Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Analytical Study on the Slewing Dynamics of Hybrid Coordinate Systems

복합좌표계 시스템의 선회동역학에 관한 해석적 연구

  • 석진영 (충남대학교 항공우주공학과)
  • Published : 2003.08.01
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Abstract

In this paper, an analytic solution method is proposed to overcome the numerical problems when the slewing dynamics of hybrid coordinate systems is investigated via time finite element analysis. It is shown that the dynamics of the hybrid coordinate systems is governed by the coupled dual differential equations for both slewing and structural modes. Structural modes are transformed into the time-based modal coordinates and analytic spatial propagation equations are derived for each space-dependent time mode. Slew angle history is obtained analytically by appropriate applications of the boundary conditions and structural propagation is re-calculated using the slew angle. Numerical examples are demonstrated to validate the proposed analytic method in comparison to the existing state transition matrix method.

본 논문에서는 선회모드와 구조모드를 가지는 복합좌표계 시스템의 선회동역학을 시간유한요소법을 이용하여 전개할 때에 발생하는 수치적 문제점을 극복할 수 있는 해석적 해법을 제안하였다. 시간유한요소법을 이용한 복합좌표계 시스템의 동역학은 선회모드와 구조모드가 서로 연성된 두 개의 행렬미분방정식으로 전개될 수 있음을 보였다. 공간전파관계식을 시간영역 모드좌표계로 변환하고, 각 시간모드에 대한 해석적 공간전파관계식을 유도하였다. 경계조건의 적용을 통해 선회각에 대한 해석적 관계식을 구하였으며, 이를 이용함으로써 각 모드에 대한 공간 특성치를 구하였다. 수치 예제를 통하여 기존의 상태천이행렬을 이용한 해법과 비교함으로써 제안된 해석적 해법을 타당성을 검증하였다.

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References

  1. T. Heyden, "They're Flying High," Newsweek, Vol. 454. Nov 15, 2000.
  2. 오춘호, "科技대형과제로 고용창출: 새정부 정책, 기술혁신.성장성에 초점," 한국경제신문, 2003. 1. 17, pp.A17.
  3. T. R. Kane, R. R. Ryan, and A. K. Banerjee, "Dynamics of a Cantilever Beam attached to a Moving Base," journal of Guidance, Control, and Dynamics, Vol. 10, No. 2, 1987, pp. 139-151. https://doi.org/10.2514/3.20195
  4. J. D. Turner, and H. M. Chun, "Optimal Distributed Control of a Flexible Spacecraft During a Large-Angle Maneuver," journal of Guidance, Control, and Dynamics, Vol. 7, No. 3, 1984, pp. 257-264. https://doi.org/10.2514/3.19853
  5. J. L. Junkins, Z. H. Rahman, and H. Bang, Near-Minimum-Time Control of Distributed Parameter Systems: Analytical and Experimental Results, Journal of Guidance, Control, and Dynamics, Vol. 14, No. 2, 1991, pp. 406-415. https://doi.org/10.2514/3.20653
  6. Z-H. Luo, "Direct Strain Feedback Control of Flexible Robot Arms: New Theoretical and Experimental Results," IEEE Transactions on Automatic Control, Vol. 38, No. 11, 1993, pp.1610-1622 https://doi.org/10.1109/9.262031
  7. M. S. de Querioz, D. M. Dawson, M. Agrawal, and F. Zhang, "Adaptive Nonlinear Boundary Control of a Flexible Link Robot Arm," JEEE Transactions on Robotics and Automation, Vol. 15, No. 4, 1999, pp.779-787. https://doi.org/10.1109/70.782034
  8. L. Meirovitch, and H. Baruh, "Control of Self-Adjoint Distributed Parameter Systems," Journal of Guidance, Control, and Dynamics, Vol. 5, No. 1, 1982, pp. 60-66. https://doi.org/10.2514/3.56140
  9. D. J. Leo, and D. J. Inman, "Pointing Control and Vibration Suppression of a Slewing Flexible Frame," Journal of Guidance, Control, and Dynamics, Vol. 17, No. 3, 1994, pp.529-536. https://doi.org/10.2514/3.21230
  10. D. Wilson, G. Parker, G. Starr, and R. Robinett, "Modeling and Robust Conrol of a Flexible Manipulator," Proceedings of 35th Aerospace Sciences Meeting & Exhibit, January 6-10, 1997, Reno, NV, USA.
  11. J. Suk, and Y. Kim, "Time Domain Finite Element Analysis of Dynamic Systems," AIAA Journal, Vol. 36, No. 7, 1998, pp. 1312-1319. https://doi.org/10.2514/2.516
  12. L. J. Hou and D. A. Peters, "Application of Triangular Space-Time Finite Elements to Problems of Wave Propagation," Journal of Sound and Vibration, Vol.173, 1994, pp. 611-632. https://doi.org/10.1006/jsvi.1994.1250
  13. 석진영, 정은태, 김유단, "유연한 구조물의 공간전파에 관한 해석적 해법," 대한기계학회 논문집 A권, 제25권, 제12호, 2001년, pp. 2040-2047.
  14. M. Borri, G. Ghiringhelli, M. Lanz, P. Mantegazza, and T. Merlini, "Dynamic Response of Mechanical Systems by a Weak Hamiltonian Formulation," Computers and Structures, Vol. 20, No. 1-3, 1985, pp. 495-508. https://doi.org/10.1016/0045-7949(85)90098-7
  15. H. Oz, and E. Adiguzel, "Hamiltons law of Varying Action, Part I: Assumed-Time-Modes Method," Journal of Sound and Vibration, Vol. 179, No. 4, 1995, pp. 697-710. https://doi.org/10.1006/jsvi.1995.0045
  16. H. Oz, and E. Adiguzel, "Hamiltons law of Varying Action, Part II: Direct Optimal Control of Linear Systems," Journal of Sound and Vibration, Vol. 179, No. 4, 1995, pp. 711-724. https://doi.org/10.1006/jsvi.1995.0046
  17. D. W. Hodges, and R. R. Bless, "Weak Hamiltonian Finite Element Method for Optimal Control Problems," Journal of Guidance, Control, and Dynamics, Vol. 14, No.1, 1991, pp. 148-156. https://doi.org/10.2514/3.20616
  18. D. W. Hodges, R. R. Bless, A. J. Calise, and M. Leung, "Finite Element Method for Optimal Guidance of an Advanced Launch Vehicle," Journal of Guidance, Control, and Dynamics, Vol. 15, No. 3, 1992, pp. 664-671. https://doi.org/10.2514/3.20889
  19. J. Suk, S. Boo, and Y. Kim, "Lyapunov Control Law for Slew Maneuver Using Time Finite Element Analysis," Journal of Guidance, Control, and Dynamics, Vol. 24, No. 1, 2001, pp.87-94. https://doi.org/10.2514/2.4679
  20. 석진영, 문종윤, 김유단, "유연우주비행체의 선회 및 진동억제를 위한 최적입력 형상화에 관한 연구," 한국항공우주학회지, 제25권, 제6호, 1997, pp.110-123.