**5. Simulink modeling**

During the lowering, the A3 chamber of the cylinder should provide the flow *Q*Vc2,down. The pump/motor P2 is able to pump out a flow equal to *Q*Vr2. In this case, the total volume of Δ*V*down,III

h

v,p

h

Δ*V t Q Q Q lA R R* up,IV up Vc2,up Vl2 Vt2 = × + - =× - ( ) 1A Q ( ) . (23)

Δ*V t Q Q Q lA R R* down,IV down Vr2 Vl2 Vc2,down = × + - =× - ( ) 1Q A ( ) . (24)

Δ Δ Δ 0 . *VV V* t,IV up,IV down,IV =+ = (25)

h

æ ö

ç ÷ è ø

 h

1 ) . (21)

(22)

Δ*V t Q Q Q lA R R* down,III down Vr2 Vl2 Vc2,down = × + - =× × + - - ( ) 1 v,p Q v,p A (

t,III up,III down,III 1 Q ( ) v,p

= + =× - - ç ÷

In Case IV, the leakage flow from the pump/motor P1 is directed to the hydraulic accumulator A and the leakage flow of the pump/motor P2 is directed to the hydraulic accumulator B. During the lifting, A3 chamber flow of the cylinder *Q*Vc2,up and leakage flow *Q*Vl2 should be removed by the pump/motor P2, but the pump/motor P2 is able to actually pump out the flow of *Q*Vt2. Thus, during the whole stroke, the change in the volume of the fluid chamber Δ*V*up,IV

During the lowering, the A3 chamber of the cylinder should pump out the *Q*Vc2,down volume flow. The required pumping flow rate of P2 is *Q*Vr2 and the additional leakage flow is *Q*Vl2. In this case, the change in the volume Δ*V*down,IV is obtained with Equations (4), (6), (10) and (13):

Four cases of the locations of pump/motor leakages were investigated. The different imple‐ mentation variants were determined by the changes in the volume of the cylinder as a function

<sup>1</sup> ΔΔ Δ *V V V lA R* 1 .

is obtained with Equations (4), (5), (10) and (13):

The entire cycle volume change Δ*V*t, III in Case III is:

is obtained with Equations (2), (6), (9) and (12):

The entire cycle change in the volume Δ*V*t, IV in Case IV is:

**3.4. Case IV**

156 New Applications of Electric Drives

**4. Summary**

Matlab Simulink R2015a and Simscape SimHydraulics and the SimPowerSystems component library were used for creating the simulation model. The following assumptions were made:


The simulation model for the test setup (introduced in Figure 2) is shown in Figure 9.

**Figure 9.** Simulation model of the DDH system.

Figure 10 illustrates the simulation results: reference signal, motor speed and cylinder position. A maximum payload of 150 kg was utilized for the simulation.

**Figure 10.** Simulation results of the DDH system: reference signal, motor speed and cylinder position.

The movement of the cylinder is smooth and identical to the first prototype demonstrated in Figure 5. The flows in volume A (the line with accumulator A), B (the line with accumulator B) and C (line between the pump/motor P1 and the cylinder) are illustrated in Figure 11.

**Figure 11.** Simulation results of the DDH system: flow in lines A, B and C.

**Figure 9.** Simulation model of the DDH system.

158 New Applications of Electric Drives

A maximum payload of 150 kg was utilized for the simulation.

Figure 10 illustrates the simulation results: reference signal, motor speed and cylinder position.

**Figure 10.** Simulation results of the DDH system: reference signal, motor speed and cylinder position.

The movement of the cylinder is smooth and identical to the first prototype demonstrated in Figure 5. The flows in volume A (the line with accumulator A), B (the line with accumulator B) and C (line between the pump/motor P1 and the cylinder) are illustrated in Figure 11.

Flows B and C are mirrors of each other, which corresponds to correct behavior. Conversely, flow A has an initial drop which corresponds to sucking in oil from accumulator A during the initial lifting motion.

Figure 12 illustrates the experimental results for two system configurations with hydraulic accumulators: A and A + B. The pressure with accumulator A (red line) configuration goes up to 2.7 MPa, whereas the proposed combination A + B maintains the pressure in the range of 0.7 MPa.

**Figure 12.** Simulation results of the pressure in the DDH system only with accumulator A (red line) and with accumu‐ lators A + B (black line).

The system pressure is illustrated in Figure 13, where *p*1 is the P1 pump/motor pressure, *p*3 is the P2 pump/motor pressure, and *p*2, *p*4 are the "tank" line pressures (line with accumulator A).

**Figure 13.** Simulation results of the pressure in the DDH system: *p*1 is the P1 pump/motor pressure, *p*3 is the P2 pump/ motor pressure, and *p*2, *p*4 are the "tank" line pressures (accumulator A).

The pressure *p*<sup>3</sup> ranges between 0.93 MPa and 1 MPa during the whole lifting–lowering cycle with a maximum payload of 150 kg. The tank pressure (*p*2 and *p*4) varies between 0.38 MPa and 0.18 MPa. Thus, according to the simulation, Cases II, III and IV do not fulfill the require‐ ments of the leakage line where the maximum allowed constant pressure is 0.3 MPa and in the short term, it is 1 MPa. According to the results shown in Figure 13, from the proposed connection cases in Figure 7, only Case I can be used for the realization of the DDH setup, where both external leakage lines are connected to line A (accumulator A).
