I enjoyed reading "Pursuing Sustainability With VFDs," (Control, Sept. 2011, p. 75). However, I think Dick Caro could have done a better job of explaining why flow control with a VSD on a pump is for the most part linear.
He stated, "A few correspondents argued that since the head changes at different flow rates due to pipe friction, a real installation could not be exactly linear. However, the controlled variable—flow rate—is linear." This implies that flow rate is independent of pressure drop, and it isn't. That's how a flow control valve works with a constant-speed pump, changing the pressure drop to modify the flow.
But the Pump Affinity Laws also state that the head a pump develops is proportional to the speed squared. And, as luck would have it, per the D'Arcy-Weisbach Equation, the friction loss in piping with turbulent flow is proportional to the velocity squared. So if you have a piping system where the pressure drop is proportional to the velocity squared (no fixed pressure drops, turbulent flow, etc.) you are in luck.Your control is perfectly linear. Rarely is the flow laminar, but frequently a portion of the pressure drop is unrelated to flow.
So Dick's statement that the VSD imparts linear flow control is correct, but only for very specific installations where most of the pressure drop is due to turbulent flow in piping, which is true of most common chemical industrial piping installations. Due consideration should be given to any nonlinearity if you want the best control. But even having said that, there are changes in pressure drop that are totally unrelated to flow, such as changing tank levels. The flow control loop must be able to deal with any such irregularities.