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

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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.

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References

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  3. Borrelli, F., Bemporad, A., Morari, M.: Predictive control for linear and hybrid systems. Camb. February 20, 2011 (2011)

    MATH  Google Scholar 

  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)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cerven, W.T., Bullo, F.: Constructive controllability algorithms for motion planning and optimization. IEEE Trans. Autom. Control 48(4), 575–589 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  8. Consolini, L., Maggiore, M., Nielsen, C., Tosques, M.: Path following for the pvtol aircraft. Automatica 46(8), 1284–1296 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  11. Davila, J.: Exact tracking using backstepping control design and high-order sliding modes. IEEE Trans. Autom. control 58(8), 2077–2081 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Davila, J., Fridman, L., Levant, A.: Second-order sliding-mode observer for mechanical systems. IEEE Trans. Autom. Control 50(11), 1785–1789 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fantoni, I., Lozano, R.: Non-linear control for underactuated mechanical systems. Springer Science & Business Media, Berlin (2001)

    MATH  Google Scholar 

  14. Fantoni, I., Lozano, R., Castillo, P.: A simple stabilization algorithm for the pvtol aircraft. In: 15th IFAC World Congress (2002)

  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)

  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)

  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)

    Article  MATH  Google Scholar 

  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. 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)

  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)

    Article  Google Scholar 

  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)

  22. Han, J.: From pid to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  25. Khalil, H.K., Grizzle, J.: Nonlinear systems, vol. 3. Prentice Hall, Upper Saddle River (2002)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  29. Maqsood, A., Go, T.H.: Multiple time scale analysis of aircraft longitudinal dynamics with aerodynamic vectoring. Nonlinear Dyn. 69(3), 731–742 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

  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)

  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)

  35. Olfati-Saber, R.: Global configuration stabilization for the vtol aircraft with strong input coupling. IEEE Trans. Autom. Control 47(11), 1949–1952 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  36. Ortega, R., Garcia-Canseco, E.: Interconnection and damping assignment passivity-based control: A survey. Eur. J. control 10(5), 432–450 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  40. Sastry, S.: Nonlinear systems: analysis, stability, and control, vol. 10. Springer, New York (1999)

    Book  MATH  Google Scholar 

  41. Sepulchre, R., Jankovic, M., Kokotovic, P.: Constructive nonlinear control. Springer, Berlin (1997)

    Book  MATH  Google Scholar 

  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)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

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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.

Author information

Authors and Affiliations

  1. CIC-Instituto Politécnico Nacional, Av. Juan de Dios Bátiz s/n, U.P.A.L.M, Col. San Pedro Zacatenco, A.P. 75476, México, D.F. 07738, Mexico

    Carlos Aguilar-Ibañez & Julio Mendoza-Mendoza

  2. ESCOM-Instituto Politécnico Nacional, Av. Juan de Dios Bátiz s/n, Mexico, D.F. 07738, Ciudad de México, México

    Miguel S. Suarez-Castanon

  3. ESIME AZC-Instituto Politécnico Nacional, Av. de Las Granjas 682, 02250, Ciudad de México, México

    Jose de Jesus Rubio

  4. Control Automático - CINVESTAV del IPN, Av. Instituto Politécnico Nacional 2508, 07360, Ciudad de México, México

    Juan Carlos Martínez-García

Authors
  1. Carlos Aguilar-Ibañez
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  2. Miguel S. Suarez-Castanon
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  3. Julio Mendoza-Mendoza
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  4. Jose de Jesus Rubio
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  5. Juan Carlos Martínez-García
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Corresponding author

Correspondence to Carlos Aguilar-Ibañez.

Additional information

This research was suported by Secretarí a de Investigación y Posgrado del Instituto Politécnico Nacional, under research grants 20160268 and 20161637.

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Aguilar-Ibañez, C., Suarez-Castanon, M.S., Mendoza-Mendoza, J. et al. Output-Feedback Stabilization of the PVTOL Aircraft System Based on an Exact Differentiator. J Intell Robot Syst 90, 443–454 (2018). https://doi.org/10.1007/s10846-017-0660-0

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  • DOI: https://doi.org/10.1007/s10846-017-0660-0

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