I would like to know what people think about using PID controls on a liquid transfer

Several people have mentioned positive displacement pumps. The key to these is the amount of leakage on the pump. The lower the leakage on the pump is, the more predictable the flow will be. In my field of work (not plastics!) I would only use a PID loop if the leakage on the pump was too high to have open-loop control. Perhaps your engineering company are trying to cut costs by using lower spec pumps and then specifiying PID flow control to compensate for the leakage. What type of pumps have they specified?
 

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