Application of direct adaptive fuzzy slidingmode control into a class of non-affine discrete nonlinear systems

  • Xiao-yu Zhang


Direct adaptive fuzzy sliding mode control design for discrete non-affine nonlinear systems is presented for trajectory tracking problems with disturbance. To obtain adaptiveness and eliminate chattering of sliding mode control, a dynamic fuzzy logical system is used to implement an equivalent control, in which the parameters are self-tuned online. Stability of the sliding mode control is validated using the Lyapunov analysis theory. The overall system is adaptive, asymptotically stable, and chattering-free. A numerical simulation and an application to a robotic arm with two degrees of freedom further verify the good performance of the control design.

Key words

Nonlinear system Discrete system Dynamic fuzzy logical system Direct adaptive Sliding mode control 

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  1. Allaoua, B., Laoufi, A., 2013. A novel sliding mode fuzzy control based on SVM for electric vehicles propulsion system. Energy Procedia, 36:120–129. Scholar
  2. Castillo-Toledo, B., di Gennaro, S., Loukianov, A.G., et al., 2008. Discrete time sliding mode control with application to induction motors. Automatica, 44(12):3036–3045. Scholar
  3. Chen, D., Liu, Y., Ma, X., et al., 2012a. Control of a class of fractional-order chaotic systems via sliding mode. Nonl. Dyn., 67(1):893–901. Scholar
  4. Chen, D., Zhang, R., Sprott, J.C., et al., 2012b. Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control. Nonl. Dyn., 70(2):1549–1561. Scholar
  5. Corradini, M.L., Fossi, V., Giantomassi, A., et al., 2012. Discrete time sliding mode control of robotic manipulators: development and experimental validation. Contr. Eng. Pract., 20(8):816–822. Scholar
  6. Edwards, C., Spurgeon, S., 1998. Sliding Mode Control: Theory and Applications. CRC Press.zbMATHGoogle Scholar
  7. Farhoud, A., Erfanian, A., 2014. Fully automatic control of paraplegic FES pedaling using higher-order sliding mode and fuzzy logic control. IEEE Trans. Neur. Syst. Rehabil. Eng., 22(3):533–542. Scholar
  8. Furuta, K., 1990. Sliding mode control of a discrete system. Syst. Contr. Lett., 14(2):145–152. Scholar
  9. Guo, L., Hung, J.Y., Nelms, R.M., 2011. Comparative evaluation of sliding mode fuzzy controller and PID controller for a boost converter. Electr. Power Syst. Res., 81(1):99–106. Scholar
  10. Ho, T.H., Ahn, K.K., 2012. Speed control of a hydraulic pressure coupling drive using an adaptive fuzzy sliding-mode control. IEEE/ASME Trans. Mechatron., 17(5):976–986. Scholar
  11. Hsu, C.F., Chung, I.F., Lin, C.M., 2009. Self-regulating fuzzy control for forward DC-DC converters using an 8-bit microcontroller. IET Power Electron., 2(1):1–12. Scholar
  12. Hwang, C.L., Wu, H.M., Shih, C.L., 2009. Fuzzy slidingmode underactuated control for autonomous dynamic balance of an electrical bicycle. IEEE Trans. Contr. Syst. Technol., 17(3):658–670. Scholar
  13. Khandekar, A.A., Malwatkar, G.M., Patre, B.M., 2013. Discrete sliding mode control for robust tracking of higher order delay time systems with experimental application. ISA Trans., 52(1):36–44. Scholar
  14. Lee, J.X., Vukovich, G., 1997. Identification of nonlinear dynamic systems—a fuzzy logic approach and experimental demonstrations. Proc. IEEE Int. Conf. on Systems, Man, and Cybernetics, p.1121–1126. Scholar
  15. Lewis, F.L., Dawson, D.M., Abdallah, C.T., 2006. Robot Manipulator Control: Theory and Practice. Marcel Dekker, Inc., USA.Google Scholar
  16. Lian, Y., Gómez, G., Masdemont, J.J., et al., 2014. Stationkeeping of real Earth-Moon libration point orbits using discrete-time sliding mode control. Commun. Nonl. Sci. Numer. Simul., 19(10):3792–3807. Scholar
  17. Monsees, G., Scherpen, J.M.A., 2002. Adaptive switching gain for a discrete-time sliding mode controller. Int. J. Contr., 75(4):242–251. Scholar
  18. Morioka, H., Wada, K., Sabanovic, A., et al., 1995. Neural network based chattering free sliding mode control. Proc. 34th SICE Annual Conf., p.1303–1308. Scholar
  19. Pai, M.C., 2014. Discrete-time output feedback quasi-sliding mode control for robust tracking and model following of uncertain systems. J. Franklin Inst., 351(5):2623–2639. Scholar
  20. Pande, V.N., Mate, U.M., Kurode, S., 2013. Discrete sliding mode control strategy for direct real and reactive power regulation of wind driven DFIG. Electr. Power Syst. Res., 100:73–81. Scholar
  21. Poursamad, A., Davaie-Markazi, A.H., 2009. Robust adaptive fuzzy control of unknown chaotic systems. Appl. Soft Comput., 9(3):970–976. Scholar
  22. Reddy, G.D., Park, Y., Bandyopadhyay, B., et al., 2009. Discrete-time output feedback sliding mode control for spatial control of a large PHWR. Automatica, 45(9):2159–2163. Scholar
  23. Sarpturk, S.Z., Istefanopulos, Y., Kaynak, O., 1987. On the stability of discrete-time sliding mode control systems. IEEE Trans. Autom. Contr., 32(10):930–932.CrossRefGoogle Scholar
  24. Shahraz, A., Boozarjomehry, R.B., 2009. A fuzzy sliding mode control approach for nonlinear chemical processes. Contr. Eng. Pract., 17(5):541–550. Scholar
  25. Sira-Ramirez, H., 1989. Nonlinear variable structure systems in sliding mode: the general case. IEEE Trans. Autom. Contr., 34(11):1186–1188. Scholar
  26. Utkin, V.I., 1977. Variable structure systems with sliding modes. IEEE Trans. Autom. Contr., 22(2):212–222. Scholar
  27. Wang, L., 1995. Design and analysis of fuzzy identifiers of nonlinear dynamic systems. IEEE Trans. Autom. Contr., 40(1):11–23. Scholar
  28. Wang, S., Yu, D., 2000. Error analysis in nonlinear system identification using fuzzy system. J. Softw., 11(4):447–452.Google Scholar
  29. Wang, W., Liu, X., 2010. Fuzzy sliding mode control for a class of piezoelectric system with a sliding mode state estimator. Mechatronics, 20(6):712–719. Scholar
  30. Yau, H.T., Wang, C.C., Hsieh, C.T., et al., 2011. Nonlinear analysis and control of the uncertain micro-electromechanical system by using a fuzzy sliding mode control design. Comput. Math. Appl., 61(8):1912–1916. Scholar
  31. Zhang, D.Q., Panda, S.K., 1999. Chattering-free and fast response sliding mode controller. IEE Proc. Contr. Theory Appl., 146(2):171–177. Scholar
  32. Zhang, X., 2009. Adaptive sliding mode-like fuzzy logic control for nonlinear systems. J. Commun. Comput., 6(1):53–60.Google Scholar
  33. Zhang, X., Guo, F., 2014. Sliding mode-like fuzzy logic control with boundary layer self-tuning for discrete nonlinear systems. Proc. 7th Int. Conf. on Intelligent Systems and Knowledge Engineering, p.479–490. Scholar
  34. Zhang, X., Su, H.Y., 2004. Sliding mode variable structure state norm control of SISO linear systems. Contr. Eng. China, 11(5):413–418 (in Chinese).Google Scholar
  35. Zhang, X., Chen, W., Shen, B., 2015. Direct adaptive fuzzy sliding mode control for a class of non-affine discrete nonlinear systems. Proc. 12th Int. Conf. on Fuzzy Systems and Knowledge Discovery, p.355–360. Scholar
  36. Zhu, M.C., Li, Y.C., 2010. Decentralized adaptive fuzzy sliding mode control for reconfigurable modular manipulators. Int. J. Robust Nonl. Contr., 20(4):472–488. Scholar

Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Electronic and Information EngineeringNorth China Institute of Science and TechnologyBeijingChina

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