International Journal of Fuzzy Systems

, Volume 19, Issue 1, pp 167–178 | Cite as

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

  • Pablo J. Prieto
  • Nohe R. Cazarez-Castro
  • Luis T. Aguilar
  • Dianelis Garcia


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.


Chattering Fuzzy system Pneumatic actuator Position control Sliding surface 

List of Symbols


Boundary layer (m/s2)


Slope of sliding surface (s−1)


Inferior area of the chamber (m2)


Superior area of the chamber (m2)


Valve orifice area (m2)


Cylinder rod transversal section (m2)


Friction force (N)


Gain of the pneumatic plant.


Mass (kg)


Atmospheric pressure (m2)


Output pressure (Pa)


Input pressure (Pa)


Air mass flow (kg/s)


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




Temperature (°K)


Control action


Velocity of the piston (m/s)


Volume of the inferior chamber (m3)


Volume of the superior chamber (m3)


Cylinder piston displacement (m)


Sliding surface function (m/s2)



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.


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


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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Pablo J. Prieto
    • 1
  • Nohe R. Cazarez-Castro
    • 1
  • Luis T. Aguilar
    • 2
  • Dianelis Garcia
    • 3
  1. 1.Tecnologico Nacional de Mexico-Instituto Tecnologico de TijuanaTijuanaMexico
  2. 2.Instituto Politécnico Nacional, CITEDIMesa de Otay, TijuanaMexico
  3. 3.Universidad Central “Martha Abreu” de las VillasSanta ClaraCuba

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