DOI QR코드

DOI QR Code

Direct Adaptive Fuzzy Sliding Mode Control for Under-actuated Uncertain Systems

Su, Shun-Feng;Hsueh, Yao-Chu;Tseng, Cio-Ping;Chen, Song-Shyong;Lin, Yu-San

  • Received : 2015.12.01
  • Accepted : 2015.12.25
  • Published : 2015.12.25

Abstract

The development of the control algorithms for under-actuated systems is important. Decoupled sliding mode control has been successfully employed to control under-actuated systems in a decoupling manner with the use of sliding mode control. However, in such a control scheme, the system functions must be known. If there are uncertainties in those functions, the control performance may not be satisfactory.In this paper, the direct adaptive fuzzy sliding mode control is employed to control a class of under-actuated uncertain systems which can be regarded as a combination of several subsystems with one same control input. By using the hierarchical sliding control approach, a sliding control law is derived so as to make every subsystem stabilized at the same time. But, since the system considered is assumed to be uncertain, the sliding control law cannot be readily facilitated. Therefore, in the study, based on Lyapunov stable theory a fuzzy compensator is proposed to approximate the uncertain part of the sliding control law. From those simulations, it can be concluded that the proposed compensator can indeed cope with system uncertainties. Besides, it can be found that the proposed compensator also provide good robustness properties.

Keywords

Adaptive fuzzy control;Under-actuated systems;Sliding mode control

References

  1. R. Xu and U. Ozguner, "Sliding mode control of a class of underactuated system," Automatica, vol. 44, no. 1, pp. 233-241, 2008. http://dx.doi.org/10.1016/j.automatica.2007.05.014 https://doi.org/10.1016/j.automatica.2007.05.014
  2. R. Olfati-Saber, "Normal forms for underactuated mechanical systems with symmetry," IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 305-308, 2002. http://dx.doi.org/10.1109/9.983365 https://doi.org/10.1109/9.983365
  3. X. Xin and M. Kaneda, "Swing-up control for a 3-DOF gymnastic robot with passive first joint: design and analysis," IEEE Transactions on Robotics, vol. 23, no. 6, pp. 1277-1285, 2007. http://dx.doi.org/10.1109/tro.2007.909805 https://doi.org/10.1109/TRO.2007.909805
  4. R. Fierro, F. L. Lewis, and A. Lowe, "Hybrid control for a class of underactuated mechanical systems," IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, vol. 29, no. 6, pp. 649-654, 1999. http://dx.doi.org/10.1109/3468.798069 https://doi.org/10.1109/3468.798069
  5. F. Yorgancioglu and H. Komurcugil, "Decoupled slidingmode controller based on time-varying sliding surfaces for fourth-order systems," Expert Systems with Applications, vol. 37, no. 10, pp. 6764-6774, 2010. http://dx.doi.org/10.1016/j.eswa.2010.03.049 https://doi.org/10.1016/j.eswa.2010.03.049
  6. L. W. Lee and I. H. Li, "A Fourier series-based adaptive sliding-mode controller for nonlinear pneumatic servo systems," in Proceedings of 2010 IEEE International Conference on Fuzzy Systems, Barcelona, 2010, pp. 1-5. http://dx.doi.org/10.1109/FUZZY.2010.5584533 https://doi.org/10.1109/FUZZY.2010.5584533
  7. D. W. Kim, H. W. Yang, J. S. Yoon, and H. P. Kim, "Decoupled adaptive fuzzy sliding-mode control," in Proceedings of 2001 IEEE International Symposium on Computational Intelligence in Robotics and Automation, Banff, Canada, 2001, pp. 96-101. http://dx.doi.org/10.1109/CIRA.2001.1013179 https://doi.org/10.1109/CIRA.2001.1013179
  8. Y. J. Mon and C. M. Lin, "Hierarchical fuzzy sliding-mode control," in Proceedings of 2002 IEEE International Conference on Fuzzy Systems, Honolulu, HI, 2002, pp. 656-661. http://dx.doi.org/10.1109/FUZZ.2002.1005070 https://doi.org/10.1109/FUZZ.2002.1005070
  9. D. Qian, J. Yi, and D. Zhao, "Robust control using sliding mode for a class of under-actuated systems with mismatched uncertainties," in Proceedings of 2007 IEEE International Conference on Robotics and Automation, Roma, Italy, 2007, pp. 1449-1454. http://dx.doi.org/10.1109/ROBOT.2007.363188 https://doi.org/10.1109/ROBOT.2007.363188
  10. C. M. Lin and Y. J. Mon, "Decoupling control by hierarchical fuzzy sliding-mode controller," IEEE Transactions on Control Systems Technology, vol. 13, no. 4, pp. 593-598, 2005. http://dx.doi.org/10.1109/TCST.2004.843130 https://doi.org/10.1109/TCST.2004.843130
  11. S. Y. Shin, J. Y. Lee, M. Sugisaka, and J. J. Lee, "Decoupled fuzzy adaptive sliding mode control for underactuated systems with mismatched uncertainties," in Proceedings of 2010 IEEE International Conference on Information and Automation, Harbin, China, 2010, pp. 599-604. http://dx.doi.org/10.1109/ICINFA.2010.5512406 https://doi.org/10.1109/ICINFA.2010.5512406
  12. H. F. Ho, Y. K. Wong, and A. B. Rad, "Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems," Simulation Modelling Practice and Theory, vol. 17, no. 7, pp. 1199-1210, 2009. http://dx.doi.org/10.1016/j.simpat.2009.04.004 https://doi.org/10.1016/j.simpat.2009.04.004
  13. J. C. Lo and Y. H. Kuo, "Decoupled fuzzy sliding-mode control," IEEE Transactions on Fuzzy Systems, vol. 6, no. 3, pp. 426-435, 1998. http://dx.doi.org/10.1109/91.705510 https://doi.org/10.1109/91.705510
  14. L. Marton, A. S. Hodel, B. Lantos, and J. Y. Hung, "Underactuated robot control: comparing LQR, subspace stabilization, and combined error metric approaches," IEEE Transactions on Industrial Electronics, vol. 55, no. 10, pp. 3724-3730, 2008. http://dx.doi.org/10.1109/TIE.2008.923285 https://doi.org/10.1109/TIE.2008.923285
  15. M. S. Park, D. Chwa, and S. K. Hong, "Decoupling control of a class of underactuated mechanical systems based on sliding mode control," in Proceedings of SICE-ICASE International Joint Conference, Busan, Korea, 2006, pp. 806-810. http://dx.doi.org/10.1109/SICE.2006.315338 https://doi.org/10.1109/SICE.2006.315338
  16. L. C. Hung and H. Y. Chung, "Decoupled sliding-mode with fuzzy-neural network controller for nonlinear systems," International Journal of Approximate Reasoning, vol. 46, no. 1, pp. 74-97, 2007. http://dx.doi.org/10.1016/j.ijar.2006.08.002 https://doi.org/10.1016/j.ijar.2006.08.002
  17. L. X. Wang, A Course in Fuzzy Systems and Control. Upper Saddle River, NJ: Prentice-Hall, 1997.
  18. J. L. Castro, "Fuzzy logic controllers are universal approximators," IEEE Transactions on Systems, Man and Cybernetics, vol. 25, no. 4, pp. 629-635, 1995. http://dx.doi.org/10.1109/21.370193 https://doi.org/10.1109/21.370193
  19. J. A. Farrell and M. M. Polycarpou, Adaptive Approximation Based Control: Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches. Hoboken, NJ: Wiley, 2006.
  20. L. X. Wang, "Stable adaptive fuzzy control of nonlinear systems," IEEE Transactions on Fuzzy Systems, vol. 1, no. 2, pp. 146-155, 1993. http://dx.doi.org/10.1109/91.227383 https://doi.org/10.1109/91.227383
  21. Y. C. Hsueh, S. F. Su, C.W. Tao, and C. C. Hsiao, "Robust L2-gain compensative control for direct-adaptive fuzzycontrol-system design," IEEE Transactions on Fuzzy Systems, vol. 18, no. 4, pp. 661-673, 2010. http://dx.doi.org/10.1109/tfuzz.2010.2045761 https://doi.org/10.1109/TFUZZ.2010.2045761
  22. Y. C. Hsueh and S. F. Su, "Learning error feedback design of direct adaptive fuzzy control systems," IEEE Transactions on Fuzzy Systems, vol. 20, no. 3, pp. 536-545, 2011. http://dx.doi.org/10.1109/TFUZZ.2011.2178854 https://doi.org/10.1109/TFUZZ.2011.2178854
  23. J. Cao, X. Ji, P. Li, and H. Liu, "Design of adaptive interval type-2 fuzzy control system and its stability analysis," International Journal of Fuzzy Systems, vol. 13, no. 4, pp. 334-343, 2011.
  24. C. H. Lee and H. Y. Hsueh, "Observer-based adaptive control for a class of nonlinear non-affine systems using recurrent-type fuzzy logic systems," International Journal of Fuzzy Systems, vol. 15, no. 1, pp. 55-65, 2013.
  25. Y. C. Hsueh and S. Shun-Feng, "Direct adaptive fuzzy decoupled sliding control for a class of under-actuated uncertain systems," in Proceedings of 2011 International Conference on Machine Learning and Cybernetics, Guilin, China, 2011, pp. 226-231. http://dx.doi.org/10.1109/ICMLC.2011.6016703 https://doi.org/10.1109/ICMLC.2011.6016703

Cited by

  1. Robust trajectory tracking control for an underactuated autonomous underwater vehicle based on bioinspired neurodynamics vol.15, pp.5, 2018, https://doi.org/10.1177/1729881418806745
  2. A survey on the application of fuzzy systems for underactuated systems pp.2041-3041, 2018, https://doi.org/10.1177/0959651818791027
  3. A Robust Suboptimal Current Control of an Interlink Converter for a Hybrid AC/DC Microgrid vol.11, pp.6, 2018, https://doi.org/10.3390/en11061382
  4. Control for Underactuated Systems Using Sliding Mode Observer vol.16, pp.2, 2018, https://doi.org/10.1007/s12555-016-0730-2