文章快速检索 高级检索

1. 北京航空航天大学 航空科学与工程学院, 北京 100083;
2. 北京航空航天大学 自动化科学与电气工程学院, 北京 100083

LPV robust tracking control for chain smooth switched morphing aircraft
JIA Zhen1, DONG Chaoyang1, WANG Qing2
1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-03-29; Accepted: 2016-07-01; Published online: 2016-10-10 08:58
Foundation item: National Natural Science Foundation of China (61273083, 61403028)
Corresponding author. DONG Chaoyang, E-mail: dongchaoyang@buaa.edu.cn
Abstract: Aimed at morphing aircraft with variable sweepback, this paper studies the issue of modeling and control for a class of morphing aircrafts. Fitting the relationship between aerodynamic parameters and sweepback, we developed linear parameter varying (LPV) model by Jacobian linearization approach. Then a smooth switching system approach with limited switching sequence, chain switching, is modeled, and the sufficient conditions are provided to ensure the finite-time boundedness and robust performance index of the chain smooth switched system. A solving algorithm of stabilizer for smooth switching controller is proposed, and the solving steps for gain control are presented. Based on the generalized system theory, the sufficient conditions for robust stability of the attitude tracking system are proposed. The numerical example simulation results are given to illustrate the validity of the devised approach.
Key words: robust control     smooth switching     switching system     morphing aircrafts     chain switching

1 LPV变体飞行器建模

 (1)

 (2)

 形态 ν/(°) Jyf/(kg·m2) mT/kg mw/kg ma/kg xw/m xa/m B/m S/m2 cA/m 巡航 15 3 107.5 907.8 272 26.36 0 -3.2 6.803 3 4.362 1 0.710 1 高速 60 3 107.5 907.8 272 26.36 -0.607 2 3.065 6 3.84 6.079 2 1.911 7 注: ν—后掠角; Jyf—俯仰转动惯量; mT—总重; ma—配重；xa—配重质心位置; B—翼展。

 (3)

 (4)

2 链式切换LPV系统

ν的取值区间Θ划分为J个子区间，对应于J个子区间，可得到J个LPV子系统，定义切换律，则得到开环切换LPV系统为

 (5)

 (6)

 (7)

3 控制器设计 3.1 鲁棒平滑切换镇定控制器设计

1) 当w (t)≡0时，系统是全局一致渐近稳定的。

2) 对于给定的常数γ＞0，在零初始条件且u (t)≡0的情况下，对于∀w(t)∈L2[0, ∞)，满足：

 (8)

 (9)

 (10)

 (11)
 (12)
 (13)

 (14)

 (15)

 (16)

 (17)

1) 首先为系统选取Lyapunov函数为

Vi(x (t))=xT(t) Pi－1x (t)  iΩM

 (18)

＜0对于满足ΓTΓI的任意矩阵Γ成立的充要条件是存在常数εi＞0，使得

 (19)

 (20)

 (21)

 (22)

 (23)

2) 证明切换系统的全局一致渐近稳定性

w (t)≡0，在[tk, t) 内，有

 (24)

 (25)

3) 令ϕ(t)=zT(t) z (t)－γ2wT(t) w(t)，类似稳定性的证明，在[tk, t) 内，有

 (26)
 (27)

 (28)

 (29)

 (30)

 (31)

 (32)

 (33)

 (34)

Mi, j, k=AjPi+PiAjT+λiPi+BjKkPi+PiKkTBjT

 (35)

 (36)

 (37)

 (38)

3.2 跟踪控制与鲁棒H性能分析

 (39)

 (40)

 (41)

 (42)

 (43)

 (44)
 (45)
 (46)

τiMτiM, *=(ln μi)/λi

 (47)

 (48)

 (49)

 (50)

 (51)

 (52)

 (53)

 (54)

4 仿真验证

 构型 反馈控制增益 Kx, i Kβ, i M15 M20 M25 M30 M35 M40 M45 M50 M55 M60

 图 1 迎角响应曲线 Fig. 1 Angle of attack response curves
 图 2 俯仰角速率响应曲线 Fig. 2 Pitch angle rate response curves
 图 3 油门开度响应曲线 Fig. 3 Throttle position response curves
 图 4 升降舵偏角响应曲线 Fig. 4 Elevator angle response curves
 图 5 迎角跟踪误差曲线 Fig. 5 Angle of attack tracking error curves

5 结论

1) 针对变体飞行器在稳态飞行中快速变形的情况，基于构型依赖驻留时间方法分析具有链式切换律的平滑切换系统的全局渐近稳定性和鲁棒H性能。

2) 进一步设计了一种平滑切换镇定控制器的求解算法，将原有的硬切换方案转换为鲁棒平滑切换控制，并给出了一种基于LMI条件和递推算法的控制增益求解步骤。

3) 基于广义系统理论提出了保证变体飞行器姿态跟踪系统鲁棒稳定的充分条件，设计了广义系统鲁棒平滑切换跟踪控制器，从而确保变形过程中系统对姿态角指令的跟踪精度。

 [1] WEISSHAAR T A. Morphing aircraft systems:Historical perspectives and future challenges[J]. Journal of Aircraft, 2013, 50 (2): 337–353. DOI:10.2514/1.C031456 [2] CROSSLEY W A, SKILLEN M D, FROMMER J B. Morphing aircraft sizing using design optimization[J]. Journal of Aircraft, 2011, 48 (2): 612–622. DOI:10.2514/1.C031180 [3] SOFLA A Y N, MEGUID S A, TAN K T, et al. Shape morphing of aircraft wing:Status and challenges[J]. Materials and Design, 2010, 31 (3): 1284–1292. DOI:10.1016/j.matdes.2009.09.011 [4] HUANG R, QIU Z P. Transient aeroelastic responses and flutter analysis of a variable-span wing during the morphing process[J]. Chinese Journal of Aeronautics, 2013, 26 (6): 1430–1438. DOI:10.1016/j.cja.2013.07.047 [5] POPOV A V, GRIGORIE L T, BOTEZ R. Closed-loop control validation of a morphing wing using wind tunnel tests[J]. Journal of Aircraft, 2010, 47 (4): 1309–1317. DOI:10.2514/1.47281 [6] BALDELL D H, LEE D H, PEÑR S S, et al. Modeling and control of an aeroelastic morphing vehicle[J]. Journal of Guidance, Control, and Dynamics, 2008, 31 (6): 1687–1699. DOI:10.2514/1.35445 [7] RUBAGOTTI M, ZACCARIAN L, BEMPORAD A. A Lyapunovmethod for stability analysis of piecewise-affine systems over non-invariant domains[J]. International Journal of Control, 2016, 89 (5): 950–959. DOI:10.1080/00207179.2015.1108456 [8] CHUMALEE S, WHIDBORNE J F. Gain-scheduled H∞ control via parameter-dependent Lyapunov functions[J]. International Journal of Systems Science, 2015, 46 (1): 125–138. DOI:10.1080/00207721.2013.775386 [9] ROMDLONY M Z, JAYAWARDHANA B. Stabilization with guaranteed safety using control Lyapunov-Barrier function[J]. Automatica, 2016, 66 : 39–47. DOI:10.1016/j.automatica.2015.12.011 [10] ANIMESH C, DANIEL T G, RICK L. Time-varying dynamics of a micro air vehicle with variable-sweep morphing[J]. Journal of Guidance, Control, and Dynamics, 2012, 35 (3): 890–903. DOI:10.2514/1.55078 [11] 乐挺, 王立新, 艾俊强. Z型翼变体飞机的纵向多体动力学特性[J]. 航空学报, 2010, 31 (4): 679–686. YUE T, WANG L X, AI J Q. Longitudinal multibody dynamic characteristics of Z-wing morphing aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2010, 31 (4): 679–686. (in Chinese) [12] YUE T, WANG L X, AI J Q. Longitudinal linear parameter varying modeling and simulation of morphing aircraft[J]. Journal of Aircraft, 2013, 50 (6): 1673–1681. DOI:10.2514/1.C031316 [13] 薛静, 杨亚洁, 刘宇, 等. 基于L1自适应控制的无人机横侧向控制[J]. 西北工业大学学报, 2015, 33 (1): 40–44. XUE J, YANG Y J, LIU Y, et al. Lateral roll angle control of UAV based on L1 adaptive control method[J]. Journal of Northwestern Polytechnical University, 2015, 33 (1): 40–44. (in Chinese) [14] SEIGLER T M, NEAL D A. Analysis of transition stability for morphing aircraft[J]. Journal of Guidance, Control, and Dynamics, 2009, 32 (6): 1947–1953. DOI:10.2514/1.44108 [15] CUI L, CHEN L, DUAN D P. Gain-scheduling model predictive control for unmanned airship with LPV system description[J]. Journal of Systems Engineering and Electronics, 2015, 26 (5): 1043–1051. DOI:10.1109/JSEE.2015.00113 [16] YUE T, WANG L X, AI J Q. Gain self-scheduled H∞ control for morphing aircraft in the wing transition process based on an LPV model[J]. Chinese Journal of Aeronautics, 2013, 26 (4): 909–917. DOI:10.1016/j.cja.2013.06.004 [17] 段广仁, 王好谦. 多模型切换控制及其在BTT导弹设计中的应用[J]. 航空学报, 2005, 26 (2): 144–147. DUAN G R, WANG H Q. Multi-model switching control and its application to BTT missile design[J]. Acta Aeronautica et Astronautica Sinica, 2005, 26 (2): 144–147. (in Chinese) [18] HOU Y Z, WANG Q, DONG C Y. Gain scheduled control:Switched polytopic system approach[J]. Journal of Guidance, Control, and Dynamics, 2011, 34 (2): 623–629. DOI:10.2514/1.51699 [19] HOU Y Z, DONG C Y, WANG Q. Stability analysis of switched linear systems with locally overlapped switching law[J]. Journal of Guidance, Control, and Dynamics, 2010, 33 (2): 396–403. DOI:10.2514/1.45795

#### 文章信息

JIA Zhen, DONG Chaoyang, WANG Qing

LPV robust tracking control for chain smooth switched morphing aircraft

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(4): 831-841
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0246