Nonlinear modeling of an electrohydraulic actuation system via experiments and its characterization by means of neural network

  • J. Das
  • Santosh Kr. Mishra
  • R. Saha
  • S. Mookherjee
  • D. Sanyal
Technical Paper


The friction and end-cushioning effects in the actuator have been taken care in consideration in the modeling of the actuation method related to an electrohydraulic system. A much simpler friction model that retains all the features of the existing models has been developed for this purpose. In addition, a systematic experimental characterization procedure has been proposed that has been utilized in a supplementary manner for the development of the elaborate nonlinear system model. An artificial neural-network model has been constructed by training with experimental data keeping in mind the variation of discharge through the proportional valve with pressure and command signal. All the nonlinear subsystem models thus obtained have been incorporated simultaneously in MATLAB/SIMULINK to monitor the actuation dynamics. The variations of the theoretical and investigated (via experiments) displacements of the piston against different command signals have been found to be quite close to each other.


Electrohydraulics Hydraulic system modeling Identification Artificial neural network Simulation 

List of symbols


Cross-sectional area of actuator piston, (m2)


Cross-sectional area of flow in pipe, (m2)


Coefficient of discharge

Cvi (i = 1–4)

Main-flow coefficient corresponding to the pressure drop ΔPi, (m3/(VPa1/2))


Actuator bore diameter, (m)


Cushion rod diameter, (m)


Cushion bush diameter, (m)


Actuator piston rod diameter, (m)


Error between measured output value t k and the network predicted value y k


Feed forward voltage (V)


Frictional force (N)

fRV(Qs), fNRV(Qr)

Pressure-discharge characteristics for the relief valve and nonreturn valve, respectively, (Pa)


Spring constant, (N/m)


Inner length of actuator cylinder, (m)


Length of cushion rod, (m)


Lip length between cushion rod and actuator piston rod, (m)


Pipe length between pump delivery and the supply port of PV, (m)


Pipe length between PV and chamber 1 of actuator, (m)


Pipe length between PV and chamber 2 of actuator, (m)


Pipe length between NRV and the return port of PV, (m)


Moving mass of the actuator, (kg)


Pressures at the two control ports A and B of the PV, respectively, (Pa)

Pc1, Pc2

Cushioning volume pressures in chambers 1 and 2, respectively, (Pa)


Pressures at the return port of PV and inlet to the NRV, respectively, (Pa)


Pressures at the pump exit and inlet to the PV, respectively, (Pa)


Precision error of the discharge of the PV, (m3)


Precision error of exit pressure of pump, (bar)


Precision error of actuating pressure in chamber 1, (bar)


Precision error of return line, (bar)


Pressure of the return line to the tank, (Pa)

P1, P2

Piston-actuating pressures in chambers 1 and 2, respectively, (Pa)

Qa1, Qa2

Discharges through actuator control ports 1 and 2, respectively, (m3)

Qv1, Qv2

Discharges through ports v1 and v2, respectively, of PV, (m3)


Stroke of the actuator, (m)


Bias limit of the discharge of the PV, (m3)


Bias error of exit pressure of pump, (bar)


Bias error of actuating pressure in chamber 1, (bar)


Bias error of the return line to the tank, (bar)


Coverage factor

\(V_{10} ,V_{20}\)

Initial volumes in chambers 1 and 2, respectively, of the actuator, (m3)


Total experimental uncertainty, (m3)


Width of actuator piston, (m)




Displacement of actuator, (m)

Greek symbols


Bulk modulus of the oil, (Pa)


Density of oil, (kg/m3)


Damping coefficient of the PV



Nonreturn valve


Needle valve


Linear variable differential transformer


Pressure transducer


Proportional valve


Relief valve


Standard deviation


Shut-off valve



This work has been supported by AR&DB New Delhi and SAP-DRS of UGC New Delhi and Jadavpur University for equipment, and Prof. Dipankar Sanyal, Dr. Saikat Mookherjee, and Dr. Rana Saha of Mechanical Engineering Department, Jadavpur University, Kolkata for the help and valuable suggestions.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • J. Das
    • 1
  • Santosh Kr. Mishra
    • 1
  • R. Saha
    • 2
  • S. Mookherjee
    • 2
  • D. Sanyal
    • 2
  1. 1.Department of Mining Machinery EngineeringIndian Institute of Technology (ISM)DhanbadIndia
  2. 2.Department of Mechanical EngineeringJadavpur UniversityKolkataIndia

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