Output-Feedback Stabilization of the PVTOL Aircraft System Based on an Exact Differentiator

  • Carlos Aguilar-Ibañez
  • Miguel S. Suarez-Castanon
  • Julio Mendoza-Mendoza
  • Jose de Jesus Rubio
  • Juan Carlos Martínez-García
Article
  • 49 Downloads

Abstract

An output-feedback control strategy for the regulation of a planar vertical take-off and landing aircraft is presented here. The strategy consists of two controllers that work simultaneously. The first controller stabilizes the vertical variable, and is based on a simple feedback-linearization procedure, in combination with a nonlinear controller (which behaves as a terminal slide mode). The other controller stabilizes the horizontal and angular variables to the desired rest position, and was designed using an energy-control method. The velocities were exactly estimated with a second-order sliding-mode observer. Because this observer computes the velocities in finite time, the control strategy can be designed independently. The effectiveness of the closed-loop system was tested through numerical simulations and compared with other control strategies.

Keywords

PVTOL aircraft Sliding mode observer Energy-based control Exact differentiator 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

This research was supported by the Secretaría de Investigación y Posgrado of the Instituto Politecnico Nacional (SIP-IPN) under Research Grants 20171586 and 20171948.

References

  1. 1.
    Acosta, J.A., Ortega, R., Astolfi, A., Mahindrakar, A.D.: Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one. IEEE Trans. Autom. Control 50(12), 1936–1955 (2005)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Benosman, M., Liao, F., Lum, K.Y.: Output trajectory tracking for the pvtol aircraft through control allocation. In: 2007. CCA 2007. IEEE International Conference on Control Applications, pp. 880–885. IEEE (2007)Google Scholar
  3. 3.
    Borrelli, F., Bemporad, A., Morari, M.: Predictive control for linear and hybrid systems. Camb. February 20, 2011 (2011)MATHGoogle Scholar
  4. 4.
    Cárdenas, R., Aguilar, L.T.: Output feedback sliding mode control of a pvtol including actuators dynamics. In: Control Applications (CCA), 2011 IEEE International Conference on, pp. 1482–1486. IEEE (2011)Google Scholar
  5. 5.
    Castaños, F., Fridman, L.: Analysis and design of integral sliding manifolds for systems with unmatched perturbations. IEEE Trans. Autom. Control 51(5), 853–858 (2006)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Cerven, W.T., Bullo, F.: Constructive controllability algorithms for motion planning and optimization. IEEE Trans. Autom. Control 48(4), 575–589 (2003)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Chemori, A., Marchand, N.: Global discrete-time stabilization of the pvtol aircraft based on fast predictive control. In: Proceedings of the 17th World Congress The International Federation of Automatic Control (2008)Google Scholar
  8. 8.
    Consolini, L., Maggiore, M., Nielsen, C., Tosques, M.: Path following for the pvtol aircraft. Automatica 46(8), 1284–1296 (2010)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Corona-Sánchez, J.J., Rodríguez-Cortés, H.: Experimental real-time validation of an attitude nonlinear controller for the quadrotor vehicle. In: Unmanned Aircraft Systems (ICUAS), 2013 International Conference on, pp. 453–460. IEEE (2013)Google Scholar
  10. 10.
    Corona-Sánchez, J.J., Rodríguez-Cortés, H.: Trajectory tracking control for a rotary wing vehicle powered by four rotors. J. Intell. Robot. Syst. 70(1-4), 39–50 (2013)CrossRefGoogle Scholar
  11. 11.
    Davila, J.: Exact tracking using backstepping control design and high-order sliding modes. IEEE Trans. Autom. control 58(8), 2077–2081 (2013)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Davila, J., Fridman, L., Levant, A.: Second-order sliding-mode observer for mechanical systems. IEEE Trans. Autom. Control 50(11), 1785–1789 (2005)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Fantoni, I., Lozano, R.: Non-linear control for underactuated mechanical systems. Springer Science & Business Media, Berlin (2001)MATHGoogle Scholar
  14. 14.
    Fantoni, I., Lozano, R., Castillo, P.: A simple stabilization algorithm for the pvtol aircraft. In: 15th IFAC World Congress (2002)Google Scholar
  15. 15.
    Fantoni, I., Palomino, A., Castillo, P., Lozano, R., Pégard, C.: Control strategy using vision for the stabilization of an experimental pvtol aircraft setup. In: Current Trends in Nonlinear Systems and Control, pp. 407–419. Springer (2006)Google Scholar
  16. 16.
    Frye, M.T., Ding, S., Qian, C., Li, S.: Global finite-time stabilization of a pvtol aircraft by output feedback. In: CDC/CCC 2009. Proceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference, pp. 2831–2836. IEEE (2009)Google Scholar
  17. 17.
    Gandolfo, D., Rosales, C., Patiño, D., Scaglia, G., Jordan, M.: Trajectory tracking control of a pvtol aircraft based on linear algebra theory. Asian J. Control 16(6), 1849–1858 (2014)CrossRefMATHGoogle Scholar
  18. 18.
    Garcia, P.C., Lozano, R., Dzul, A.E.: Modelling and control of mini-flying machines. Springer Science & Business Media, Berlin (2006)Google Scholar
  19. 19.
    Gruszka, A., Malisoff, M., Mazenc, F.: On tracking for the pvtol model with bounded feedbacks. In: American Control Conference (ACC) 2011, pp. 1428–1433. IEEE (2011)Google Scholar
  20. 20.
    Guadarrama-Olvera, J.R., Corona-Sánchez, J. J., Rodríguez-Cortés, H.: Hard real-time implementation of a nonlinear controller for the quadrotor helicopter. J. Intell. Robot. Syst. 73(1-4), 81–97 (2014)CrossRefGoogle Scholar
  21. 21.
    Gupta, A., Mejari, M., Ketkar, V., Datar, M., Singh, N.M.: Nonlinear model predictive control of pvtol aircraft under state and input constraints. In: Proceedings of Conference on Advances In Robotics, pp. 1–6. ACM (2013)Google Scholar
  22. 22.
    Han, J.: From pid to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009)CrossRefGoogle Scholar
  23. 23.
    Hauser, J., Sastry, S., Meyer, G.: Nonlinear control design for slightly non-minimum phase systems: application to v/stol aircraft. Automatica 28(4), 665–679 (1992)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Huang, C.S., Yuan, K.: Output tracking of a non-linear non-minimum phase pvtol aircraft based on non-linear state feedback control. Int. J. Control 75(6), 466–473 (2002)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Khalil, H.K., Grizzle, J.: Nonlinear systems, vol. 3. Prentice Hall, Upper Saddle River (2002)Google Scholar
  26. 26.
    Lin, F., Zhang, W., Brandt, R.D.: Robust hovering control of a pvtol aircraft. IEEE Trans. Control Syst. Technol. 7(3), 343–351 (1999)CrossRefGoogle Scholar
  27. 27.
    Lozano, R., Castillo, P., Dzul, A.: Global stabilization of the pvtol: real-time application to a mini-aircraft. Int. J. Control 77(8), 735–740 (2004)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Lu, X.Y., Spurgeon, S.K., Postxethwaite, I.: Robust variable structure control of a pvtol aircraft. Int. J. Syst. Sci. 28(6), 547–558 (1997)CrossRefMATHGoogle Scholar
  29. 29.
    Maqsood, A., Go, T.H.: Multiple time scale analysis of aircraft longitudinal dynamics with aerodynamic vectoring. Nonlinear Dyn. 69(3), 731–742 (2012)MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Marconi, L., Isidori, A., Serrani, A.: Autonomous vertical landing on an oscillating platform: an internal-model based approach. Automatica 38(1), 21–32 (2002)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Martin, P., Devasia, S., Paden, B.: A different look at output tracking: control of a vtol aircraft. In: 1994., Proceedings of the 33rd IEEE Conference on Decision and Control, vol. 3, pp. 2376–2381. IEEE (1994)Google Scholar
  32. 32.
    Munoz, L.E., Santos, O., Castillo, P.: Robust nonlinear real-time control strategy to stabilize a pvtol aircraft in crosswind. In: 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1606–1611. IEEE (2010)Google Scholar
  33. 33.
    Nielsen, C., Consolini, L., Maggiore, M., Tosques, M.: Path following for the pvtol: A set stabilization approach. In: 2008. CDC 2008. 47th IEEE Conference on Decision and Control, pp. 584–589. IEEE (2008)Google Scholar
  34. 34.
    Notarstefano, G., Hauser, J., Frezza, R.: Trajectory manifold exploration for the pvtol aircraft. In: CDC-ECC’05. 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference, pp. 5848–5853. IEEE (2005)Google Scholar
  35. 35.
    Olfati-Saber, R.: Global configuration stabilization for the vtol aircraft with strong input coupling. IEEE Trans. Autom. Control 47(11), 1949–1952 (2002)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Ortega, R., Garcia-Canseco, E.: Interconnection and damping assignment passivity-based control: A survey. Eur. J. control 10(5), 432–450 (2004)MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Palomino, A., Castilto, P., Fantoni, I., Lozano, R., Pégard, C.: Control strategy using vision for the stabilization of an experimental pvtol aircraft setup. IEEE Trans. Control Syst. Technol. 13(5), 847–850 (2005)CrossRefGoogle Scholar
  38. 38.
    Qiu, H., Duan, H.: Receding horizon control for multiple uav formation flight based on modified brain storm optimization. Nonlinear Dyn. 78(3), 1973–1988 (2014)CrossRefGoogle Scholar
  39. 39.
    Rubio, J.d.J., Cruz, J.P., Zamudio, Z., Salinas, A.: Comparison of two quadrotor dynamic models. IEEE Latin Amer. Trans. 12(4), 531–537 (2014)CrossRefGoogle Scholar
  40. 40.
    Sastry, S.: Nonlinear systems: analysis, stability, and control, vol. 10. Springer, New York (1999)CrossRefMATHGoogle Scholar
  41. 41.
    Sepulchre, R., Jankovic, M., Kokotovic, P.: Constructive nonlinear control. Springer, Berlin (1997)CrossRefMATHGoogle Scholar
  42. 42.
    Sira-Ramirez, H., Fliess, M.: Regulation of non-minimum phase outputs in a pvtol aircraft. In: 1998. Proceedings of the 37th IEEE Conference on Decision and Control, vol. 4, pp. 4222–4227. IEEE (1998)Google Scholar
  43. 43.
    Teel, A.R.: A nonlinear small gain theorem for the analysis of control systems with saturation. IEEE Trans. Autom. Control 41(9), 1256–1270 (1996)MathSciNetCrossRefMATHGoogle Scholar
  44. 44.
    Turker, T., Oflaz, T., Gorgun, H., Cansever, G.: A stabilizing controller for pvtol aircraft. In: 2012 American Control Conference (ACC), pp. 909–913. IEEE (2012)Google Scholar
  45. 45.
    Venkatesh, C., Mehra, R., Kazi, F., Singh, N.: Passivity based controller for underactuated pvtol system. In: 2013 IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT), vol. 1–5. IEEE (2013)Google Scholar
  46. 46.
    Wood, R., Cazzolato, B.: An alternative nonlinear control law for the global stabilization of the pvtol vehicle. IEEE Trans. Autom. Control 52(7), 1282–1287 (2007)MathSciNetCrossRefMATHGoogle Scholar
  47. 47.
    Wood, R., Cazzolato, B., Halim, D.: A global non-linear control design for a pvtol vehicle with aerodynamics. In: 2005 and 2005 European Control Conference. CDC-ECC’05. 44th IEEE Conference on Decision and Control, pp. 7478–7483. IEEE (2005)Google Scholar
  48. 48.
    Xian, B., Diao, C., Zhao, B., Zhang, Y.: Nonlinear robust output feedback tracking control of a quadrotor UAV using quaternion representation. Nonlinear Dynamics 79(4), 2735–2752 (2015)MathSciNetCrossRefMATHGoogle Scholar
  49. 49.
    Zavala-Río, A., Fantoni, I., Lozano, R.: Global stabilization of a pvtol aircraft model with bounded inputs. Int. J. Control 76(18), 1833–1844 (2003)MathSciNetCrossRefMATHGoogle Scholar
  50. 50.
    Zhu, B., Wang, Q., Huo, W.: Longitudinal–lateral velocity control design and implementation for a model-scaled unmanned helicopter. Nonlinear Dyn. 76(2), 1579–1589 (2014)CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Carlos Aguilar-Ibañez
    • 1
  • Miguel S. Suarez-Castanon
    • 2
  • Julio Mendoza-Mendoza
    • 1
  • Jose de Jesus Rubio
    • 3
  • Juan Carlos Martínez-García
    • 4
  1. 1.CIC-Instituto Politécnico NacionalMéxicoMexico
  2. 2.ESCOM-Instituto Politécnico NacionalMexicoMéxico
  3. 3.ESIME AZC-Instituto Politécnico NacionalCiudad de MéxicoMéxico
  4. 4.Control Automático - CINVESTAV del IPNCiudad de MéxicoMéxico

Personalised recommendations