Derive transfer function of control system with disturbance.

StevieNewRoad · Nov 19, 2013

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 · Nov 20, 2013

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:

Block diagram of a unity-feedback control loop: R(s) enters a summing junction, then a P+I controller Kp(1 + 1/(Tis)) and a plant 0.8/((1+6s)(1+2s)), with disturbance D(s) added at a second summing junction, then a 1/(2.4s) block giving output C(s). The forward path is enclosed by a blue loop labelled f, and the feedback path is labelled 1/a.

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

jhae2.718 · Nov 20, 2013

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

Derive transfer function of control system with disturbance.

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