Control Valve positioner/actuator Transfer function?

[blacksnow]

How to evaluate the transfer function of control valve,
Such that,
Output/Input = Stem Displacement / Positioner Input (i.e. 4 to 20 mA) = Delta x (s) / Delta I (s)

Considering, Cv, Kv, Flow Rate, Dead Band, Hysteresis are known and Pressure difference across Valve is constant.

What is the general form of Transfer function for such type of input and output and how to find gain and time constant?

What will be the order of the transfer function, 1st order or second order?

Thanks.

Regards
WAQAR

[nutcha]

Consult vendor for my suggestions.