Skip to main content

Fuzzy Slope Adaptation for the Sliding Mode Control of a Pneumatic Parallel Platform

International Journal of Fuzzy Systems volume 19, pages 167–178 (2017)Cite this article

Abstract

An alternative of fuzzy-based sliding mode control is reported in this paper so as to reduce chattering for a two degrees-of-freedom (2-DOF) platform driven by electro-pneumatic actuators. According to surface function values, a Mamdani fuzzy inference system is introduced to change the control action over the actuators and the slope of sliding surface to minimize chattering. In addition, although pneumatic actuators present high nonlinearities, experimental results are reported with attenuation of chattering and convergence toward the reference, in spite of the existence trade off between accuracy and system behavior for sliding mode controller.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Abbreviations

ε :

Boundary layer (m/s2)

λ :

Slope of sliding surface (s−1)

A 1 :

Inferior area of the chamber (m2)

A 2 :

Superior area of the chamber (m2)

A e :

Valve orifice area (m2)

A v :

Cylinder rod transversal section (m2)

F f :

Friction force (N)

K p :

Gain of the pneumatic plant.

M :

Mass (kg)

P A :

Atmospheric pressure (m2)

P a :

Output pressure (Pa)

P s :

Input pressure (Pa)

Qm :

Air mass flow (kg/s)

R :

Perfect gas constant related to unit mass (J/kg/°K)

s :

Seconds

T :

Temperature (°K)

u(t):

Control action

v :

Velocity of the piston (m/s)

V 1 :

Volume of the inferior chamber (m3)

V 2 :

Volume of the superior chamber (m3)

y :

Cylinder piston displacement (m)

s(e):

Sliding surface function (m/s2)

References

  1. Abdelsalam, M.M., Areed, M.F.: Decoupled fuzzy sliding mode control for a synchronous motor speed control. Int. J. Comput. Appl. 47, 29–35 (2012)

    Google Scholar 

  2. Amer, A.F., Sallam, E.A., Elawady, W.M.: Adaptive fuzzy sliding mode control using supervisory fuzzy control for 3 dof planar robot manipulators. Appl. Soft Comput. 11, 4943–4953 (2011)

    Article  Google Scholar 

  3. Beyhan, S.: Adaptive fuzzy terminal sliding-mode observer with experimental applications. Int. J. Fuzzy Syst. 62, 1–10 (2013)

    MathSciNet  Google Scholar 

  4. Boldbaatar, E.-A., Lin, C.-M.: Self-learning fuzzy sliding-mode control for a water bath temperature control system. Int. J. Fuzzy Syst. 17, 31–38 (2015)

    Article  Google Scholar 

  5. Brun, X., Belgharbi, M., Sesmat, S., Thomasset, D., Scavarda, S.: Control of an electropneumatic actuator: comparison between some linear and non-linear control laws. Proc. Inst. Mech. Eng., Part I 213, 387–406 (1999)

    Google Scholar 

  6. Burrows, C.R.: Fluid Power Servomechanisms. Van Nostrand, London (1972)

    Google Scholar 

  7. Cao, L., Sheng, T., & Chen, X.: A non-singular terminal adaptive fuzzy sliding-mode controller. In Proceedings of the IEEE Digital Manufacturing and Automation Conference. IEEE, pp. 74–80 (2011)

  8. Chang, M.-K.: An adaptive self-organizing fuzzy sliding mode controller for a 2-dof rehabilitation robot actuated by pneumatic muscle actuators. Control Eng. Pract. 18, 13–22 (2010)

    Article  Google Scholar 

  9. Chang, Y.-H., Yang, C.-Y., Chan, W.-S., Lin, H.-W., Chang, C.-W.: Adaptive fuzzy sliding-mode formation controller design for multi-robot dynamic systems. Int. J. Fuzzy Syst. 16, 121 (2014)

    Google Scholar 

  10. Chettouh, M., Toumi, R., Hamerlain, M.: High-order sliding modes for a robot driven by pneumatic artificial rubber muscles. Adv. Robot. 22, 689–704 (2008)

    Article  Google Scholar 

  11. Fridman, L., Levant, A.: Sliding Mode Control in Engineering, vol. 3. Marcel Dekker, Inc., New York (2002)

    MATH  Google Scholar 

  12. Girin, A., Plestan, F., Brun, X., Glumineau, A., & Smaoui, M.: High gain and sliding mode observers for the control of an electropneumatic actuator. In Proceedings of the IEEE International Conference on Control Application, pp. 3128–3133 (2006)

  13. Glumineau, A., Fridman, L., Plestan, F.: Variable structure systems techniques in applications vss/smc. Control Eng. Pract. 21, 669–670 (2013)

    Article  Google Scholar 

  14. Islam, S., Liu, P.X.: Robust sliding mode control for robot manipulators. IEEE Trans. Ind. Electron. 58, 2444–2453 (2011)

    Article  Google Scholar 

  15. ISO-6358.: Pneumatic fluid power—Components using compressible fluids—Determinations of flow-rate characteristics (1989)

  16. Kim, S.-W., Lee, J.-J.: Design of a fuzzy controller with fuzzy sliding surface. Fuzzy Sets Syst. 71, 359–367 (1995)

    MathSciNet  Article  Google Scholar 

  17. Korondi, P., & Gyeviki, J.: Robust position control for a pneumatic cylinder. In Proceedings of the IEEE Power Electronics and Motion Control Conference, pp. 513–518 (2006)

  18. Krivts, I.L., Krejnin, G.V.: Pneumatic Actuating Systems for Automatic Equipment: structure and Design. Taylor & Francis Group, New York (2006)

    Book  Google Scholar 

  19. Laghrouche, S., Liu, J., Ahmed, F.S., Harmouche, M., Wack, M.: Adaptive second-order sliding mode observer-based fault reconstruction for pem fuel cell air-feed system. IEEE Trans. Control Syst. Technol. 23, 1098–1109 (2015)

    Article  Google Scholar 

  20. Laghrouche, S., Plestan, F., Glumineau, A.: Higher order sliding mode control based on integral sliding mode. Automatica 43, 531–537 (2007)

    MathSciNet  Article  MATH  Google Scholar 

  21. Li, H., Gao, H., Shi, P., Zhao, X.: Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach. Automatica 50, 1825–1834 (2014)

    MathSciNet  Article  MATH  Google Scholar 

  22. Lin, C.-M., Hsu, C.-F., Chen, T.-Y.: Adaptive fuzzy total sliding-mode control of unknown nonlinear systems. Int. J. Fuzzy Syst. 14, 434–443 (2012)

    MathSciNet  Google Scholar 

  23. Liu, J., Laghrouche, S., Harmouche, M., Wack, M.: Adaptive-gain second-order sliding mode observer design for switching power converters. Control Eng. Pract. 30, 124–131 (2014a)

    Article  Google Scholar 

  24. Liu, J., Laghrouche, S., Wack, M.: Observer-based higher order sliding mode control of power factor in three-phase ac/dc converter for hybrid electric vehicle applications. Int. J. Control 87, 1117–1130 (2014b)

    MathSciNet  Article  MATH  Google Scholar 

  25. Mamdani, E.H.: Application of fuzzy algorithms for control of simple dynamic plant. In Proceedings of the Institution of Electrical Engineers, IET volume 121, pp. 1585–1588 (1974)

  26. Merlet, J.: Parallel Robots, vol. 128, 2nd edn. Springer, Paris (2006)

    MATH  Google Scholar 

  27. Nazir, M.B., Wang, S.: Optimized fuzzy sliding mode control to enhance chattering reduction for nonlinear electro-hydraulic servo system. Int. J. Fuzzy Syst. 12, 291–299 (2010)

    Google Scholar 

  28. Noroozi, N., Roopaei, M., Jahromi, M.Z.: Adaptive fuzzy sliding mode control scheme for uncertain systems. Commun. Nonlinear Sci. Numer. Simul. 14, 3978–3992 (2009)

    MathSciNet  Article  MATH  Google Scholar 

  29. Rubio, E., Hernández, L., Aracil, R., Saltaren, R., & Guerra, J.: Implementation of Decoupled Model- Based Controller in a 2-DOF Pneumatic Platform used in Low- Cost Driving Simulators. In Proceedings of the IEEE Electronics, Robotics and Automotive Mechanics, pp. 338–343 (2009)

  30. Shi, G., Shen, W.: Hybrid control of a parallel platform based on pneumatic artificial muscles combining sliding mode controller and adaptive fuzzy cmac. Control Eng. Pract. 21, 76–86 (2013)

    Article  Google Scholar 

  31. Slotine, J.J., Li, W.: Applied Nonlinear Control. Prentice Hall, Upper Saddle River (1991)

    MATH  Google Scholar 

  32. Utkin, V., Guldner, J., Shijun, M.: Sliding Mode Control in Electro-mechanical Systems, vol. 34. CRC Press, Boca Raton (1999)

    Google Scholar 

  33. Utkin, V.I.: Sliding Modes in Control and Optimization: communications and Control Engineering Series. Springer, Berlin (1992)

    Book  MATH  Google Scholar 

  34. Wu, L., Su, X., Shi, P.: Sliding mode control with bounded L 2 gain performance of Markovian jump singular time-delay systems. Automatica 48, 1929–1933 (2012)

    MathSciNet  Article  MATH  Google Scholar 

Download references

Acknowledgments

The authors thank the suggestions of Dr. Xavier Brun, of the Institut National des Sciences Appliques de Lyon, France. The authors gratefully acknowledge the anonymous reviewers whose comments strengthened the paper.

Funding

This paper have been partially funded by Tecnologico Nacional de Mexico under Grants 5424.14-P, 5424.14.15-PR, and 5627.15-P.

Author information

Authors and Affiliations

  1. Tecnologico Nacional de Mexico-Instituto Tecnologico de Tijuana, B.C., Tijuana, Mexico

    Pablo J. Prieto & Nohe R. Cazarez-Castro

  2. Instituto Politécnico Nacional, CITEDI, Avenida Instituto Politécnico Nacional 1310, 22510, Mesa de Otay, Tijuana, B.C., Mexico

    Luis T. Aguilar

  3. Universidad Central “Martha Abreu” de las Villas, Santa Clara, VC, Cuba

    Dianelis Garcia

Authors
  1. Pablo J. Prieto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nohe R. Cazarez-Castro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luis T. Aguilar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dianelis Garcia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nohe R. Cazarez-Castro.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Prieto, P.J., Cazarez-Castro, N.R., Aguilar, L.T. et al. Fuzzy Slope Adaptation for the Sliding Mode Control of a Pneumatic Parallel Platform. Int. J. Fuzzy Syst. 19, 167–178 (2017). https://doi.org/10.1007/s40815-016-0163-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-016-0163-3

Keywords

  • Chattering
  • Fuzzy system
  • Pneumatic actuator
  • Position control
  • Sliding surface