具有极点约束的高超声速飞行器非脆弱
最优H2/LQR控制

上海交通大学学报（自然版） ›› 2011, Vol. 45 ›› Issue (03): 423-428.

具有极点约束的高超声速飞行器非脆弱
最优H2/LQR控制

黄宜庆, 王莉, 孙长银

(1. 东南大学自动化学院，南京 210096; 2. 扬州大学能源与动力工程学院，江苏扬州 225127)

出版日期:2011-03-30 发布日期:2011-03-30
基金资助:
国家自然科学基金资助项目（60953001，91016004，61004046）

Non-fragile Optimal H2/LQR Control with Regional Pole Placement for Hypersonic Vehicle

HUANG Yi-Qing, WANG Li, SUN Chang-Yin

(1. School of Automation, Southeast University, Nanjing 210096, China; 2. School of Energy and Power Engineering, Yangzhou University, Yangzhou 225127, Jiangsu, China)

Online:2011-03-30 Published:2011-03-30

摘要/Abstract

摘要： 针对吸气式高超声速飞行器，提出了一种具有极点约束的非脆弱最优H2/LQR（线性二次型调节器)控制方法.根据吸气式高超声速飞行器的非线性纵向运动方程，推出了一种新的飞行器线性不确定模型，为吸气式高超声速飞行器设计了一种多目标非脆弱控制器.在控制器的设计中，不但考虑了系统的极点配置、最优H2性能和鲁棒保性能3种指标，而且兼顾了因飞行条件不确定性和建模误差引起的控制器增益的变化，利用线性矩阵不等式方法推导了多目标非脆弱控制器的存在条件.仿真实例说明了非脆弱控制器在高超声速飞行器控制中的优越性和有效性.

关键词: 非脆弱控制, 最优H2/ 线性二次型调节器控制, 区域极点配置, 高超声速飞行器

Abstract: A kind of robust mixed nonfragile optimal H2/LQR control with regional pole placement was proposed for an airbreathing hypersonic vehicle (AHV). A new linear uncertain model was developed according to a nonlinear longitudinal model of an AHV and then a multiobjective nonfragile controller was designed that includes regional pole placement, robust guaranteed cost control and optimal H2 control performance indexes for the proposed linear uncertain model. The paper also took the gain variation of the controller into account due to parametric uncertainties of an AHV flight condition and the errors existed in modeling. The existed conditions of the multiobjective nonfragile controller were deduction by linear matrix inequalities (LMIs). Finally, the simulation comparisons between nonfragile controller and traditional controller that without considering the gain variation illustrate the advantages and effectiveness of our approach.

Key words: non-fragile control, optimal H2/LQR （linear quadratic regulator） control, regional pole placement, hypersonic vehicle

中图分类号:

V 249.1

黄宜庆, 王莉, 孙长银. 具有极点约束的高超声速飞行器非脆弱
最优H2/LQR控制[J]. 上海交通大学学报（自然版）, 2011, 45(03): 423-428.

HUANG Yi-Qing, WANG Li, SUN Chang-Yin. Non-fragile Optimal H2/LQR Control with Regional Pole Placement for Hypersonic Vehicle[J]. Journal of Shanghai Jiaotong University, 2011, 45(03): 423-428.

参考文献

［1］Michael A, Bolender. An overview on dynamics and controls modeling of hypersonic vehicles［C］// Proceedings of the American Control Conference. St. Louis, MO: IEEE Press, 2009:25072512.

［2］Naidu D S, Banda S S, Buffington J L. Unified approach to H2 and H∞ optimal control of a hypersonic vehicle［C］// Proceedings of the American Control Conference. San Diego, CA: IEEE Press, 1999:27372741.

［3］Wang Q, Stengel R F. Robust nonlinear control of a hypersonic aircraft ［J］. Journal of Guidance, Control, and Dynamics, 2000, 23(4):577585.

［4］Gao H J, Si Y L, Li H Y, et al. Modeling and control of an airbreathing hypersonic vehicle［C］//Proceedings of the 7th Asian Control Conference. Hong Kong : IEEE Press ,2009:304307.

［5］Gibson T E, Crespo L G, Annaswamy A M. Adaptive control of hypersonic vehicles in the Presence of modeling uncertainties［C］// Proceedings of the American Control Conference. St. Louis, MO: IEEE Press, 2009:31783183.

［6］Yan B B, Lu C K, Yu W W, et al, Fuzzy CMAC control design for an airbreathing hypersonic cruise vehicle［C］// The 4th IEEE Conference on Industrial Electronics and Applications. Xi’an: IEEE Press, 2009: 298301.

［7］Yee J S, Yang G H, Wang J L. Nonfragile H∞ flight controller design for a high performance aircraft［C］//Proceedings of the American Control Conference. Chicago, IL: IEEE Press, 2000:18571861.

［8］Liu L P, Han Z Z, Li W L. H∞ nonfragile observerbased sliding mode control for uncertain timedelay systems ［J］. Journal of the Franklin Institute, 2010, 347(2):567576.

［9］Song B, Xu S Y, Xia J W, et al. Design of robust nonfragile Hinfinity filters for uncertain stochastic systems with distributed delays ［J］. Asian Journal of Control, 2010, 12(1):3945.

［10］ Shu Z, Lam J, Xiong J L. Nonfragile exponential stability assignment of discretetime linear systems with missing data in actuators ［J］. IEEE Transactions on Automatic Control, 2009, 54(3):625630.

［11］ Famularo D, Dorato P. Robust nonfragile LQ controller the static state feedback case ［J］. Int J Control, 2000,73(2):159165.

［12］俞立. 鲁棒控制线性矩阵不等式处理方法［M］.北京: 清华大学出版社, 2002.

［13］黄宜庆, 黄友锐, 章魁. 直线伺服系统的双目标非脆弱控制器的设计与仿真［J］. 智能系统学报, 2009，4(1):8590.

HUANG Yiqing, HUANG Yourui, ZHANG Kui. Design and simulation on a dualobject nonfragile controller for linear motor servo system ［J］. CAAI Transactions on Intelligent Systems, 2009, 4(1):8590.

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