Racking my brains over a transfer function

It is once again a compensated circuit (now a monomania here) – supposed to allow for the motor’s internal resistance to get constant speed operation – or close to it – regardless of speed.

However, despite much scribbling and many sheets of paper, I cannot derive a transfer function that proves to me that Vemf can ever be proportional only to Vin (actually -Vin as the control voltage has to be negative) regardless of motor current – let alone which resistor ratio choices will guarantee this relationship.

Also, I think the text is telling me that replacing R3 with a variable resistor will let me tune the situation as the motor warms up and Rm changes but, to me, it seems that it will adjust gain at the same time.

According to the text, Rs needs to be less than Rm.R1/R2 (which seems to make sense)

And R3 needs to be equal to R2/( (Rm/Rs) – (R2/R1) ), which looks like it would be need to be open-circuit if Rs was the same as Rm.R1/R2 rather than less? – but even that simplified circuit is beating me.


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