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Integrated model-based backstepping control for an electro-hydraulic system

  • Dang Xuan Ba
  • Kyoung Kwan Ahn
  • Dinh Quang Truong
  • Hyung Gyu Park
Article

Abstract

The demand to obtain an accurate and high efficiency hydraulic actuator has been increasing in heavy industries. However, the existence of uncertain, nonlinear, and unknown terms in system dynamics limits the performance of the hydraulic actuator significantly. To deal with these problems, this paper proposes an advanced control approach, named the integrated model-based backstepping (IBS) controller, for position-tracking control of a pump-controlled Electro Hydraulic System (PEHS). First, a mathematical model of the studied system is fully derived in which the structure of the system elements is clearly presented. Second, to realize the control performance in both transient and steady-state responses, and to simplify the design procedure, an advanced backstepping technique is then employed to compensate for the nonlinearities and unknown terms, while the uncertainties are well treated by a novel identification method based on the obtained model. Third, the stability of the closed-loop system is theoretically maintained using Lyapunov functions. Finally, the effectiveness and feasibility of the proposed method are confirmed by comparing with a tuned proportional-integral-derivative (PID) controller and a direct backstepping (DBS) controller in the real-time tracking control of the PEHS to follow various trajectories under different testing conditions.

Keywords

Electro-hydraulic system Backstepping control Nonlinear control Integrated control Model-based control 

Nomenclature

x

displacement of the main cylinder or system position

P1

pressure in chamber 1 of the main cylinder

P2

pressure in chamber 2 of the main cylinder

Q1

flow rate at chamber 1 of the main cylinder

Q2

flow rate at chamber 2 of the main cylinder

QcLi

internal leakages of the main cylinder

CcLi

coefficient of internal leakages of the main cylinder

QcLe1

external leakages at chamber 1 of the main cylinder

QcLe2

external leakages at chamber 2 of the main cylinder

A1

effective area at chamber 1 of the main cylinder

A2

effective area at chamber 2 of the main cylinder

dt

stroke length of the main cylinder

Q1p

supply flow at side 1 of the pump

Q2p

supply flow at side 2 of the pump

QpLi

internal leakages of the pump

CpLi

coefficient of internal leakages of the pump

QpLe1

external leakages at side 1 of the pump

QpLe2

external leakages at side 2 of the pump

D

pump displacement

w

pump speed

ηV

volumetric efficiency of the pump

JHP

inertia moment of the pump

TfHP

coefficient of viscous friction torque of the pump

Kdr

driver gain

u

input voltage supplied to driver

M

total mass effecting to the system motion

βe

effective bulk modulus of the hydraulic fluid

\(\hat \bullet \)

estimate of ●

\(\tilde \bullet \triangleq \hat \bullet - \bullet \)

estimation error of ●

max

maximum value of ●

min

minimum value of ●

≜●max−●min

width of the feasible range of ●

Δ≜sup(|●|)

supreme absolute value of ●

\(R_{f\left. i \right|i \triangleq 0..4.}\)

estimation rate matrices

li|i≜2,3.

estimation error gains

fi|i≜0..4.

uncertain functions

ϒi|i≜0..4.

certain vectors extracted from the uncertain functions

Ξi|i≜0..4.

uncertain vectors extracted from the uncertain functions

νi|i≜0..4.

unknown terms extracted from the uncertain functions

δ

modeling error

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Copyright information

© Korean Society for Precision Engineering and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Dang Xuan Ba
    • 1
  • Kyoung Kwan Ahn
    • 2
  • Dinh Quang Truong
    • 2
  • Hyung Gyu Park
    • 2
  1. 1.School of Mechanical Engineering, Graduate SchoolUniversity of UlsanUlsanSouth Korea
  2. 2.School of Mechanical EngineeringUniversity of UlsanUlsanSouth Korea

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