Exercise 3.28 In   we stated that the sensitivity of a perturbed plant S

I  GK
 is related to that of the nominal plant S I  GK
 by S SI  EOT


where EO G
GG
 This exercise deals with how the above result may be derived in a systematic though cumbersome manner using LFTs see also

Skogestad and Morari  a

a First nd F such that S I  GK
 FlFK and nd J such that K FlJ T see Exercise 

b Combine these LFTs to nd S FlN T What is N in terms of G and G 

Note that since J we have from A 

N  F F
J

J
F
 J

 J
F

J


c Evaluate S FlN T and show that S I
GG
TI
I
GG
T

d Finally show that this may be rewritten as S SI  EOT