Hello,
I think your feedback might not be correct. I will abbreviate (X1-X2) as Y:
Y = G1(s) * (F(s)*W + C(s)*(R - Y)) ;
Y + G1(s)*C(s)*Y = G1(s)*F(s)*W + G1(s)*C(s)*R ;
Y = [G1(s)*F(s)]/[1+G1(s)*C(s)] * W + [G1(s)*C(s)]/[1+G1(s)*C(s)] * R ;
But if you apply your feedback structure, this will yield (with a general output U, which is NOT the one in you sketch)
Y = F(s)*G1(s) * (U - C(s)*Y) ;
Y + F(s)*G1(s)*C(s)*Y = F(s)*G1(s)*U ;
Y = [F(s)*G1(s)]/[1 + F(s)*G1(s)*C(s)] * U ;
Note that this transfer function does neither correspond to the transfer function from W -> Y nor the transfer function from R -> Y.
Regarding your "Set Point": If I understand you right, you want to have R also as input for your transfer function. Thus you could use a MIMO Transfer function:
web(fullfile(docroot, 'control/ug/mimo-transfer-function-models.html'))
In your case the tf would be a "row" vector tf, mapping from an input [W; R] to the output Y. It might be easier then to convert this into a state space model:
web(fullfile(docroot, 'control/ref/ss.html'))
Hope this helps.
Kind regards, Stefan
