Well stated katmar, and that is what I was alluding to in the last sentence of the first paragraph in my response. It may in fact be a pump design issue, and that is why I thought he needs the help of someone well versed in this who can observe the situation first hand and come up with real suggestions, rather that keep fretting about how to do it with free advice from the keyboards of people with other jobs.
That said, I have made PI control loops with VFDs work in situations such as this with regular success, as have many other of the poster and readers of this forum. This is a common problem that we have all faced at one time or another, and in my opinion, the solution is available to him with the equipment he already has. I leave open the possibility that I am wrong and he needs to replace the pump, but I put that as a last resort.
"Our virtues and our failings are inseparable, like force and matter. When they separate, man is no more."
Nikola Tesla