Derive transfer function of control system with disturbance.

[StevieNewRoad]

This is a revision question rather than homework as I have the answer and working.

I have attached the block diagram and first part of the answer which explains how to derive the transfer function from first principles. I understand the principles behind this and how the RHS of the equation was derived, but I am unsure of why the left hand side is:

C(s)2.4s rather than C(s)/2.4s

I will be able to remember this for my exam, but I would rather know why.

Any help much appreciated

regards

SNR

 

[gneill]

The document doesn't explain the derivation from first principles, it just present a result. So. Time to get out your pencil and paper

Start by writing the loop-formula expression for the system to obtain the transfer function. Save a lot of pencil lead by defining a couple of variables to represent the portions of interest:

What do you get for C(s) = H(s)R(s) in terms of f and a?

 

[jhae2.718]

Another comment: is your system linear? Would superposition apply?