17-24.
LI You-nian，ZHENG Kun-peng，CHEN Xing-yang．Rapidity limitation analysis of three-loop acceleration autopilot[J]．Journal of Projectiles, Rockets, Missiles, and Guidance, 2013, 33(3):17-24.(in Chinese)
[7] 王嘉鑫，林德福，祁载康. 战术导弹三回路过载驾驶仪时频特性分析[J]．兵工学报，2013，34(7)：828-834.
WANG Jia-xin，LIN De-fu，QI Zai-kang．Analysis of tactical missile three-loop lateral acceleration autopilot in the time and frequency domain[J]．Acta Armamentarii, 2013, 34(7):828-834.(in Chinese)
[8] 朱敬举，祁载康，夏群力. 三回路驾驶仪的极点配置方法设计[J]．弹箭与制导学报，2007，27(4)：8-12.
ZHU Jing-ju, QI Zai-kang, XIA Qun-li. Pole assignment method for three-loop autopilot design[J]．Journal of Projectiles, Rockets, Missiles, and Guidance, 2007, 27(4):8-12.(in Chinese)
[9] 温求遒，夏群力，祁载康. 三回路驾驶仪开环穿越频率约束极点配置设计[J]．系统工程与电子技术，2009，31(2)：420-423.
WEN Qiu-qiu，XIA Qun-li，QI Zai-kang．Pole placement design with open-loop crossover frequency constraint for three-loop autopilot[J]．System Engineering and Electronics, 2009, 31(2):420-423. (in Chinese)
[10] 杨育荣，李友年，王建琦，等. 三回路自动驾驶仪频域设计法[J]. 航空兵器, 2010(6):33-36.
YANG Yu-rong, LI You-nian, WANG Jian-qi, et al．Frequency domain design of three-loop autopilot[J]. Aero Weaponry, 2010(6):33-36. (in Chinese)
[11] 刁兆师，单家元. 基于预测校正的三回路驾驶仪极点配置设计[J]. 系统工程与电子技术, 2012, 34(8):1668-1674.
DIAO Zhao-shi，SHAN Jia-yuan．Pole assignment design with prediction-correction technology for three-loop autopilots[J]. System Engineering and Electronics, 2012, 34(8):1668-1674.(in Chinese)
[12] 王辉，林德福，祁载康. 导弹伪攻角三回路驾驶仪设计分析[J]. 系统工程与电子技术, 2012, 34(1):129-135.
WANG Hui，LIN De-fu，QI Zai-kang．Design and analysis of missile three-loop autopilot with pseudo-angle of attack feedback[J]．System Engineering and Electronics, 2012, 34(1):129-135.(in Chinese)
[13] 徐俊, 曹军义, 曹秉刚, 等. 空空导弹分数阶三回路自动驾驶仪的分析与参数优化[J]. 西安交通大学学报, 2011,45(12): 33-38.
XU Jun,CAO Jun-yi, CAO Bing-gang, et al. Fractional three-loop autopilot of air-to-air missile with parameter optimization[J]. Journal of Xi’an Jiaotong University, 2011, 45(12):33-38.(in Chinese)
[14] Wise K A. Robust stability analysis of adaptive missile autopilots[C]∥AIAA Guidance, Navigation, and Control Conference.Honolulu, HI:AIAA, 2008:2008-6999.
[15] 林德福. 战术导弹自动驾驶仪设计与制导律分析[M]. 北京: 北京理工大学出版社, 2012:64-71.
LIN De-fu. Autopilot design and guidance law analysis for tactical missiles[M].Beijing:Beijing Institute of Technology Press, 2012:64-71.(in Chinese)
[16] 郑鹍鹏, 华建林, 姜殿民. 三回路驾驶仪控制下的导弹静不稳定性边界[J]. 四川兵工学报, 2013, 34(5):27-30.
ZHENG Kun-peng，HUA Jian-lin，JIANG Dian-min. Static-unstable stabilizing limitation of missile under control of three loop autopilot[J]. Journal of Sichuan Ordnance, 2013, 34(5):27-30.(in Chinese)
[17] Wise K A. Singular value robustness tests for missile autopilot uncertainties[J].Journal of Guidance, Control, and Dynamics, 1991, 14(3):597-606.
[18] Wedell E, Chuang C H, Wie B. Stability robustness margin computation for structured real-parameter perturbations[J]. Journal of Guidance, Control, and Dynamics, 1991, 14(3):607-614.
[19] Wise K A. Missile autopilot robustness using the real multiloop stability margin[J]. Journal of Guidance, Control, and Dynamics, 1993, 16(2):354-362.
[20] Wie B, Lu J. Two real critical constraints for real parameter margin computation[J]. Journal of Guidance, Control, and Dynamics, 1994, 17(3):561-569.
[21] Tsourdos A, White B A, Bruyere L. Robust analysis for missile lateral acceleration control using finite inclusion theorem[J]. Journal of Guidance, Control, and Dynamics, 2005, 28(2):679- 685.
[22] Bruyere L, Tsourdos A, White B A. Polynomial approach for design and robust analysis of lateral missile control [J]. International Journal of Systems Science, 2006, 37(8):585-597.
[23] 孙宝彩, 祁载康, 林德福, 等. 巡飞导弹BTT自动驾驶仪设计与仿真[J]. 弹箭与制导学报, 2007, 27(5):21-28.
SUN Bao-cai, QI Zai-kang, LIN De-fu, et al.BTT autopilot design and simulation for loiter attack angle[J]．Journal of Projectiles, Rockets, Missiles, and Guidance, 2007, 27(5):21-28.(in Chinese)

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