Dynamic Modeling for Airship Equipped With Ballonets and Ballast
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摘要: 研究飞艇的动力学建模,将飞艇的机体视为浮力与重力相等的浸没刚体,且考虑了飞艇机体与升降气囊以及压块之间的动力学耦合作用.整体的动力学方程首先通过Newton-Euler定律和Kirchhoff方程推出.此外,应用Hamilton与Lagrange半直积约化理论,可以将动力学方程解释为Lie-Poisson系统或者Euler-Poincaré系统.这两种动力学描述在基于能量的控制设计中有着重要作用.
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关键词:
- 飞艇 /
- 动力学建模 /
- Kirchhoff方程 /
- 半直积约化
Abstract: Total dynamics of an airship is modeled. The body of an airship was taken as a submerged rigid body with neutral buoyancy, i. e., buoyancy with value equal to that of gravity, and the coupled dynamics between the body with ballonets and ballast was considered. The total dynamics of the airship was firstly derived by Newton-Euler laws and Kirchhoff's equations. Furthermore, by using Hamiltonian and Lagrangian semi-direct product reduction theories, the dynamics was formulated as a Lie-Poisson system, and also an Euler-Poincar system. These two formulations can be exploited for the control design using energy-based methods for Hamiltonian or Lagrangian system.-
Key words:
- airship /
- dynamical modeling /
- Kirchhoff’s equation /
- semi-direct product reduction
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[1] Gomes Sergio B,Varella,Ramos Josure Jr G.Airship dynamic modeling for autonomous operation[A].In:Robotics & Automation,IEEE Ed.Proceeding of the 1998 IEEE International Conferrence on Robotics & Automation[C].Leuven,Balgium:IEEE.1998,3462—3467. [2] Sagatun Svein I,Fossen Thor I.Lagrangian formulation of underwater vehicles' dynamics[A].In:Proceeding of the 1991 IEEE International Conference on Systems, Man, and Cybernetics[C].1991,1029—1034. [3] Leonard N E.Stability of a bottom-heavy underwater vehicle[J].Automatica,1997,33(3):331—346. doi: 10.1016/S0005-1098(96)00176-8 [4] Marsden J E,Ratiu T S,Weinstein A.Semi-direct products and reduction in mechanics[J].Transaction of American Mathematics Society,1984,281(1):147—177. doi: 10.1090/S0002-9947-1984-0719663-1 [5] Cendra H,Holm D D,Marsden J E,et al.Lagrangian reduction, the Euler-Poincaré equations, and semidirect products[J].American Mathematics Society Translation,1997,186(1):1—25. [6] Holm D D,Marsden J E,Ratiu T S.The Euler-Poincaré equations and semi-direct products with application to continuum theories[J].Advances in Mathematics,1998,137(1):1—81. doi: 10.1006/aima.1998.1721 [7] Ortega R,Spong Mark W,Gómez-Estern F,et al.Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment[J].IEEE Transaction on Automatic Control,2002,47(12):1218—1233. doi: 10.1109/TAC.2002.800770 [8] Bloch A M,Leonard N E,Marsden J E.Controlled Lagrangian and the stabilization of mechanical systems—Ⅰ the first matching theorem[J].IEEE Transaction on Automatic Control,2000,45(12):2253—2270. doi: 10.1109/9.895562 [9] Kirchhoff G.Uber die bewegung eines rotationskorpers in einer flussigkeit[J].Crelle's Journal,1869,71(3):237—273. [10] Lamb H.Hydrodynamics[M].London:Cambridge University Press,1932,12—120. [11] Marsden J E.Introduction to Mechanics and Symmetry[M].second edition.Berlin:Springer-Verlag, 1994,369—396.
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