Advertisement

Output Feedback Tracking Control of Flat Systems via Exact Feedforward Linearization and LPV Techniques

  • Liming Chen
  • Yingmin JiaEmail author
Article
  • 7 Downloads

Abstract

In this article, an output feedback control scheme is proposed for trajectory tracking of differentially flat systems. After applying the exact feedforward linearization, the tracking error dynamics is linearized as a linear time-varying (LTV) system, where only the state matrix is time-varying while the input and output matrices are time-invariant. Using linear parameter-varying (LPV) techniques based on polytopes, for the LTV system the controller matrices, which are set to be affine on time-varying parameters, are calculated by solving a set of linear matrix inequalities (LMIs). An example for trajectory tracking of a two-wheeled mobile robot is given to show the effectiveness of the proposed method.

Keywords

Flat systems H control mobile robots output feedback control 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Fliess, J. Lévine, P. Martin, and P. Rouchon, “Flatness and defect of nonlinear systems: introductory theory and examples,” International Journal of Control, vol. 61, no. 6, pp. 1327–1361, 1995.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    M. Fliess, J. Lévine, P. Martin, and P. Rouchon, “A Lie–Bäcklund approach to equivalence and flatness of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 44, no. 5, pp. 922–937, 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M. Fliess and J. Rudolph, “Local tracking observers for flat systems,” Proceedings of the Symposium on Control, Optimization and Supervision, CESA’96 IMACS Multiconference, Lille, France, pp. 213–217, 1996.Google Scholar
  4. [4]
    J. Deutscher, “A linear differential operator approach to flatness based tracking for linear and non–linear systems,” International Journal of Control, vol. 76, no. 3, pp. 266–276, 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    F. Cazaurang, “Commande robuste des systèmes plats: application à la commande d’une machine synchrone,” Doctoral dissertation, Université Sciences et Technologies–Bordeaux I, 1997.Google Scholar
  6. [6]
    M. Zerar, F. Cazaurang, and A. Zolghadri, “Robust tracking of nonlinear MIMO uncertain flat systems,” IEEE International Conference on Systems, Man and Cybernetics, Hague, Netherlands, pp. 536–541, 2004.Google Scholar
  7. [7]
    M. Zerar, F. Cazaurang, and A. Zolghadri, “Coupled linear parameter varying and flatness–based approach for space re–entry vehicles guidance,” IET Control Theory and Applications, vol. 3, no. 8, pp. 1081–1092, 2009.MathSciNetCrossRefGoogle Scholar
  8. [8]
    V. Hagenmeyer and E. Delaleau, “Exact feedforward linearization based on differential flatness,” International Journal of Control, vol. 76, no. 6, pp. 537–556, 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    V. Hagenmeyer and E. Delaleau, “Robustness analysis of exact feedforward linearization based on differential flatness,” Automatica, vol. 39, pp. 1941–1946, 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    V. Hagenmeyer and E. Delaleau, “Robustness analysis with respect to exogenous perturbations for flatness–based exact feedforward linearization,” IEEE Transactions on Automatic Control, vol. 55, no. 3, pp. 727–731, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    A. Luviano–Juárez, J. Cortés–Romero, and H. Sira–Ramírez, “Trajectory tracking control of a mobile robot through a flatness–based exact feedforward linearization scheme,” Journal of Dynamic Systems, Measurement, and Control, vol. 137. no. 5, 2015.Google Scholar
  12. [12]
    R. Morales and H. Sira–Ramírez, “Trajectory tracking for the magnetic ball levitation system via exact feedforward linearisation and GPI control,” International Journal of Control, vol. 83, no. 6, pp. 1155–1166, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    L. Lavigne, F. Cazaurang, and B. Bergeon, “Modelization of disturbed flat system for robust control design,” Proc. of 5th IFAC Symposium on Nonlinear Control System (NOLCOS’ 01), Saint Petersbourg, Russia, vol. 2, pp. 759–762, 2001.Google Scholar
  14. [14]
    L. Chen, Y. Jia, and J. Du, “Robust control of flat systems using sliding mode approach,” Proc. of American Control Conference, Boston, MA, USA, pp. 4749–4753, 2016.Google Scholar
  15. [15]
    P. Apkarian, P. Gahinet, and G. Becker, “Self–scheduled H¥ control of linear parameter–varying systems: a design example,” Automatica, vol. 31, no. 9, pp. 1251–1261, 1995.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    P. Gahinet, “Explicit controller formulas for LMI–based H¥ synthesis,” Automatica, vol. 32, no. 7, pp. 1007–1014, 1996.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    C. Scherer, P. Gahinet, and M. Chilali, “Multiobjective output–feedback control via LMI optimization,” IEEE Transactions on Automatic Control, vol. 42, no. 7, pp. 896–911, 1997.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    F. Wu, “A generalized LPV system analysis and control synthesis framework,” International Journal of Control, vol. 74, no. 7, pp. 745–759, 2001.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    L. Chen and Y. Jia, “Variable–poled tracking control of a two–wheeled mobile robot using differential flatness,” Journal of Robotics, Networking and Artificial Life, vol. 1, no. 1, pp. 12–16, 2014.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Seventh Research Division and the Center for Information and Control, School of Automation Science and Electrical EngineeringBeihang University (BUAA)BeijingChina

Personalised recommendations