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.

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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


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Correspondence to Mohd Fua’ad Rahmat.

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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).

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