# Determine transfer function from block diagram

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Giorgos Papakonstantinou on 11 Apr 2016
Edited: Rick Rosson on 12 Apr 2016
I am having trouble to define in matlab the transfer function of the following block diagram. Gc represents the controller which produces a signal Fs,
G11 is in series with Gc.
So they may be combined to:
series(Gc, G11)
Based on superposition principal I can assume that the disturbance signal z0*G12 is zero. Thus I may find the transfer function of the closed loop path. That is:
feedback(series(Gc, G11),1)
How can I find the transfer function of the system by also take into account the disturbance z0*G12?
Giorgos Papakonstantinou on 12 Apr 2016
Anyone?

Rick Rosson on 12 Apr 2016
Edited: Rick Rosson on 12 Apr 2016
H = feedback(series(Gc,G11)+G12*Z0,1);
where Z0 is the Laplace Transform of the disturbance signal z0(t), assuming the disturbance signal is deterministic.
If, on the other hand, the disturbance signal is stochastic, then Z0 is the square root of the Power Spectral Density of z0(t). In particular, if z0(t) represents white noise, then Z0 is simply a constant with respect to frequency, with a value equal to the RMS voltage of the disturbance signal's autocorrelation function.
Giorgos Papakonstantinou on 12 Apr 2016
Thank you for you answer. I will get back to you when I try it.

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