Camcanpro can try increasing the gains but the distrubances will always be noticed. The question is can the gains be high enough to stay within 1% of the SP.
You don't but we found out that either pump velocity control is not steady or the down stream back pressure is changing the system curve and therefore the operating point.
Peter, I respect the length and breadth of your knowledge immensely, but in this instance I have to say that controlling flowrate to within 1% tolerance with a PID is achievable in most situations, even when the gods are against us with destination back-pressures, source gas breakthrough, pump cavitation, crude vessel top-pressure controls etc. etc.
Of course I understand that sudden and unpredictable disturbances caused by one or more of many events can really "challenge" the tried and tested PID algorithms, and in these situations we do our best with lots of D gain - although sometimes we cannot rely on the PID on its own and add some sort of additional control (aka - fudges) when we see, or can predict, these disturbances.
There are many cases where accurate, controllable, flow control is essential - blending, dosing, pasteurisation, etc.
Blending and Dosing are very similar processes, but accurate ratio control is required, so we may be modulating the SPs on the "slaved" flow loops.
Pasteurisation is a real challenge, as the flowrate through the pasteuriser must be maintained accurately.
When the OBV (Outlet Buffer Tank) becomes full, the product must be purged out of the pasteuriser to the OBV, replacing the product with water. So we get a source pressure change when the inlet changes over from the Inlet Buffer Tank (IBV), to the water main. When the purge volume is achieved, the water in the pasteuriser goes into recirculation, and we suddenly lose the OBV back-pressure (head).
Similarly, it all happens in reverse when we want to go "forward-flow" again, the water in the pasteuriser is diverted to drain when the product is re-introduced (a step-change in the source pressure from the IBV), and after the "prime" volume, the outlet route is changed over to the OBV (a step-change in the outlet pressure).
All the time these pressure changes are taking place, the flowrates and temperatures in the heat-exchangers must be maintained accurately, to maintain the number of "Pasteurisation Units" (a calculation which has exponential terms). Often, cascade PID controllers are used to speed up the response times, especially in the temperature control PIDs.
To say that we must have stable flow with a fixed control valve, or pump speed, to be able to achieve accurate flow control with a PID is wrong - we put PID control in place to couteract the effects of source/destination pressures.
All that said, our hardware must be up to the job as well. Control Valves must react quickly enough to the control system demands, drives must react quickly enough to the control system demands (most are shipped with acceleration/deceleration ramps enabled by default - i take them out). I don't want my fast-acting PIDs being throttled by sluggish response from drives and control valves.
The trend that the OP posted clearly shows a typical "unresponsive" PID reaction to a change in the PV, it is slow to respond to changes in flow, and when it does respond, it overshoots, and then has to sluggishly respond in the opposite direction, and because it is slow to respond, it overshoots again.
I'll say it again - this loop just needs tuning....