http://iet.metastore.ingenta.com
1887

Asymptotic generalised dynamic inversion attitude control

Asymptotic generalised dynamic inversion attitude control

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This study introduces a generalised dynamic inversion control methodology for asymptotic spacecraft attitude trajectory tracking. An asymptotically stable second-order servo-constraint attitude deviation dynamics is evaluated along spacecraft equations of motion, resulting in a linear relation in the control vector. A control law that enforces the servo-constraint is derived by generalised inversion of the relation using the Greville formula. The generalised inverse in the particular part of the control law is scaled by a decaying dynamic factor that depends on desired attitude trajectories and body angular velocity components. The scaled generalised inverse uniformly converges to the standard Moore–Penrose generalised inverse, causing the particular part to converge uniformly to its projection on the range space of the controls coefficient generalised inverse, and driving spacecraft attitude variables to nullify attitude deviation. The auxiliary part of the control law acts on the controls coefficient nullspace, and it provides the spacecraft internal stability with the aid of the null-control vector. The null-control vector construction is made by means of novel semidefinite nullprojection control Lyapunov function and state-dependent null-projected Lyapunov equation. The generalised dynamic inversion control signal is multiplied by an exponential factor during transient closed-loop response to enhance the control signal in terms of magnitude and rate of change. Illustrating examples show efficacy of the methodology.

References

    1. 1)
      • R. Su . On the linear equivalents of nonlinear systems. Syst. Control Lett. , 48 - 52
    2. 2)
      • L.R. Hunt , R. Su , G. Meyer . Global transformations of nonlinear systems. IEEE Trans. Autom. Control , 24 - 31
    3. 3)
      • T. Dwyer . Exact nonlinear control of large angle rotational maneuvers. IEEE Trans. Autom. Control , 9 , 769 - 774
    4. 4)
      • R.A. Paielli , R.E. Bach . Attitude control with realization of linear error dynamics. J. Guidance, Control, Dyn. , 1 , 182 - 189
    5. 5)
      • A.H. Bajodah . Singularly perturbed feedback linearization with linear attitude deviation dynamics realization. Nonlinear Dyn. , 4 , 321 - 343
    6. 6)
      • A.H. Bajodah . Generalized dynamic inversion spacecraft control design methodologies. IET Control Theory Appl. , 2 , 239 - 251
    7. 7)
      • T.N.E. Greville . The pseudoinverse of a rectangular or singular matrix and its applications to the solutions of systems of linear equations. SIAM Rev. , 1 , 38 - 43
    8. 8)
      • E.H. Moore . On the reciprocal of the general algebraic matrix. Bull. Am. Math. Soc. , 394 - 395
    9. 9)
      • R. Penrose . A generalized inverse for matrices. Proc. Cambridge Philosophical Society , 406 - 413
    10. 10)
      • B. Siciliano , O. Khatib . (2008) Springer handbook of robotics.
    11. 11)
      • F.E. Udwadia , R.E. Kalaba . (1996) Analytical dynamics, a new approach.
    12. 12)
      • C.F. Gauss . Ueber ein neues algemeines grundgesetz der mechanik. Zeit. Fuer reine angew. Math. , 232 - 235
    13. 13)
      • V. De Sapio , O. Khatib , S. Delp . Least action principles and their application to constrained and task-level problems in robotics and biomechanics. Multibody Syst. Dyn. , 3 , 303 - 322
    14. 14)
      • F.E. Udwadia . Optimal tracking control of nonlinear dynamical systems. Proc. R. Soc. Lond. A , 2341 - 2363
    15. 15)
      • J. Peters , M. Mistry , F. Udwadia , J. Nakanishi , S. Schaal . A unifying framework for robot control with redundant DOFs. Auton. Robots , 1 , 1 - 12
    16. 16)
      • D.R. Baker , C.W. Wampler . On inverse kinematics of redundant manipulators. Int. J. Robot. Res. , 2 , 3 - 21
    17. 17)
      • A. Liegeois . Automatic supervisory control of the configuration and behavior of multi-body mechanisms. IEEE Trans. Systems, Man, Cybernet. , 12 , 868 - 871
    18. 18)
      • R.V. Mayorga , F. Janabi-Sharifi , A.K.C. Wong . A fast approach for the robust trajectory planning of redundant robot manipulators. J. Robot. Syst. , 2 , 147 - 161
    19. 19)
      • H. Yoon , P. Tsiotras . Singularity analysis of variable-speed control moment gyros. J. Guidance, Control, Dyn. , 3 , 374 - 386
    20. 20)
      • Y. Nakamura , H. Hanafusa . Inverse kinematic solutions with singularity robustness for robot manipulator control. J. Dyn. Syst. Meas., Control , 8 , 163 - 171
    21. 21)
      • C.W. Wampler . Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods. IEEE Trans. Syst., Man, Cybernet. , 93 - 101
    22. 22)
      • H.S. Oh , S.R. Vadali . Feedback control and steering laws for spacecraft using single gimbal control moment gyros. J. Astronaut. Sci. , 2 , 183 - 203
    23. 23)
      • A.H. Bajodah . Stabilization of underactuated spacecraft dynamics via singularly perturbed feedback linearization. J. King Abdulaziz Univ. Eng. Sci. , 2 , 35 - 53
    24. 24)
      • A. Iqqidr , B. Kalitine , R. Outbib . Semidefinite Lyapunov functions stability and stabilization. Math. Control, Signals Syst. , 2 , 95 - 106
    25. 25)
      • M. Bensoubaya , A. Ferfera , A. Iqqidr . Stabilization of nonlinear systems by use of semidefinite Lyapunov functions. Appl. Math. Lett. , 7 , 11 - 17
    26. 26)
      • H.K. Khalil . (1988) Nonlinear systems.
    27. 27)
      • M.D. Shuster . A survey of attitude representation. J. Astronaut. Sci. , 4 , 439 - 517
    28. 28)
      • A.H. Bajodah , D.H. Hodges , Y.H. Chen . Inverse dynamics of servo-constraints based on the generalized inverse. Nonlinear Dyn. , 179 - 196
    29. 29)
      • S. Bhat , D. Bernstein . A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon. Syst. Control Lett. , 1 , 63 - 70
    30. 30)
      • D. Bernstein . (2005) Matrix mathematics: theory, facts, and formulas with application to linear system theory.
    31. 31)
      • J.J.E. Slotine , W. Li . (1991) Applied nonlinear control.
    32. 32)
      • C.R. McInnes . Satellite attitude slew manoeuvres using inverse control. Aeronaut. J. , 259 - 265
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2009.0008
Loading

Related content

content/journals/10.1049/iet-cta.2009.0008
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address