Advertisement

Global asymptotic regulation control for MIMO mechanical systems with unknown model parameters and disturbances

  • Xin Hu
  • Xinjiang WeiEmail author
  • Huifeng Zhang
  • Jian Han
  • Xiuhua Liu
Original Paper
  • 34 Downloads

Abstract

A global asymptotic regulation control scheme based on the adaptive disturbance estimation is proposed for the MIMO mechanical systems with unknown model parameters and disturbances. By transforming the motion model of the mechanical system and the disturbances into the parametric forms, respectively, the disturbance rejection control for the MIMO mechanical systems is converted into the adaptive control problem. The robust adaptive control law is then designed using the adaptive backstepping method. Stability analysis shows that the designed control law achieves the global asymptotic regulation of the output vector. Simulations on regulation control of two marine vessels verify the effectiveness of the proposed control scheme.

Keywords

Mechanical systems Unknown model parameters Unknown disturbances Disturbance observer Adaptive backstepping method 

Notes

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

Funding

This study was funded by National Natural Science Foundation of China (Grant No. 61374108).

References

  1. 1.
    Jin, X.: Iterative learning control for non-repetitive trajectory tracking of robot manipulators with joint position constraints and actuator faults. Int. J. Adapt. Control Signal Process. 31(6), 859–875 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Chen, M., Shi, P., Lim, C.C.: Adaptive neural fault-tolerant control of a 3-DOF model helicopter system. IEEE Trans. Syst. Man Cybern. Syst. 46(2), 260–270 (2016)CrossRefGoogle Scholar
  3. 3.
    Wu, D.F., Ren, F.K., Qiao, L., Zhang, W.D.: Active disturbance rejection controller design for dynamically positioned vessels based on adaptive hybrid biogeography-based optimization and differential evolution. ISA Trans. 78, 56–65 (2018)CrossRefGoogle Scholar
  4. 4.
    Park, J.H., Shen, H., Chang, X.H., Lee, T.H.: Reliable \({\mathscr {H}}_{\infty }\) \(H_\infty \) Event-triggered control for Markov Jump Systems. In: Recent Advances in Control and Filtering of Dynamic Systems with Constrained. Springer, Cham (2018)Google Scholar
  5. 5.
    Sun, H.B., Li, S.H., Sun, C.Y.: Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dynamics 73(1–2), 229–244 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gu, X.D., Zhu, W.Q.: Stochastic optimal control of predatorcprey ecosystem by using stochastic maximum principle. Nonlinear Dynamics 85(2), 1177–1184 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Zhang, C.L., Li, S.H., Yang, N.: A generalized active disturbance rejection control method for nonlinear uncertain systems subject to additive disturbance. Nonlinear Dynamics 83(4), 2361–2372 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Liu, H., Guo, L., Zhang, Y.M.: An anti-disturbance PD control scheme for attitude control and stabilization of flexible spacecrafts. Nonlinear Dynamics 67(3), 2081–2088 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Cao, S.Y., Zhao, Y.F.: Anti-disturbance fault-tolerant attitude control for satellites subject to multiple disturbances and actuator saturation. Nonlinear Dynamics 89(4), 2657–2667 (2017)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Chen, M., Wu, Q.X., Jiang, C.S.: Disturbance-observer-based robust synchronization control of uncertain chaotic systems. Nonlinear Dynamics 70(4), 2421–22432 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Chen, M., Chen, W.H.: Sliding mode control for a class of uncertain nonlinear system based on disturbance observer. Int. J. Adapt. Control Signal Process. 24(1), 51–64 (2010)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Chen, W.H., Yang, J., Guo, L., Li, S.H.: Disturbance-observer-based control and related methodsłan overview. IEEE Trans. Ind. Electron. 63(2), 1083–1095 (2016)CrossRefGoogle Scholar
  13. 13.
    Guo, L.: Anti-disturbance Control for Systems with Multiple Disturbances. CRC Press, Boca Raton (2014)Google Scholar
  14. 14.
    Li, S.H., Yang, J., Chen, W.H., Chen, X.S.: Disturbance Observer-based Control-methods and Applications. CRC Press, Boca Raton, FL, USA (2014)Google Scholar
  15. 15.
    Ohishi, K., Nakao, M., Ohnishi, K., Miyachi, K.: Microprocessor-controlled DC motor for load-insensitive position servo system. IEEE Trans. Ind. Electron. IE–34(1), 44–49 (1987)CrossRefGoogle Scholar
  16. 16.
    Chen, W.H., Ballance, D.J., Gawthrop, P.J., O’Reilly, J.: A nonlinear disturbance observer for robotic manipulators. IEEE Trans. Ind. Electron. 47(4), 932–938 (2000)CrossRefGoogle Scholar
  17. 17.
    Chen, W.H.: Disturbance observer-based control for nonlinear systems. IEEE/ASME Trans. Mechatron. 9(4), 706–710 (2004)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Guo, L., Chen, W.H.: Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. Int. J. Robust Nonlinear Control 15(3), 109–125 (2005)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Wei, X.J., Guo, L.: Composite disturbance-observer-based control and terminal sliding mode control for non-linear systems with disturbances. Int. J. Control 82(6), 1082–1098 (2009)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Wei, X.J., Wu, Z.J., Karimi, H.R.: Disturbance observer-based disturbance attenuation control for a class of stochastic systems. Automatica 63, 21–25 (2016)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Wei, X.J., Zhang, H.F., Sun, S.X., Karimi, H.R.: Composite hierarchical antidisturbance control for a class of discrete-time stochastic systems. Int. J. Robust Nonlinear Control 28(9), 3292–3302 (2018)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Yao, X.M., Guo, L.: Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer. Automatica 49(8), 2538–2545 (2013)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Yao, X.M., Guo, L., Wu, L.G., Dong, H.R.: Static anti-windup design for nonlinear Markovian jump systems with multiple disturbances. Inf. Sci. 418–419, 169–183 (2017)CrossRefGoogle Scholar
  24. 24.
    Basturk, H.I., Krstić, M.: Adaptive wave cancelation by acceleration feedback for ramp-connected air cushion-actuated surface effect ships. Automatica 49(9), 2591–2602 (2013)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Hu, X., Du, J.L., Sun, Y.Q.: Robust adaptive control for dynamic positioning of ships. IEEE J. Ocean. Eng. 42(4), 826–835 (2017)CrossRefGoogle Scholar
  26. 26.
    Du, J.L., Hu, X., Krstić, M., Sun, Y.Q.: Dynamic positioning of ships with unknown parameters and disturbances. Control Eng. Pract. 76, 22–30 (2018)CrossRefGoogle Scholar
  27. 27.
    Ding, Z.T.: Asymptotic rejection of unknown sinusoidal disturbances in nonlinear. Automatica 43(1), 174–177 (2007)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Wen, X.Y., Meng, H., Li, Z.Q.: Estimation of unknown frequency disturbance based on system output using virtual disturbance observer. In: Proceeding of the 2016 IEEE International Conference on Industrial Technology, pp. 1771–1776. Taipei, Taiwan (2016)Google Scholar
  29. 29.
    Shen, H., Li, F., Wu, Z.G., Park, J.H., Sreeram, V.: Fuzzy-model-based non-fragile control for nonlinear singularly perturbed systems with semi-Markov jump parameters. IEEE Trans. Fuzzy Syst. pp. 1–12 (2018).  https://doi.org/10.1109/TFUZZ.2018.2832614
  30. 30.
    Shen, H., Li, F., Xu, S.Y., Sreeram, V.: Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations. IEEE Trans. Autom. Control 63(8), 2709–2714 (2018)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Sun, H.B., Guo, L.: Neural network-based DOBC for a class of nonlinear systems with unmatched disturbances. IEEE Trans. Neural Netw. Learn. Syst. 28(2), 482–489 (2017)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Wei, X.J., Chen, N.: Composite hierarchical anti-disturbance control for nonlinear systems with DOBC and fuzzy control. Int. J. Robust Nonlinear Control 24(2), 1052–1060 (2016)MathSciNetGoogle Scholar
  33. 33.
    Yang, J., Ding, Z.T., Chen, W.H., Li, S.H.: Output-based disturbance rejection control for non-linear uncertain systems with unknown frequency disturbances using an observer backstepping approach. IET Control Theory Appl. 10(9), 362–373 (2014)MathSciNetGoogle Scholar
  34. 34.
    Chen, M., Tao, G., Jiang, B.: Dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation. IEEE Trans. Neural Netw. Learn. Syst. 26(9), 2086–2097 (2015)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Zheng, Z.W., Sun, L., Xie, L.H.: Error-constrained LOS path following of a surface vessel with actuator saturation and faults. IEEE Trans. Syst. Man Cybern. Syst. pp. 1–12 (2018).  https://doi.org/10.1109/TSMC.2017.2717850
  36. 36.
    Nikiforov, V.O.: Observers of external deterministic disturbances II. Objects with unknown parameters. Autom. Remote Control 65(10), 1531–1541 (2004)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Li, Y.M., Tong, S.C., Li, T.S.: Adaptive fuzzy backstepping control of static var compensator based on state observer. Nonlinear Dynamics 73(1–2), 133–142 (2013)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Li, Y.M., Ren, C.E., Tong, S.C.: Adaptive fuzzy backstepping output feedback control of nonlinear uncertain time-delay systems based on high-gain filters. Nonlinear Dynamics 69(3), 781–792 (2012)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Wu, Z.J., Xie, X.J., Shi, P., Xia, Y.Q.: Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching. Automatica 45(4), 997–1004 (2009)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Krstić, M., Kanellakopoulos, I., Kokotović, P.: Nonlinear Adapt. Control Design. John Wiley & Sons Inc, New York, NY, USA (1995)zbMATHGoogle Scholar
  41. 41.
    Ge, S.S., Wang, J.: Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients. IEEE Trans. Autom. Control 48(8), 1463–1469 (2003)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Cai, Z., de Queiroz, M.S., Dawson, D.M.: A sufficiently smooth projection operator. IEEE Trans. Autom. Control 51(1), 135–139 (2006)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Fossen, T.I., Strand, J.P.: Passive nonlinear observer design for ships using Lyapunov methods: full-scale experiments with a supply vessel. Automatica 35(1), 3–16 (1999)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Torsetnes, G.: Nonlinear control and observer design for dynamic positioning using contraction theory. In: Master’s thesis, Norwegian University of Science and Technology, Trondheim, Norway (2004)Google Scholar
  45. 45.
    de Souza, E., Bhattacharyya, S.P.: Controllability, observability and the solution of \(\text{ AX }-\text{ XB }=\text{ C }\). Linear Algebra Appl. 39, 167–188 (1981)MathSciNetCrossRefGoogle Scholar
  46. 46.
    Tao, G.: A simple alternative to the Barbalat lemma. IEEE Trans. Autom. Control 42(5), 698 (1997)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematics and Statistics ScienceLudong UniversityYantaiPeople’s Republic of China
  2. 2.School of Information and Electrical EngineeringLudong UniversityYantaiPeople’s Republic of China

Personalised recommendations