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


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.

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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 :


T :

Temperature (°K)


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)


Sliding surface function (m/s2)


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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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Correspondence to Nohe R. Cazarez-Castro.

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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).

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