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Time-varying sliding mode control for a class of uncertain MIMO nonlinear system subject to control input constraint

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Abstract

To solve the regulator problem of a class of uncertain MIMO nonlinear systems subject to control input constraint, three types of time-varying sliding mode control laws are proposed. The sliding surfaces pass the initial value of the system at the initial time, and are shifted/rotated towards the predetermined ones. The controller parameters are optimized by genetic algorithm (GA). Lyapunov method is adopted to prove the stability and robustness to the parameter uncertainties and external disturbance. By mean of time-varying sliding mode control law, the reaching phase in the conventional sliding mode control is eliminated, and the system is guaranteed to have robustness from the very beginning. Taking the control of two-link manipulator and attitude tracking of rigid spacecraft as two examples, we illustrate the features of the time-varying sliding mode control. The simulation results show the validity of the control law to a class of uncertain MIMO systems. Better robustness against the uncertainties and external disturbance could be achieved by time-varying sliding mode control without violating the constraint on control input.

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References

  1. Guan P, Liu X J, Liu J Z. Adaptive fuzzy sliding mode control for flexible satellite. Eng Appl Artif Intel, 2005, 18: 451–459

    Article  Google Scholar 

  2. Bang H, Ha C K, Kim J H. Flexible spacecraft attitude maneuver by application of sliding mode control. Acta Astronaut, 2005, 57: 841–850

    Article  Google Scholar 

  3. Meliksah E, Okyay K. Neuro sliding mode control of robotic manipulators. Mechatronics, 2000, 10: 239–263

    Article  Google Scholar 

  4. Choi S B, Park D W, Jayasuriya S. A time-varying sliding surface for fast and robust tracking control of second-order uncertain systems. Automatica, 1994, 30: 899–904

    Article  MATH  MathSciNet  Google Scholar 

  5. Andrzej B. A comment on a time-varying sliding surface for fast and robust tracking control of second-order uncertain systems. Automatica, 1995, 31: 1893–1895

    Article  MATH  Google Scholar 

  6. Andrzej B. Time-varying sliding modes for second-order systems. IEE Proceed Control Theory Appl, 1996, 143: 455–462

    Article  Google Scholar 

  7. Zhang J, Zhang Y, Chen Z, et al. A control scheme based on discrete time-varying sliding surface for position control systems. In: Proceedings of the 5th World Congress on Intelligent Control and Automation. Piscataway: IEEE, 2004. 1175–1178

    Chapter  Google Scholar 

  8. Franck B, Daniel P, Gérard A C. A time-varying sliding surface for robust position control of a dc motor drive. IEEE Trans Ind Electron, 2002, 49: 462–473

    Article  Google Scholar 

  9. Guan C, Zhu S. Adaptive time-varying sliding mode control for hydraulic servo system. In: Proceedings of the 8th lnternational Conference on Control Automation Robotics and Vision. Piscataway: IEEE, 2004. 1774–1779

    Google Scholar 

  10. Sivert A, Betin F, Faqirl A, et al. Robust control of an induction machine drive using a time-varying sliding surface. In: Proceedings of the 2004 IEEE International Symposium on Industrial Electronics. Piscataway: IEEE, 2004. 1369–1374

    Chapter  Google Scholar 

  11. Corradinia M L, Orlandob G. Linear unstable plants with saturating actuators: robust stabilization by a time varying sliding surface. Automatica, 2007, 43: 88–94

    Article  Google Scholar 

  12. Metin U, Salamci G, Serdar T. Sliding mode control design with time-varying sliding surfaces for a class of nonlinear systems. In: Proceedings of the 2006 IEEE International Conference on Control Applications. Piscataway: IEEE, 2006. 996–1001

    Google Scholar 

  13. Kim J J, Lee J J, Park K B, et al. Design of new time-varying sliding surface for robot manipulator using variable structure controller. Electron Lett, 1993, 29: 195–196

    Article  Google Scholar 

  14. Crassidis J L, Markley F L. Sliding mode control using modified Rodrigues parameters. J Guid Control Dynam, 1996, 19: 1381–1383

    Article  MATH  Google Scholar 

  15. Mitsuo G, Runwei C. A survey of penalty techniques in genetic algorithms. In: Proceedings of IEEE International Conference on Evolutionary Computation. Piscataway: IEEE, 1996. 804–809

    Google Scholar 

  16. Lalit M, Patnaik M. Genetic algorithms: a survey. Computer, 1994, 27: 17–26

    Google Scholar 

  17. Slotine J J E, Li W. Applied Nonlinear Control. Beijing: China Machine Press, 2006. 268–269

    Google Scholar 

  18. Tu S C. Attitude Dynamics and Control of Satellite. Beijing: Astronautical Press, 2002. 33–35

    Google Scholar 

  19. Shuster M D. A survey of attitude representations. Astronaut Sci, 1993, 41: 439–517

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Automatic Control, Beijing Institute of Technology, Beijing, 100081, China

    YongQiang Jin, XiangDong Liu & ChaoZhen Hou

  2. Aerospace System Engineering Shanghai, Shanghai, 201108, China

    YongQiang Jin & Wei Qiu

Authors
  1. YongQiang Jin
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  2. XiangDong Liu
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  3. Wei Qiu
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  4. ChaoZhen Hou
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Correspondence to YongQiang Jin.

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Jin, Y., Liu, X., Qiu, W. et al. Time-varying sliding mode control for a class of uncertain MIMO nonlinear system subject to control input constraint. Sci. China Ser. F-Inf. Sci. 53, 89–100 (2010). https://doi.org/10.1007/s11432-010-0009-9

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  • DOI: https://doi.org/10.1007/s11432-010-0009-9

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