# large differences between continuous and discrete tf

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River Rock on 30 Oct 2014
Edited: River Rock on 30 Oct 2014
Hello,
While working on an assignment, I noticed some differences between continuous and discrete tf and I cannot figure out where's the problem. Here's a script where I have isolated it:
% RST
Te = 0.05;
num = [0,0,0,0.426762811098847,0.479098720565413];
den = [1,-1.38166420132806,1.58283601345288,-1.30344677697330,0.921017027200194];
Gd = tf(num,den,Te);
Rc = [ 0.2960 -0.1046 -1.0714 1.1482];
Sc = [ 1.0000 0.4172 -0.8199 -0.5973];
Tc = [ 0.2682];
% sensitivity TF
K1d=tf(Tc,Sc,Te);
K1c=tf(Tc,Sc);
K2d=tf(Rc,Sc,Te);
K2c=tf(Rc,Sc);
Gc = d2c(Gd,'tustin');
Lc = series (K2c,Gc);
Ld = series (K2d,Gd);
Sc = inv(1+Lc);
Sd = inv(1+Ld);
Tc = feedback(Lc,1);
Td = feedback(Ld,1);
K2Sd = K2d*Sd;
K2Sc = K2c*Sc;
GSc = Gc * Sc;
GSd = Gd * Sd;
% plots
subplot(2,2,1);
sigma(Sc,Sd); title('S');
subplot(2,2,2);
bodemag(Tc,Td);title('T');
subplot(2,2,3);
bodemag(K2Sc,K2Sd);title('KS');
subplot(2,2,4);
bodemag(GSc,GSd);title('GS');
and the output:
Since I'm working with sensitivity functions, I guess that the discrete version (green plots) is closer to reality, and the problem might start at the d2c call.
Do you have any idea where do these differences come from?
Thank you.