Pump controll

Pumps and the systems they work in are not usually linear, in fact more parabolic than anything. How are you controlling the pump from 0 -X % of maximum flow, speed control? Are you starting the pump from 0 speed? What kind of pump is it? Centrifugal, or piston, PD type? Is the pump in a piping system of some kind, or is it discharging immediately into free air or out over a lake or something?

PID controllers don't usually control pumps. You can either let pumps run at a constant synchronous speed and control flow or pressure, via a pressure, or a flow transmitter feeding its signal into a PID that in turn outputs to the actuator for a control valve. Or you can control the pump's speed electronically using a VFD, or a throttle if it happens to be an IC engine. I suppose you could control the pump's VFD, or throttle using a PID controller, if you want to.

It looks like you are effecting some kind of control of the pump's speed, just not very accurately at higher speeds. And you seem to get 14-16 mA from your flowmeter when above 60% of flow. 14 mA when around 60%. 12 mA at 50% flow. 10 mA at 40% and 6-7 mA when at 30%. I'd say that's not too bad for a start. Seems like it kinda' works. A bit noisy at low flow. Maybe there's some overspeed on the runup, but it looks like it eventually settles down more or less.

Thank you for your reply!

I forgot to mention that I use a VFD to control the pump. The pump is a submerged pump that draws water from a pool of dirty water into a pipe to be cleaned in a filter. The water levels in the pool vary depending on weather and other factors. The pump is supposed to run for periods up to one or two days. That’s why I want to regulate it to make sure the pump flow stays at the desired flow even if the water levels in the pool vary during the run.

OK. Knowing that makes it easier to predict what will happen.

The pump probably won't care much about changes in depth of the pool as long as there is still enough water that the flow is not affected and no vortex is formed sucking air into the pump inlet. At any given speed the pump will maintain its flow and differential head associated with that speed. If you were making a fountain and the pond level drops a foot, so would the height of the fountain. If the pond raises a foot, the height of the fountain will rise a foot too. That's constant differential head.

The differential head will change if the flow or speed changes. Differential head (directly related to discharge pressure) is related to the square of the pump's speed. If 1000 rpm makes a 10ft fountain height (ft of head) then 900 rpm will make around 10m/1000^2 * 900^2 = 8.1m. Flow will tend to vary linearly with the pump speed.

Anytime you change speed there will be some time lag between the speed change and the observed flow because the pump and the water in the pipe and filter has to accelerate and that takes a little time and extra energy. Once the flow has accelerated flow should begin to stabilize.

Flow is the easiest variable to control with a PID (you will only use P & I)
Start with some fairly conservative numbers like gain of 0.5 and 10 seconds per repeat and go from there.
I usually set the controller so the minimum output is about 30% for a centrifugal pump.