Advertisement

Nonlinear Dynamics

, Volume 82, Issue 1–2, pp 599–610 | Cite as

An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

  • Saleh Mobayen
Original Paper

Abstract

In this paper, an adaptive fast terminal sliding mode control technique combined with a global sliding mode control scheme is investigated for the tracking problem of uncertain nonlinear third-order systems. The proposed robust tracking controller is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Under the uncertainty and nonlinearity effects, the reaching phase is removed and the chattering phenomenon is eliminated. This scheme guarantees robustness against nonlinear functions, parameter uncertainties and external disturbances. The derivative of the state variable is replaced by a delay term in the form of an Euler approximation of the derivative function. Furthermore, the knowledge of upper bounds of the system uncertainties is not required, which is more flexible in the real implementations. Simulation results are presented to show the effectiveness of the suggested method.

Keywords

Fast terminal sliding mode Adaptive tuning Global sliding surface Third-order nonlinear system Tracking Robustness 

References

  1. 1.
    Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43, 678–682 (1998)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Mobayen, S., Majd, V.J.: Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances. Nonlinear Dyn. 70, 171–180 (2012)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Tong, S.C., Li, Y.M., Feng, G., Li, T.S.: Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems. IEEE Trans. Syst. Man Cybern. B 41, 1124–1135 (2011)CrossRefGoogle Scholar
  4. 4.
    Mobayen, S.: Finite-time stabilization of a class of chaotic systems with matched and unmatched uncertainties: an LMI approach. Complex. (2014). doi: 10.1002/cplx.21624
  5. 5.
    Tong, S., Li, Y., Shi, P.: Observer-based adaptive fuzzy backstepping output feedback control of uncertain MIMO pure-feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 20, 771–785 (2012)CrossRefGoogle Scholar
  6. 6.
    Mobayen, S.: Design of LMI-based sliding mode controller with an exponential policy for a class of underactuated systems. Complex. (2014). doi: 10.1002/cplx.21636
  7. 7.
    Boulkroune, A., Bouzeriba, A., Hamel, S., Bouden, T.: A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems. Nonlinear Dyn. 78(1), 433–447 (2014)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Boulkroune, A., M’saad, M.: Fuzzy adaptive observer-based projective synchronization for nonlinear systems with input nonlinearity. J. Vib. Control 18(3), 437–450 (2012)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Mobayen, S.: Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback. Nonlinear Dyn. 76, 827–838 (2014)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Boulkroune, A., Bouzeriba, A., Hamel, S., Bouden, T.: Adaptive fuzzy control-based projective synchronization of uncertain nonaffine chaotic systems. Complex. (2014). doi: 10.1002/cplx.21596
  11. 11.
    Sun, T., Pei, H., Pan, Y., Zhou, H., Zhang, C.: Neural network-based sliding mode adaptive control for robot manipulators. Neurocomputing 74, 2377–2384 (2011)CrossRefGoogle Scholar
  12. 12.
    Mobayen, S.: Finite-time tracking control of chained-form nonholonomic systems with external disturbances based on recursive terminal sliding mode method. Nonlinear Dyn. 80, 669–683 (2015)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Rao, D.V., Sinha, N.K.: A sliding mode controller for aircraft simulated entry into spin. Aerosp. Sci. Technol. 28, 154–163 (2013)CrossRefGoogle Scholar
  14. 14.
    Pisano, A., Usai, E.: Output-feedback control of an underwater vehicle prototype by higher-order sliding modes. Automatica 40, 1525–1531 (2004)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Song, Z., Li, H., Sun, K.: Finite-time control for nonlinear spacecraft attitude based on terminal sliding mode technique. ISA Trans. 53, 117–124 (2014)CrossRefGoogle Scholar
  16. 16.
    Allen, M., Zazzera, F.B., Scattolini, R.: Sliding mode control of a large flexible space structure. Control Eng. Pract. 8, 861–871 (2000)CrossRefGoogle Scholar
  17. 17.
    Mobayen, S.: An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems. Nonlinear Dyn. 79, 1075–1084 (2015)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Hsu, C.F., Lee, B.K.: FPGA-based adaptive PID control of a DC motor driver via sliding-mode approach. Expert Syst. Appl. 38, 11866–11872 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Ouassaid, M., Maaroufi, M., Cherkaoui, M.: Observer-based nonlinear control of power system using sliding mode control strategy. Electr. Power Syst. Res. 84, 135–143 (2012)Google Scholar
  20. 20.
    Mobayen, S., Javadi, S.: Disturbance observer and finite-time tracker design of disturbed third-order nonholonomic systems using terminal sliding mode. J. Vib. Control (2015). doi: 10.1177/1077546315576611
  21. 21.
    Mobayen, S.: An LMI-based robust tracker for uncertain linear systems with multiple time-varying delays using optimal composite nonlinear feedback technique. Nonlinear Dyn. 80, 917–927 (2015)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Mobayen, S.: Fast terminal sliding mode tracking of non-holonomic systems with exponential decay rate. IET Control Theory Appl. (2015). doi: 10.1049/iet-cta.2014.1118
  23. 23.
    Mobayen, S.: An adaptive chattering-free PID sliding mode control based on dynamic sliding manifolds for a class of uncertain nonlinear systems. Nonlinear Dyn. (2015). doi: 10.1007/s11071-015-2137-7
  24. 24.
    Mobayen, S.: Finite-time robust-tracking and model-following controller for uncertain dynamical systems. J. Vib. Control. (2014). doi: 10.1177/1077546314538991
  25. 25.
    Mobayen, S.: Design of LMI-based global sliding mode controller for uncertain nonlinear systems with application to Genesio’s chaotic system. Complex. (2014). doi: 10.1002/cplx.21545
  26. 26.
    Mobayen, S., Majd, V.J., Sojoodi, M.: An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems. Math. Comput. Simul. 85, 1–10 (2012)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Chiang, M.H.: The velocity control of an electro-hydraulic displacement-controlled system using adaptive fuzzy controller with self-tuning fuzzy sliding mode compensation. Asian J. Control 13, 492–504 (2011)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Li, L., Song, G., Ou, J.: Adaptive fuzzy sliding mode based active vibration control of a smart beam with mass uncertainty. Struct. Control Health Monit. 18, 40–52 (2011)Google Scholar
  29. 29.
    Zhu, M., Li, Y.: Decentralized adaptive fuzzy sliding mode control for reconfigurable modular manipulators. Int. J. Robust Nonlinear Control 20, 472–488 (2010)CrossRefMathSciNetMATHGoogle Scholar
  30. 30.
    Bessa, W.M., Paula, A.S., Savi, M.A.: Adaptive fuzzy sliding mode control of a chaotic pendulum with noisy signals. ZAMM J. Appl. Math. Mech. 94, 256–263 (2014)CrossRefMathSciNetGoogle Scholar
  31. 31.
    Ning, X.L., Tan, P., Huang, D.Y., Zhou, F.L.: Application of adaptive fuzzy sliding mode control to a seismically excited highway bridge. Struct. Control Health Monit. 16, 639–656 (2009)CrossRefGoogle Scholar
  32. 32.
    Pai, M.C.: Robust tracking and model following for uncertain time-delay systems with input nonlinearity. Complex. (2014). doi: 10.1002/cplx.21578
  33. 33.
    Roopaei, M., Sahraei, B.R., Lin, T.C.: Adaptive sliding mode control in a novel class of chaotic systems. Commun. Nonlinear Sci. Numer. Simul. 15, 4158–4170 (2010)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Mondal, S., Mahanta, C.: Chattering free adaptive multivariable sliding mode controller for systems with matched and mismatched uncertainty. ISA Trans. 52, 335–341 (2013)CrossRefGoogle Scholar
  35. 35.
    Pukdeboon, C., Siricharuanun, P.: Nonsingular terminal sliding mode based finite-time control for spacecraft attitude tracking. Int. J. Control Autom. Syst. 12, 530–540 (2014)CrossRefGoogle Scholar
  36. 36.
    Yang, J., Li, S., Su, J., Yu, X.: Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances. Automatica 49, 2287–2291 (2013)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Yang, L., Yang, J.: Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems. Int. J. Robust Nonlinear Control 21, 1865–1879 (2011)CrossRefMathSciNetMATHGoogle Scholar
  38. 38.
    Yu, X., Man, Z.: Fast terminal sliding mode control design for nonlinear dynamical systems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 49, 261–264 (2002)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Mobayen, S., Yazdanpanah, M.J., Majd, V.J.: A finite time tracker for nonholonomic systems using recursive singularity-free FTSM. In: 2011 American Control Conference, pp. 1720–1725, San Francisco, CA (2011)Google Scholar
  40. 40.
    Qi, L., Shi, H.: Adaptive position tracking control of permanent magnet synchronous motor based on RBF fast terminal sliding mode control. Neurocomputing 115, 23–30 (2013)CrossRefGoogle Scholar
  41. 41.
    Mobayen, S.: Fast terminal sliding mode controller design for nonlinear second-order systems with time-varying uncertainties. Complex. (2014). doi: 10.1002/cplx.21600
  42. 42.
    Cao, Q., Li, S., Zhao, D.: Adaptive motion/force control of constrained manipulators using a new fast terminal sliding mode. Int. J. Comput. Appl. Technol. 49, 150–156 (2014)CrossRefGoogle Scholar
  43. 43.
    Zheng, J., Wang, H., Man, Z., Jin, J., Fu, M.: Robust motion control of a linear motor positioner using fast nonsingular terminal sliding mode. IEEE/ASME Trans. Mechatron. (2014). doi: 10.1109/TMECH.2014.2352647
  44. 44.
    Lu, Y.S., Chiu, C.W., Chen, J.S.: Time-varying sliding mode control for finite-time convergence. Nonlinear Dyn. 92, 257–268 (2010)Google Scholar
  45. 45.
    Tai, T.L., Lu, Y.S.: Global sliding mode control with chatter alleviation for robust eigenvalue assignment. J. Syst. Control Eng. 220, 573–584 (2006)Google Scholar
  46. 46.
    Cong, B.L., Chen, Z., Liu, X.D.: On adaptive sliding mode control without switching gain overestimation. Int. J. Robust Nonlinear Control 24, 515–531 (2014)MathSciNetCrossRefMATHGoogle Scholar
  47. 47.
    Wu, M., Chen, J.S.: A discrete-time global quasi-sliding mode control scheme with bounded external disturbance rejection. Asian J. Control 16, 1839–1848 (2014)MathSciNetCrossRefMATHGoogle Scholar
  48. 48.
    Yang, C., Ke, Z., Lei, D.: Research on global fast terminal sliding mode guidance law. Comput. Meas. Control 2013(2), 391–393 (2013)Google Scholar
  49. 49.
    Weifeng, Y., Juntao, F., Yuzheng, Y., Shixi, H.: Adaptive global fast terminal sliding mode control of MEMS gyroscope. In: 2013 32nd Chinese Control Conference, pp. 3135–3140, Xi’an, China (2013)Google Scholar
  50. 50.
    Bartoszewicz, A., Nowacka, A.: Sliding-mode control of the third-order system subject to velocity, acceleration and input signal constraints. Int. J. Adapt. Control Signal Process. 21, 779–794 (2007)MathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    Moulay, E., Peruquetti, W.: Finite time stability and stabilization of a class of continuous systems. J. Math. Anal. Appl. 323, 1430–1443 (2006)MathSciNetCrossRefMATHGoogle Scholar
  52. 52.
    Isidori, A.: Nonlinear Control Systems—An Introduction, 2nd edn. Springer, New York (1989)CrossRefMATHGoogle Scholar
  53. 53.
    Yang, Y., Zhou, C., Jia, X.: Robust adaptive fuzzy control and its application to ship roll stabilization. Inf. Sci. 142, 177–194 (2002)CrossRefMATHGoogle Scholar
  54. 54.
    Ilchmann, A., Sangwin, C.J.: Output feedback stabilisation of minimum phase systems by delays. Syst. Control Lett. 52, 233–245 (2004)MathSciNetCrossRefMATHGoogle Scholar
  55. 55.
    Huang, Y.J., Kuo, T.C., Chang, S.H.: Adaptive sliding-mode control for nonlinear systems with uncertain parameters. IEEE Trans. Syst. Man Cybern. 38(2), 534–539 (2008)CrossRefGoogle Scholar
  56. 56.
    Qin, H., Ma, J., Jin, W.Y., Wang, C.N.: Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci. China Technol. Sci. 57(5), 936–946 (2014)MathSciNetCrossRefGoogle Scholar
  57. 57.
    Ma, J., Qin, H., Song, X., Chu, R.: Pattern selection in neuronal network driven by electric autapses with diversity in time delays. Int. J. Mod. Phys. B 29(1), 1450239 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentUniversity of ZanjanZanjanIran

Personalised recommendations