Motion analysis and simulation of a stratospheric airship

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1 32 11 Vol Journal of Harbin Engineering University Nov 2011 doi /j issn V274 A Motion analysis and simulation of a stratospheric airship HU Guochang WU Meiping Mechatroincs and Automatization School National University of Defense Technology Changsha 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 huguo chang @ yahoo cn

2 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 mi Λ m - m R G m R G J + Λ J X = I g Φ Ω Ω mi 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 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 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

3 λ S1 λ S2 λ S3 λ S4 1 λ S1 λ S λ S3 λ S A 3 u e ~ 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 L i i λ L i i λ L2 λ L3 λ L i i i i Fig 2 2 longitudinal eigenvalue ~ 45 m /s Fig i i i i i i i i i i U e latitudinal eigenvalue of varying U e u e /m s - 1 λ S1 λ S2 λ S3 λ S i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i

4 b 1 U e U e / V B 1 /3 V B m /s i i i i i i Fig 4 Longitudinal eigenvector 4 3 a ~ c 3 c 5 2 a ~ b 2 a a b 5 Fig 5 Latitudinal eigenvector

5 m u 0 = 18 m /s 6 a b Δw u w q θ 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 A B I A B I A 0 0 b Δw B I 0 Fig 6 Response of the airship to initial disturbance of Δw A B 7 a b Δv 3 A B C form n 2 n A a 7 b form n 2 a ψ 4 4 1

6 a Fig 7 7 b Δv Response of the airship to initial disturbance of Δv a a b 8 a u w q θ b 8 δ e Fig 8 Response of the airship to initial disturbance of δe 9

7 a 9 Fig 9 b δ r Response of the airship to δ r 10 a

8 Fig b P Response of the airship to initial disturbance of P WANG Haifeng SONG Bifeng ZHONG Xiaopin Modeling and simulation verification of motion for an airship J Flight Dynamics AZINHEIRA J R MOUTINHO A Influence of wind speed on airship dynamics J AIAA Journal of Guidance Control and Dynamics wind speed on airship dynamic J AIAA Journal of Guidance Control and Dynamics MOUTINHO A B Modeling and nonlinear control for airship au- tonomous flight D Lisbon University of Lisbon J WANG Xiaoliang SHAN Xuefei Analysis of stability and controllability of airship J Computer Simulation LI Y W MEYER N Modeling and simulation of airship dynamics J Journal of Guidance Control and Dynamics J OUYANG Jin QU Weidong XI Yugeng Longitudinal 1 motion analysis and simulation for Lighter-than-air LTA J airship J Journal of Shanghai Jiao Tong University 2 KHOURY G A GILLET J D Airship technology M London Cambridge University Press 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 D OUYANG Jin Research on modeling and control of an unmanned airship D Shanghai Shanghai Jiao Tong University J 7 AZINHEIRA J R MOUTINBO A 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 M 14 M M

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