Formation Flying Control for Satellites: Anti-windup Based Approach

  • Josep Boada
  • Christophe Prieur
  • Sophie Tarbouriech
  • Christelle Pittet
  • Catherine Charbonnel
Part of the Springer Optimization and Its Applications book series (SOIA, volume 73)


Control theory has significantly evolved in the field of the nonlinear control. However, the methods used in the aerospace industry lie usually on linear techniques applied to linearized models. The increasing requirements in terms of operational reliability and performance ask for the development of new control techniques more complex in order to meet the new demands. Therefore, the industry is moving to the modern control theory looking for new nonlinear approaches. In particular, actuators saturation represents a nonlinear phenomenon common in almost all physical applications. This can then lead to performance degradation, limit cycle appearance, non-desired equilibrium conditions, and even system instability. The objective of this chapter is to adapt and develop the anti-windup compensator design to the control with high precision for the angular and the linear axes of a satellite. In the aerospace application field, this situation meets with the drag-free or the formation flying missions. These missions use high-precision thrusters as actuators whose capacity appears to be critically low. Moreover, thrusters have a particular modeling. Allocation functions adapted to the anti-windup design are then explored. In addition considering the current state of the art of the anti-windup design, there is a strong necessity of using symmetrizing techniques for the saturation. The main objective of this work consists in applying the developed tools on an aerospace study case. As an example, a complete methodology is proposed to control a formation flying mission controlling both attitude and relative position.


Saturating thrusters Anti-windup design Control Optimization 


  1. 1.
    Absil, O.: Science with pegase. In: Proceedings of 2nd TPF/Darwin International Conference, San Diego, CA, USA (2004)Google Scholar
  2. 2.
    Aström, K.J., Rundqwist, L.: Integrator windup and how to avoid it. In: Proceedings of the American Control Conference, Pittsburgh, PA, USA (1989)Google Scholar
  3. 3.
    Balas, G., Chiang, R., Packard, A., Safonov, M.: Robust Control Toolbox user’s guide. The MathWorks Inc., Natick, MA (2007)Google Scholar
  4. 4.
    Berg, J.M., Hammet, K.D., Schwartz, C.A., Banda, S.S.: Analysis of the destabilizing effect of daisy chained rate-limited actuators. IEEE Trans. Contr. Syst. Tech. 4, 171–176 (1996)CrossRefGoogle Scholar
  5. 5.
    Biannic, J.M., Roos, C., Tarbouriech, S.: A practical method for fixed-order anti-windup design. In: Proceedings of 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS), Pretoria, South Africa (2007)Google Scholar
  6. 6.
    Boada, J.: Satellite control with saturating inputs. Ph.D. thesis, ISAE, Toulouse, France (2010)Google Scholar
  7. 7.
    Boada, J., Prieur, C., Tarbouriech, S., Pittet, C., Charbonnel, C.: Anti-windup design for satellite control with microthrusteurs. In: Proceedings of AIAA GN&C conference, Chicago, IL, USA (2009)Google Scholar
  8. 8.
    Boada, J., Prieur, C., Tarbouriech, S., Pittet, C., Charbonnel, C.: Multi-saturation anti-windup structure for satellite control. In: Proceedings of the American Control Conference, Baltimore, MD, USA (2010)Google Scholar
  9. 9.
    Boada, J., Prieur, C., Tarbouriech, S., Pittet, C., Charbonnel, C.: Extended model recovery anti-windup for satellite control. In: Proceedings of the 16th IFAC Symposium on Automatic Control in AeroSpace, Nara, Japan (2010)Google Scholar
  10. 10.
    Boyd, S., Vandenberghe, L.S.P.: Convex Optimization. Cambridge Univesity Press, Cambridge (2004)zbMATHGoogle Scholar
  11. 11.
    Durham, D.C.: Constrained control allocation. J. Guid. Contr. Dynam. 16, 717–725 (1993)CrossRefGoogle Scholar
  12. 12.
    Galeani, A.R., Teel, A.R., Zaccarian, L.: Constructive nonlinear anti-windup design for exponentially unstable linear plants. Syst. Contr. Lett. 56(5), 357–365 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Galeani, S., Onori, A.R., Teel, A.R., Zaccarian, L.: Regional, semiglobal, global nonlinear anti-windup via switching design. In: Proceedings European Control Conference, Kos, Greece (2007)Google Scholar
  14. 14.
    Galeani, S., Tarbouriech, S., Turner, M.C., Zaccarian, L.: A tutorial on modern anti-windup design. Eur. J. Contr. 15(3–4), 418–440 (2009)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Gaulocher, S.: Commande boucle fermée multivariable pour le vol en formation de vaisseaux spatiaux. Ph.D. thesis, Université de Toulouse, Toulouse, France (2007)Google Scholar
  16. 16.
    Gomes da Silva, J.M. Jr., Tarbouriech, S.: Anti-windup design with guaranteed regions of stability: An LMI-based approach. IEEE Trans. Automat. Contr. 50(1), 106–111 (2005)Google Scholar
  17. 17.
    Grimm, G., Hatfield, J., Postlethwaite, I., Teel, A.R., Turner, M.C., Zaccarian, L.: Anti-windup for stable linear systems with input saturation: An LMI-based synthesis. IEEE Trans. Automat. Contr. 48(9), 1509–1525 (2003)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Hu, T., Lin, Z.: Control Systems with Actuator Saturation. Analysis and Design. Birkhauser, Basel (2001)zbMATHCrossRefGoogle Scholar
  19. 19.
    Kapila, V., Grigoriadis, K. (eds.): Actuator Saturation Control. Marcel Dekker, New York (2002)Google Scholar
  20. 20.
    Kerr, M.L., Turner, M.C., Postlethwaite, I.: Practical approaches to low-order anti-windup compensator design: A flight control comparison. In: IFAC World Congress, Seoul, Korea (2008)Google Scholar
  21. 21.
    Löfberg, J.: Yalmip: A toolbox for modeling and optimization in matlab. In: CACSD Conference, Taipei, Taiwan (2004)Google Scholar
  22. 22.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)zbMATHCrossRefGoogle Scholar
  23. 23.
    Peaucelle, D., Arzelier, D.: An efficient numerical solution for H 2 static output feedback synthesis. In: Proceedings of European Control Conference, Porto, Portugal (2001)Google Scholar
  24. 24.
    Pirson, L., Charbonnel, C., Udrea, B., Rennie, M., McGuinness, P., Palomo, P.: Darwin precursor demonstration mission: The ICC2 study, from GNC design to real-time test bench validation. In: Proceedings of 6th GNC ESA, Loutraki, Greece (2005)Google Scholar
  25. 25.
    Roos, C., Biannic, J.M.: A convex characterization of dynamically-constrained anti-windup controllers. Automatica 44(8), 2449–2452 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Stein, G.: Bode lecture: Respect the unstable. In: Proceedings of Conference on Decision and Control, Tampa, USA, December (1989)Google Scholar
  27. 27.
    Tarbouriech, S., Turner, M.C.: Anti-windup synthesis: An overview of some recent advances and open problems. IET Control Theory Appl. 3(1), 1–19 (2009)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Tarbouriech, S., Prieur, C., Gomes da Silva, J.M. Jr.: Stability analysis and stabilization of systems presenting nested saturations. IEEE Trans. Automat. Contr. 51(8), 1364–1371 (2006)Google Scholar
  29. 29.
    Tarbouriech, S., Garcia, G., Gomes da Silva, J.M. Jr., Queinnec, I.: Stability and stabilization of linear systems with saturating actuators. Springer, London (2011)Google Scholar
  30. 30.
    Teel, A.R., Kapoor, N.: The 2 antiwindup problem: Its definition and solution. In: Proceedings of the 4th European Control Conference, Brussels, Belgium (1997)Google Scholar
  31. 31.
    Turner, M.C., Postlethwaite, I.: A new perspective on static and low order anti-windup synthesis. Internat. J. Control 77(1), 27–44 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Zaccarian, L., Teel, A.R.: A common framework for anti-windup, bumpless transfer and reliable designs. Automatica 38(10), 1735–1744 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Zaccarian, L., Teel, A.R.: Modern Anti-Windup Synthesis. Princeton University Press, Princeton (2011)Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Josep Boada
    • 1
  • Christophe Prieur
    • 2
  • Sophie Tarbouriech
    • 3
    • 4
  • Christelle Pittet
    • 5
  • Catherine Charbonnel
    • 6
  1. 1.Albatros AeronauticsVictoriaSpain
  2. 2.Gipsa-lab, Department of Automatic ControlGrenoble CampusSaint Martin d’Hères CedexFrance
  3. 3.CNRS, LAASToulouseFrance
  4. 4.Univ de Toulouse, LAASToulouseFrance
  5. 5.Centre National d’Etudes Spatiales (CNES)ToulouseFrance
  6. 6.Thales Alenia SpaceCannesFrance

Personalised recommendations