How to analyze pneumatic flow/speed controller valve?

Hello, maybe someone can help me with this because I can't find anything online or in any literature. Where can I find the flow rate equations for a flow/speed controller component that goes on a pneumatic cylinder? Most manufacturers seem to provide graphs of flow rate and sometimes there's a corresponding value for sonic conductance or effective area (which can be converted to sonic conductance) but these values are given for the valve being fully open. I'd like to find something that relates to how much % the valve is open, any ideas?