Electro Hydraulic Pump

1.0. 1.1

Electro Hydraulic Pump

• The considered physical system and the corresponding POG block scheme:

ω _m ω _m

DC Motor DC Motor

Pump Filter

Tank Accumulator

V _a

L _a R _a

I _a I _a

J

m

J

m

b _m

b _m α α _{p p} V

V Q Q 0 0

Q _u Q _u

P 0

P 0

Q _α Q _α

1 2 3 4

5

6 7 8

9

V _r E _m

I _a

V _a

1

Motor inductance

 -

6

1 s

6

φ 1 L

a

6

I _a

- 

φ ˙

V _r

2

Motor resistance

- -

R _a

?

 ?

3

Energy conversion

EL-MR



E _m

K _m



-

K _m

^-

C _m

4

Motor inertia

- 

?

1 s

?

p 1 J

m

?

ω _m

 -

p ˙

5

Motor friction

 

b _m

6

6

- -

6

Energy conversion

MR-ID -

K _p

^-

C _p



K _p



7

Hydraulic leak

 

α _p

?

?

Q _α

- -

8

Hydraulic accumulator

Q _u

 -

6

1 s

6

V 1 C

0

6

P 0

- 

V ˙

9

P 0

Q 0

• The corresponding POG physical scheme obtained using the POG modeler:

V

0

L

_a

I

_a

R

_a

V

_ra

E

_m

T

_m

T = Km

J

_m

w

1

b

_m

T

_b

T

_p

Q

_p

G = Kp

K

0

P

0

d

0

Q

_d

Q

_b

P

_b

Electric domain Rot. Mechanical domain Hydraulic domain

1.2. DYNAMIC MODELING 1.2

• System parameters:

-- Matlab commands ---- (POG_Electro_Hydraulic_Pump_NL_SLX_m) ---

%%%%%%%%%%%% SYSTEM PARAMETERS %%%%%%%%%%%%%%%%%%%%%%%%%%

L_a=0.3*mHenry; % 2. Inductance. Internal parameter.

R_a=1*Ohm; % 3. Resistance. Internal parameter.

K_m=0.5; % 5. Parameter. Transformer/Gyrator.

J_m=1*cm^2*1*kg; % 6. Inertia. Internal parameter.

b_m=0.02*Nm/(100*rpm); % 7. Angular friction. Internal parameter.

K_p=5e-06; % 9. Parameter. Transformer/Gyrator.

K_0=100*atm/((10*cm)^3); % 10. Hyd. Capacitance. Internal parameter.

d_0=(4*mm)^3/sec/(10*atm); % 11. Hyd. Conductance. Internal parameter.

P_0=5*atm; % Pressure of the hydraulic capacitor when V=0 V_0=(15*cm)^3; % Volume of the hydraulic capacitor

%%%%%%%%%%%% INPUT VALUES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

V_a=24*Volt; % 1. Voltage. Input value.

Q_0=(4*cm)^3/sec; % 12. Volume Flow rate. Input value.

t_0=30*sec; %

---

• Simulation results ( POG Electro Hydraulic Pump NL SLX.slx ) in presence of nonlinearities:

0 20 40 60

0 5 10 15 20 25

I_a [Amp]

Armature current

0 20 40 60

0 100 200 300 400

w_1 [rpm]

Motor angular velocity

0 20 40 60

5 10 15 20 25

P_0 [atm]

Output pressure

Time [s]

0 20 40 60

0 1 2 3 4

Q_0 [liters/minutes]

Ouput volume flow rate

Time [s]

1.2. DYNAMIC MODELING 1.3

• Simulink block scheme ( POG Electro Hydraulic Pump Rele SLX.slx ) of the system controlled using a relay with hysteresis:

• Simulation results obtained by using the relay-controlled system:

0 20 40 60 80

−2 0 2 4 6 8 10 12

I_a [Amp]

Armature current

0 20 40 60 80

0 100 200 300 400

w_1 [rpm]

Motor angular velocity

0 20 40 60 80

5 6 7 8 9 10 11 12

P_0 [atm]

Output pressure

Time [s]

0 20 40 60 80

0 1 2 3 4 5 6

Q_0 [liters/minutes]

Ouput volume flow rate

Time [s]