(27)

U ⎛ s2 2

⎞⎟⎛  s ⎞⎟

⎜⎜ +         r  s +1⎟⎟⎜⎜

+1⎟⎟

G  = V2 s C  .

(25)

⎜⎝  2 

⎠⎟⎝⎜ ⎠⎟

2 +   ip2

e

r2 r 2 r1

As shown in Table 3, the main parameters set in simulation are computed from design and selection of components, as well as load simulation. The equilibrium solutions and state parameters are changed while the piston pushes forward and accumulator discharges. Besides, the range and variation of pressure and flow rate are large in WAIM process. The viscosity of polymer melt is the main factor of load characteristic, and if we ignore the melt elasticity, the cut-off frequency of the load transfer function

Fig. 7. Open-loop control structure of pressure control system

For the reason of applications of the accumulator and differential  pressure  control,  the  system is uncontrollable

can be written as

L

B′

=    L  = .

mL mL

(28)

with derivative elements. As a result, the steady-state error of the load pressure will be infinite. Due to the static characteristic of force balance in the pressure cylinder, the model based feedback of the accumulator pressure for the differential pressure control is defined as

The visco-damping coefficient BL and cut-off frequency ωL increase following the increase of melt viscosity. The natural frequency of the accumulator is defined as

u′ = kfa  pA A1  −uA3  ,

A2

(26)

a = =

, (29)

where kfa is the gain of the pressure transducer. In order to control the load pressure consistently with input, we should make pB response following the decrease of the accumulator pressure pA. Therefore, the pressure of accumulator pA is fed back to correct the input value of the proportional pressure relief valve. The pressure pB at  inlet of the relief valve is regulated according to Eq. (26). By the model-based feedback, the system is transformed to a  type 0 system. The structure of pressure control is improved and this simple controller is reliable, however, without  any other  compensation  and  load  pressure  feedback,  a large

and  ωL>ωa>250  rad/s,  which  is  much  higher  than    the

proportional relief valve. Therefore, the disturbance of parameter variation and deviations imported by linearization is negligible at low frequency.

Based on the model-based feedback of the accumulator pressure, the integral compensation is introduced to closed-loop control of the load pressure, as shown in Fig. 8. A series of Bode diagrams with different gains of integral part and non-integral compensation are shown in Fig. 9.

The magnitude of open loop is raised up with  the increase of the integral gain, so the steady-state error  will be  reduced  by  closed-loop  control.  However,  the system

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ZHOU Hua, et al: Water-Assisted Injection Molding System Based on Water Hydraulic