variable speed drive controlling induction motor


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i have to control a system in which i have a variable speed drive which control the speed of an induction motor. i want to know if i can take the gain placed in the variable speed drive as the transfer function of the variable speed drive, or i must model each part of the variable speed drive in order to obtain its transfer function. please help me.
As a first order approximation the variable speed can be described as a control block. The gain (if voltage controlled) is G=Volts/Radians/sec.

The bandwidth can be modeled as a single pole.