Proportional Control Technique

becomes unstable as the integral gain increases. The set value of kI is limited by r2, the cut-off frequency of the proportional relief valve. Further more, the actual value of kI is far less than r2, because of the poor control precision and the nonlinearity, such as large dead band and hysteresis of the valve. The load viscosity varies more largely than inertia and elasticity in WAIM for different polymers. And the load viscosity has relatively large influence on pressure control. Along with the increase of melt viscosity, the magnitude of load pressure AL2/B′L decreases, and the gain of the open-loop type 0 system with  model-based correction is reduced. So the crossover frequency of the system with integral compensation decreases. Also the damping ratio of the system decreases as the visco-damping coefficient of the load increases. We can draw a conclusion that high viscosity of the polymer melt makes the injection pressure fluctuate when a large input signal change occurs. So a small value of kI should be set to ensure the enough stability margin when high viscosity polymer is used for WAIM.

Table 3.    Main parameters for simulation

Parameter Value

Equivalent stiffness coefficient of accumulator    ka/(kN • m–1) 380 Equivalent visco-damping coefficient of accumulator

main valve port. Due to the static and coulomb friction and the structure of force amplifying lever, the width of dead zone and hysteresis of the valve is very large[23]. The valve control board is “BLS1”-type digital PID controller, including three analogue inputs, PID parameters set, open-loop and closed-loop mode for inlet pressure control. In order to analyze the static characteristic of the proportional relief valve, the control board is set on open-loop mode. In this mode, the input signal can be directly magnified to umax = +24 V, imax = 0.52 A to actuate the electromagnet.

Fig. 8.    Closed-loop control structure of pressure control system

Ba/(kg • s–1)

1 422

Cross section area of accumulator   Aa/m2 0.015

Bulk modulus of water   e/GPa 1.6

Area of piston near to port A   A1/m2 0.012

Area of piston near to port B   A2/m2 0.006

Area of piston near to port L   A3/m2 0.006

Mass of piston   m/kg 31

Visco-damping coefficient in pressure cylinder    Bp/(kg • s–1) 39

Load mass   mL/kg 3.2

Static friction   f/N 90

Equivalent load visco-damping coefficient    B'L/(kg • s–1) 60 000 Cross section area of mould cavity   AL/m2 0.002

Corner frequency of first-order inertial loop   r1/(rad • s–1) 320

Damping ratio   r 0.7

Corner frequency of second-order oscillation loop

40

r2/(rad • s–1)

5 Experiments on Pressure Control System

A fixed-displacement water hydraulic pump, with rated pressure 16 MPa and small displacement 25 mL/r, is  used in the WAIM system. The injection water pressure can be boosted to 25 MPa by the pressure cylinder, and through the accumulator, the max flow rate is above 100 L/min. A water hydraulic proportional pressure relief valve,  with max working pressure 31.5 MPa, is applied in the system. As shown in Fig. 10, this valve is three-stage with ball seat valve as the throttle control pilot stage, and the force of the proportional electromagnet is amplified by a lever. The main valve is characterized with two-stage throttle and high pressure inducting structure, which resists cavitations at the