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

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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.

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Abbreviations

x :

displacement of the main cylinder or system position

P 1 :

pressure in chamber 1 of the main cylinder

P 2 :

pressure in chamber 2 of the main cylinder

Q 1 :

flow rate at chamber 1 of the main cylinder

Q 2 :

flow rate at chamber 2 of the main cylinder

Q cLi :

internal leakages of the main cylinder

C cLi :

coefficient of internal leakages of the main cylinder

Q cLe1 :

external leakages at chamber 1 of the main cylinder

Q cLe2 :

external leakages at chamber 2 of the main cylinder

A 1 :

effective area at chamber 1 of the main cylinder

A 2 :

effective area at chamber 2 of the main cylinder

d t :

stroke length of the main cylinder

Q 1p :

supply flow at side 1 of the pump

Q 2p :

supply flow at side 2 of the pump

Q pLi :

internal leakages of the pump

C pLi :

coefficient of internal leakages of the pump

Q pLe1 :

external leakages at side 1 of the pump

Q pLe2 :

external leakages at side 2 of the pump

D :

pump displacement

w :

pump speed

η V :

volumetric efficiency of the pump

J HP :

inertia moment of the pump

T fHP :

coefficient of viscous friction torque of the pump

K dr :

driver gain

u :

input voltage supplied to driver

M :

total mass effecting to the system motion

β e :

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

l i|i≜2,3. :

estimation error gains

f i|i≜0..4. :

uncertain functions

ϒ i|i≜0..4. :

certain vectors extracted from the uncertain functions

Ξ i|i≜0..4. :

uncertain vectors extracted from the uncertain functions

ν i|i≜0..4. :

unknown terms extracted from the uncertain functions

δ :

modeling error

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Authors and Affiliations

  1. School of Mechanical Engineering, Graduate School, University of Ulsan, 93, Daehak-ro, Nam-gu, Ulsan, 44610, South Korea

    Dang Xuan Ba

  2. School of Mechanical Engineering, University of Ulsan, 93, Daehak-ro, Nam-gu, Ulsan, 44610, South Korea

    Kyoung Kwan Ahn, Dinh Quang Truong & Hyung Gyu Park

Authors
  1. Dang Xuan Ba
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  2. Kyoung Kwan Ahn
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  3. Dinh Quang Truong
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  4. Hyung Gyu Park
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Correspondence to Kyoung Kwan Ahn.

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Ba, D.X., Ahn, K.K., Truong, D.Q. et al. Integrated model-based backstepping control for an electro-hydraulic system. Int. J. Precis. Eng. Manuf. 17, 565–577 (2016). https://doi.org/10.1007/s12541-016-0069-x

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