Skip to main content

Robust Position Tracking Control of an Electro-Hydraulic Actuator in the Presence of Friction and Internal Leakage


This paper proposes an improved robust position controller for the electro-hydraulic actuator system using the varying boundary layered sliding mode control scheme. The proposed scheme has the ability to improve the position tracking performance of the actuator in the presence of friction and internal leakage. The former is represented using the LuGre model while later is modelled as a turbulent flow. To evaluate the effectiveness of the proposed method, MATLAB simulations are carried out under friction and leakage effects. Its performance is compared with the conventional PID and fuzzy PID (FPID) methods. Finally, an experimental rig that comprises of a single-rod and double acting hydraulic cylinder is set up to validate the proposed idea. The software development is carried out in the DSpace 1104 environment using a TMS320F240 digital signal processor. The superiority of the proposed method over the PID and FPID in terms of tracking position is highlighted by simulation and experimental results.

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


A 1, A 2 :

Cross-sectional area of the two chambers (m2)

a :

Nonlinear dynamics

\({\hat{a}}\) :

Estimation of nonlinear dynamics

a p :

Piston acceleration (m/s2)

\({\dot{a}_{\rm p}}\) :

Piston jerk (m/s3)

b :

Control gain

\({\hat {b}}\) :

Estimation of control gain

b min :

Lower bound of control gain

b max :

Upper bound of control gain

C d :

Discharge coefficient

C v1, C v1 :

Valve orifice coefficients

d u :

External disturbance

D :

Maximum disturbance

e :

Error trajectory

\({\dot{e}}\) :

Derivative of error

E :

Error bounded

F a :

Hydraulic actuating force (N)

F c :

Coulomb friction (N)

F f :

Hydraulic friction force (N)

\({\dot{F}_{\rm f}}\) :

Derivative of friction force

F s :

Stiction force (N)

f d :

Lumped uncertain nonlinearities

\({\dot{f}_{\rm d}}\) :

Derivative of lumped uncertain nonlinearities

I max :

Max. current for servo valve

k a :

Servo valve gain (m/V)

K f1, K f2 :

Flow gain at control ports 1 and 2

K 1R, K 2R :

Flow gain at return ports 1 and 2

K 1S, K 2S :

Flow gain at supply ports 1 and 2

k f1, k f2 :

Leakage coefficient at ports 1 and 2

k 1R, k 2R :

Leakage coefficient at return ports1 and 2

k 1S, k 2S :

Leakage coefficient at supply ports 1 and 2

k v :

Viscous friction (N s/m)

m :

Total mass of piston and load (kg)

\({\dot{p}_l, \dot{p}_2}\) :

Derivative of pressure in chambers 1 and 2 (Pa/s)

p r :

Return pressure (Pa)

p s :

Supply pressure (Pa)

p 1, p 2 :

Pressure in chambers 1 and 2 (Pa)

Q :

Discontinuous switching gain

Q S1, Q S2 :

Internal leakage flow in control ports 1 and 2 (m3/s)

Q 1, Q 2 :

Fluid flow in chambers 1 and 2 (m3/s)

Q 1R, Q 2R :

Return flow at return ports 1 and 2 (m3/s)

Q 1S, Q 2S :

Supply flow at supply ports 1 and 2 (m3/s)

Q max :

Maximum permissible flow (l/min)

S :

Sliding surface

\({\dot{S}}\) :

Derivative of sliding surface

u :

Input signal to the servo valve (V)

u eq :

Equivalent control signal (V)

u sw :

Switching control signal (V)

V :

Lyapunov function

\({\dot{V}}\) :

Derivative of Lyapunov function

v p :

Piston velocity (m/s)

v s :

Stribeck velocity (m/s)

V 1, V 2 :

Total actuator volume in chambers 1 and 2 (m3)

V i1, V i2 :

Initial volume in chambers 1 and 2 (m3)

w 1,w 2 :

Spool valve area gradients (m2)

x d :

Desired position (m)

x p :

Piston position (m)

x v :

Spool valve displacement (m)

\({\dot{x}_{\rm v}}\) :

Spool valve velocity (m/s)

\({\ddot{x}_{\rm v}}\) :

Spool valve acceleration (m/s2)

x 0 :

Equivalent orifice opening (m)

\({\dot{x}_{\rm p}}\) :

Piston velocity (m/s)

z :

Average of bristle deflection

\({\dot{z}}\) :

Derivative of average of bristle deflection

\({\omega_{\rm v}}\) :

Servo valve natural frequency (Hz)

\({\beta _{\rm e}}\) :

Effective bulk modulus (Pa)

\({\zeta_{\rm v}}\) :

Servo valve damping ratio

\({\tau_{\rm v}}\) :

Time constant (s)

\({\phi}\) :

Thickness of boundary layer

\({\phi_{a}}\) :

1st level of boundary layer

\({\phi_b}\) :

2nd level of boundary layer

\({\sigma_{0}}\) :

Bristles stiffness coefficient (N/m)

\({\sigma_{1}}\) :

Bristles damping coefficient (N s/m)

\({\rho}\) :

Fluid mass density (kg/m3)

\({\varepsilon _{\rm f}}\) :

Switching threshold of the tracking error


  1. 1

    Canudas de Wit, C., Olsson, H., Astrom, K.J., Lischinsky, P.: A new model for control of systems with friction. IEEE Trans. Autom. Control. 40(3), 419–425 (1995)

    Google Scholar 

  2. 2

    Olsson, H., Astrom, K.J., Cadunas de Wit, C., Gafvert, M., Lischinsky, P.: Friction models and friction compensation. Eur. J. Control. 4(3), 176–195 (1998)

    Google Scholar 

  3. 3

    Erylmaz B., Wilson B.H.: Combining leakage and orifice flows in a hydraulic servo valve model. ASME J. Dyn. Syst. Meas. Contr. 122, 576–579 (2000)

    Article  Google Scholar 

  4. 4

    Bobrow J.E., Lum K.: Adaptive high bandwidth control of a hydraulic actuator. ASME J. Dyn. Syst. Meas. Control. 118(4), 714–720 (1996)

    Article  MATH  Google Scholar 

  5. 5

    Plummer R., Vaughan N.D.: Robust adaptive control for hydraulic servo systems. ASME J. Dyn. Syst. Meas. Contr. 118(2), 237–244 (1996)

    Article  Google Scholar 

  6. 6

    Li, D.; Salcuden, S.E.: Modeling simulation and control of a hydraulic steward platform. In: Proc. of 1997 IEEE Int. Conf. Robot Automation, New Mexico, pp. 3360–3366 (1997)

  7. 7

    Yun I.S., Cho H.S.: Adaptive model following control of electro-hydraulic velocity control system. Proc. Inst. Elect. Eng. 135(2), 149–156 (1998)

    Google Scholar 

  8. 8

    Tafazoli S., De Silva C.W., Lawrence P.D.: Tracking control of an electrohydraulic manipulator in the presence of friction. IEEE Trans. Control Syst. Technol. 6(3), 401–411 (1998)

    Article  Google Scholar 

  9. 9

    Lischinsky, P.; Canudas de Wit, C.; Morel, G.: Friction compensation for an industrial hydraulic robot. IEEE Control Syst., February, 25–32 (1999)

  10. 10

    Sekhavat, P.; Wu, Q.; Sepehri, N.: Lyapunov-based friction compensation for accurate positioning of a hydraulic actuator. In: Proceedings of the 2004 American Control Conference, Boston, Massachusetts, USA. June 30–July 2, pp. 418–423 (2004)

  11. 11

    Iqbal S., Bhatti A.I.: Load varying polytopic based robust controller design in LMI framework for a 2DOF stabilized platform. Arab. J. Sci. Eng. 36(2), 311–327 (2011)

    Article  Google Scholar 

  12. 12

    Rami A.M., Ismail A.M., Ibraheem K.I.: State-space based H-infinity robust controller design for boiler-turbine system. Arab. J. Sci. Eng. 37(6), 1767–1776 (2012)

    Article  Google Scholar 

  13. 13

    Bonchis A., Corke P. I., Rye D.C., Ha Q.P.: Variable structure methods in hydraulic servos systems control. Automatica. 37, 589–595 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. 14

    Mihajlov M., Nikolic V., Antic D.: Position control of electro hydraulic servo system using sliding mode control enhanced by Fuzzy PI controller. Facta Universitatis Ser. Mech. Eng. 1(9), 1217–1230 (2002)

    Google Scholar 

  15. 15

    Wang, S.; Habibi, S.; Burton, R.; Sampson, E.: Sliding mode control for a model of an electrohydraulic system with discontinuous nonlinear friction. In: Proceedings of the 2006 American Control Conference, pp. 418–423, Minneapolis, Minnesota, USA. June 14–16 (2006)

  16. 16

    Zeng H., Sepehri N.: Tracking control of hydraulic actuators using LuGre friction model compensation. ASME J. Dynam. Syst. Meas. Contr. 130, 1–7 (2008)

    Article  Google Scholar 

  17. 17

    Kalyoncu M., Haydim M.: Mathematical modelling and fuzzy logic based position control of an electrohydraulic servosystem with internal leakage. Mechatronics. 19, 847–858 (2009)

    Article  Google Scholar 

  18. 18

    Ishaque K., Abdullah S.S., Ayub S., Salam Z.: Single input fuzzy logic controller for unmanned underwater vehicle. J. Intell. Robot. Syst. 59(1), 87–100 (2010)

    Article  MATH  Google Scholar 

  19. 19

    Ishaque, K.; Abdullah, S.S.; Ayub, S.; Salam, Z.: A simplified approach to design fuzzy logic controller for an underwater vehicle. Ocean Eng. 38(1), 271–284 (2010)

    Google Scholar 

  20. 20

    Hung J.Y., Gao W., Hung J.C.: Variable structure control: a survey. IEEE Trans. Ind. Electron. 40(1), 2–21 (1993)

    Article  Google Scholar 

  21. 21

    Eker I.: Second order sliding mode control with PI sliding surface and experimental application to an electromechanical plant. Arab. J. Sci. Eng. 37(7), 1969–1986 (2012)

    Article  Google Scholar 

  22. 22

    Liu Y., Handroos H.: Technical note sliding mode control for a class of hydraulic position servo. Mechatronics. 9, 111–123 (1999)

    Article  Google Scholar 

  23. 23

    Guan C., Pan S.: Adaptive sliding mode control of electro-hydraulic with nonlinear unknown parameters. Control Eng. Pract. 16, 1275–1284 (2008)

    Article  Google Scholar 

  24. 24

    Chen H.-M., Renn J.-C., Su J.-P.: Sliding mode control with varying boundary layers for an electro-hydraulic position servo system. Int. J Adv. Manuf. Tech. 26, 117–123 (2005)

    Article  Google Scholar 

  25. 25

    Zulfatman; Rahmat, M.F.: Application of self-tuning Fuzzy PID controller on industrial hydraulic actuator using system identification approach. Int. J. Smart Sens. Intell. Syst. 2(2), 246–261 (2009)

  26. 26

    Merritt H.E.: Hydraulic control systems. Wiley, New York (1967)

    Google Scholar 

  27. 27

    Yao B., Bu F., Reedy J., Chiu G.T.-C.: Adaptive robust motion control of single-rod hydraulic actuators: theory and experiments. IEEE. ASMI Trans. Mechatron. 5(1), 79–91 (2000)

    Article  Google Scholar 

  28. 28

    Jerzy W., Andrzej S., Marian W., Thomasz K.: Hysteretic effects of dry friction: modelling and experimental studies. Phil. Trans. R. Soc. A. 366, 747–765 (2008)

    Article  MATH  Google Scholar 

  29. 29

    Hang C.C., Astrom K.J., Ho W.K.: Refinements of the Ziegler–Nichols tuning formula. IEE Proc.-D. 138(2), 111–118 (1991)

    Article  Google Scholar 

  30. 30

    Buckner G.D.: Intelligent bounds on modelling uncertainty: applications to sliding mode control. IEEE Trans. Syst. Man. Cybern. Part C Appl. Rev. 32(2), 113–124 (2002)

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Mohd Fua’ad Rahmat.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Has, Z., Rahmat, M.F., Husain, A.R. et al. Robust Position Tracking Control of an Electro-Hydraulic Actuator in the Presence of Friction and Internal Leakage. Arab J Sci Eng 39, 2965–2978 (2014).

Download citation


  • Hydraulic actuator
  • Position control
  • Sliding mode
  • Internal leakage
  • Friction