Sut-Flo and Red valve seem to be the names in pinch valves.
"Good Controllability" is a relative term. If the valve gives you the results you need, then the controllability is good. You will have, I assume, a low-pressure application with limited velocity. That makes it easier to apply a pinch valve. If the fluid is whistling along at 15 M/sec at 50 bars, your valve choice would be different.
Good control is provided by the valve control surfaces going where they are supposed to be in response to a control signal. Pinch valves have huge unbalanced areas, and the flexible tube can flutter just like the neck of a whoopie cushion. But if you apply the valve at 2-3 meters/sec, it is both much less likely to flutter and much less likely to be consumed by erosion than if the velocity is higher. Spend some extra bucks and go a size larger on the actuator, and use a precision positioner.