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Bifurcation analysis of attitude control systems with switching-constrained actuators

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Abstract

On-off thrusters are frequently used as actuators for attitude control and are typically subject to switching constraints. In systems with switching actuators, different types of persistent motions may be found, and in the presence of model uncertainties, the occurrence of bifurcations in such systems can seriously affect performance. In this paper the nature of persistent motions in an attitude control system with actuators subject to switching-time restrictions is examined to provide useful information for control design in the presence of uncertainty. The main tools used are bifurcation diagrams, Poincaré maps and Lyapunov spectrum. Border-collision type bifurcations are characterized in this piecewise affine system, as well as unusual patterns of persistent motion. Multistability and complex-switching sequences are also observed, revealing the existence of motions with sensitive dependence on initial conditions.

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References

  1. Mendel, J.: On-off limit-cycle controllers for reaction-jet-controlled systems. IEEE Trans. Automatic Control 15(3), 285–299 (1970)

    Article  Google Scholar 

  2. Won, C.: Comparative study of various control methods for attitude control of a leo satellite. Aerosp. Sci. Technol. 3(5), 323–333 (1999)

    Article  MATH  Google Scholar 

  3. Oliveira, N.M., Kienitz, K.H.: Attitude controller design for a system using actuators with switching-time restrictions and delays. In: Proceedings of AIAA Guidance, Navigation, and Control Conference, Denver, CO, AIAA-2000-3967 (2000)

  4. Antropov, N.N., Diakonov, G.A., Kazeev, M.N., Khodnenko, V.P., Kim, V., Popov, G.A., Pokryshkin, A.I.: Pulsed plasma thrusters for spacecraft attitude and orbit control system. In: Proceedings of the 26th International Propulsion Conference, Kitakyushu, Japan, October 17–21, pp. 1129–1135 (1999)

  5. Avanzini, G., de Matteis, G.: Bifurcation analysis of attitude dynamics in rigid spacecraft with switching control logics. J. Guid. Control Dyn. 24(5), 953–959 (2001)

    Article  Google Scholar 

  6. Kienitz, K.H., Bals, J.: Pulse modulation for attitude control with thrusters subject to switching restrictions. Aerosp. Sci. Technol. 9(7), 635–640 (2005)

    Article  Google Scholar 

  7. Mesquita, A.R., Kienitz, K.H.: Persistent motion and chaos in attitude control with switching actuators. In: Proceedings of 16th IFAC World Congress, Prague, July 4–8, Conference CD-rom, paper Th-A03-TP/15 (2005)

  8. Grebogi, C., Ott, E., Yorke, J.A.: Crises, sudden changes in chaotic attractors, and transient chaos Physica D 7(1–3), 181–200 (1983)

    Article  MathSciNet  Google Scholar 

  9. Rempel, E.L., Chian, A.C.-L.: Intermittency induced by attractor-merging crisis in the Kuramoto-Sivashinsky equation. Phys. Rev. E 71(1), 016203 (2005)

    Article  Google Scholar 

  10. Nusse, H.E., Ott, E., Yorke, J.A.: Border-collision bifurcations: an explanation for observed bifurcation phenomena. Phys. Rev. E 49(2), 1073–1076 (1994)

    Article  MathSciNet  Google Scholar 

  11. Banerjee, S., Ranjan, P., Grebogi, C.: Bifurcation in two-dimensional piecewise smooth maps —theory and applications in switching circuits. IEEE Trans. Circuits Syst. I 47(5), 633–643 (2000)

    Article  MATH  Google Scholar 

  12. Zhusubaliyev, Zh.T., Soukhoterin, E.A., Mosekilde, E.: Border-collision bifurcations on a two-dimensional torus. Chaos Solitons Fractals 13(9), 1889–1915 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gille, J. Ch., Decaulne, P., Pélegrin, M.: Méthodes D'Étude des Systèmes Asservis Non Linéaires. Dunod, Paris, France (1967)

    MATH  Google Scholar 

  14. Alligood, K.T., Sauer, T.D., Yorke, J.A.: Chaos: An Introduction to Dynamical Systems. Springer-Verlag, New York (1996)

    MATH  Google Scholar 

  15. Müller, P.: Calculation of Lyapunov exponents for dynamic systems with discontinuities. Chaos Solitons Fractals 5(9), 1671–1681 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  16. Eckmann, J.-P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57(3), 617–656 (1985)

    Article  MathSciNet  Google Scholar 

  17. Orrell, D., Smith, L.: Visualising bifurcations in high dimensional systems: the spectral bifurcation diagram. Int. J. Bif. Chaos 13(10), 3015–3027 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  18. Moser, J.: On the theory of quasi-periodic motions. SIAM Rev. 8(2), 145–172 (1966)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Systems and Control, Institute of Aeronautical Technology (ITA), CTA, 12228-900, São José dos Campos, SP, Brazil

    A. Mesquita & K. H. Kienitz

  2. Department of Mathematics, Institute of Aeronautical Technology (ITA), CTA, 12228-900, São José dos Campos, SP, Brazil

    E. L. Rempel

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  1. A. Mesquita
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  2. E. L. Rempel
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  3. K. H. Kienitz
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Correspondence to E. L. Rempel.

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Mesquita, A., Rempel, E.L. & Kienitz, K.H. Bifurcation analysis of attitude control systems with switching-constrained actuators. Nonlinear Dyn 51, 207–216 (2008). https://doi.org/10.1007/s11071-007-9204-7

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  • DOI: https://doi.org/10.1007/s11071-007-9204-7

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