32 11 Vol 32 11 2011 11 Journal of Harbin Engineering University Nov 2011 doi 10 3969 /j issn 1006-7043 2011 11 019 410073 3 2 V274 A 1006-7043 2011 11-1501-08 Motion analysis and simulation of a stratospheric airship HU Guochang WU Meiping Mechatroincs and Automatization School National University of Defense Technology Changsha 410073 China Abstract While considering the requirements of self-action for stratospheric airships stability controllability and motion characteristics were studied Based on the nonlinear dynamic model of an airship stability was determined and structural controllability was analyzed The motion characteristics were also studied using the mode method on the basis of the linear model Lastly the motion characteristics of an airship under disturbance and control functions were analyzed using a simulation method Theoretical and simulation results indicate the motion of the airship is unstable and meanwhile the airship is structurally controllable The vertical motion can be classified into three modes of swaying slow damping and rapid damping and the transverse sideways movement includes two modes of yawing oscillation and rolling attenuation The analysis of airship motion characteristics can be the theoretical basis for the control design of a stratospheric airship Keywords stratospheric airships mode method stability structural controllability 6-8 1 9-10 11-12 2-5 2010-09-15 51309060406 1979- E-mail huguo chang200 80514@ yahoo cn 1970-13
1502 32 R 1 G R G Λ m Λ J 1 1 m J V W Ω W F + M 1 sin φtan θ cos φtan θ g Φ = 0 cos φ - sin φ 1 0 sin φ /cos θ cos φ /cos θ 1 X = f X U d f U = P F TVT F TVD μ y δ e δ r T P F TVT F TVD μ y δ e δ r 1 Fig 1 Stratospheric airship sketch d 3 1 2 1 2 1 2 3 2 6-8 mi 3 3 + Λ m - m R G 0 3 3 m R G J + Λ J 0 3 3 X = 0 3 3 0 3 3 I g Φ Ω 3 3 - Ω mi 3 3 + Λ m V - mω Ω R G - Ω J + Λ J Ω - R G Ω mv mi 3 + Λ m V W + Ω mi 3 + Λ m V W F J + Λ J Ω W + Ω J + Λ J Ω W + M 0 3 1 + 0 3 1 1 ΔX = AΔX + BΔU X = V T Ω T Φ T T V = u v 14 w T u v w 3 W T = p q r 1 p q r 3 F = j q y T φ θ ψ I 3 3 3 3 m J R G 2 2 ΔX L = A L ΔX L + B L ΔU L 3 ΔX S = A S ΔX S + B S ΔU S 4 2 2 1
11 1503 2 2 λ S1 λ S2 λ S3 λ S4 1 λ S1 λ S2 14 2 λ S3 λ S4 14 2 2 2 A 3 u e 2 1 1 ~ 45 m /s Fig 3 Latitudinal eigenvalue 1 U e Fig 1 longitudinal eigenvalue of varying U e 4 λ L1 u e / λ L2 λ L1 λ L2 λ L3 λ L4 m s - 1 λ L3 λ L4 5-0001 3-0001 7 0008 6 +0326 2i 0008 6-0326 2i λ L1 10-0001 4-0002 5 0016 2 +0500 9i 0016 2-0500 9i λ L2 λ L3 λ L4 15-0001 1-0003 8 0023 8 +0701 3i 0023 8-0701 3i 20-0000 9-0005 1 0031 5 +0910 5i 0031 5-0910 5i Fig 2 2 longitudinal eigenvalue 3 2 1 ~ 45 m /s Fig 2 2 25-0000 7-0006 3 0039 1 +1123 6i 0039 1-1123 6i 30-0000 6-0007 6 0046 9 +1338 8i 0046 9-1338 8i 35-0000 5-0008 9 0054 6 +1555 1i 0054 6-1555 1i 40-0000 5-0010 1 0062 3 +1772 3i 0062 3-1772 3i 45-0 000 4-0 011 40 070 0 +1 989 9i 0 070 0-1 989 9i U e latitudinal eigenvalue of varying U e u e /m s - 1 λ S1 λ S2 λ S3 λ S4 5 0 00 57 + 0 219 5i 0 005 7-0 219 5i 0 003 3 + 0 514 8i 0 003 3-0 514 8i 10-0 006 4 + 0 450 4i - 0 006 4-0 450 4i 0 024 6 + 0 501 3i 0 024 6-0 501 3i 15-0 018 0 + 0 526 0i - 0 018 0-0 526 0i 0 045 2 + 0 642 8i 0 045 2-0 642 8i 20-0 006 9 + 0 524 2i - 0 006 9-0 524 2i 0 043 2 + 0 861 5i 0 043 2-0 861 5i 25-0 004 5 + 0 523 1i - 0 004 5-0 523 1i 0 049 8 + 1 079 4i 0 049 8-1 079 4i 30-0 003 4 + 0 522 6i - 0 003 4-0 522 6i 0 057 8 + 1 296 6i 0 057 8-1 296 6i 35-0 002 7 + 0 522 4i - 0 002 7-0 522 4i 0 066 2 + 1 513 5i 0 066 2-1 513 5i 40-0 002 3 + 0 522 2i - 0 002 3-0 522 2i 0 074 8 + 1 730 4i 0 074 8-1 730 4i 45-0 002 0 + 0 522 1i - 0 002 0-0 522 1i 0 083 6 + 1 947 1i 0 083 6-1 947 1i
1504 32 2 3 15 3 2 8 b 1 U e U e / V B 1 /3 V B 2 3 2 18 m /s 0 028 4-0 826 1i 0 028 4 + 0 826 1i - 0 004 6-0 001 0 0 041 7 + 0 774 0i 0 041 7-0 774 0i - 0 009 1 + 0 525 0i - 0 009 1-0 525 0i 4 5 4 Fig 4 Longitudinal eigenvector 4 3 a ~ c 3 c 5 2 a ~ b 2 a a b 5 Fig 5 Latitudinal eigenvector
11 1505 3 21 300 m u 0 = 18 m /s 6 a b Δw u w q θ 2 3 6 2 A B 2 A B A 槇 B 槇 2 h 0 = A B A 槇槇 A B A B A 槇 B 槇 A B A 槇 B 槇 A B A 槇 B 槇 A B a r n m A m - r k m k n + m - k - r +1 k A r form r A B C = B I 0 0 0 0 0 0 0 - A B I 0 0 0 0 0 0 0 - A B I 0 0 0 0 0 0 0 - A 0 0 b 0 0 6 Δw 0 0 0 0 0 B I 0 Fig 6 Response of the airship to initial disturbance of Δw 0 0 0 0 0 0 - A B 7 a b Δv 3 A B C form n 2 n A 13 0 7 a 7 b form n 2 a ψ 4 4 1
1506 32 a Fig 7 7 b Δv Response of the airship to initial disturbance of Δv 2 4 2 a 4 1 8 a b 8 a u w q θ b 8 δ e Fig 8 Response of the airship to initial disturbance of δe 9
11 1507 a 9 Fig 9 b δ r Response of the airship to δ r 10 a
1508 32 Fig 10 10 b P Response of the airship to initial disturbance of P 2009 27 1 31-35 WANG Haifeng SONG Bifeng ZHONG Xiaopin Modeling and simulation verification of motion for an airship J Flight Dynamics 2009 27 1 31-35 6 AZINHEIRA J R MOUTINHO A Influence of wind speed on airship dynamics J AIAA Journal of Guidance Control and Dynamics 2002 25 6 1116-1124 5 wind speed on airship dynamic J AIAA Journal of Guidance Control and Dynamics 2008 31 2 443-444 8 MOUTINHO A B Modeling and nonlinear control for airship au- tonomous flight D Lisbon University of Lisbon 2007 33-78 9 J 2005 22 8 40-44 WANG Xiaoliang SHAN Xuefei Analysis of stability and controllability of airship J Computer Simulation 2005 22 8 40-44 10 LI Y W MEYER N Modeling and simulation of airship dynamics J Journal of Guidance Control and Dynamics 2007 30 6 1691-1700 2 11 J 2003 37 6 961-963 OUYANG Jin QU Weidong XI Yugeng Longitudinal 1 motion analysis and simulation for Lighter-than-air LTA J 2006 6 32-35 airship J Journal of Shanghai Jiao Tong University 2 KHOURY G A GILLET J D Airship technology M London Cambridge University Press 1999 58-70 3 MUELLER J B PALUSZEK M A Development of an aerodynamic model and control law design for a high altitude airship C / / AIAA Unmamed Unlimited Conferene Chicago USA 2004 4 D 1993 77-100 2003 23-78 OUYANG Jin Research on modeling and control of an unmanned airship D Shanghai Shanghai Jiao Tong University 2003 23-78 5 J 7 AZINHEIRA J R MOUTINBO A 2003 37 6 961-963 Erratum-influence of 12 LIU Y HU Y M WU Y L Stability and control analysis based on airship dynamic modeling C / / Proceedings of the IEEE International Conference on Automation and Logistics Jinan China 2007 2744-2748 13 M 14 M 2005 153-170 15 M 2 2002 98-101