Why are G1 and G2 outputs different?

clear

clc

Ts=0.0001;

kc=9000;

w0=400*2*pi;

z=tf('z',Ts);

QZ=(0.25+0.5*z^(-1)+0.25*z^(-2));

m=2;

kr=1;

RCZ=(kr*QZ*z^(-199+m)/(1-QZ*z^(-199)));

PI=(w0^2*(Ts*z)/(z-1)+2*w0);

Grc=((1+RCZ)*PI);

U1Y2=((z-1)*Grc)/(z-1+Ts*Grc);

U1Y1=kc*(Grc*Ts)/(z-1+Ts*Grc);

Gbot1=U1Y1+U1Y2

Gbot2=(((z-1)*Grc)+kc*(Grc*Ts))/(z-1+Ts*Grc)

Answer 1

[VBBV]

The order of mathematical operations in evaluating G1 and G2 are different. In case of G1 , individual terms are evaluated first and then added. In case if G2 , the numerator terms are added first and later divided by common denominator expression. You can try to use simplify function to verify that both results are essentially same.

[宏伟 张]

Thanks,"Gbot3=(z*Grc-Grc+kc*Grc*Ts)/(z-1+Ts*Grc)" is correct!

Answer 2

[宏伟 张]

clear

clc

Ts=0.0001;

kc=9000;

w0=400*2*pi;

z=tf('z',Ts);

QZ=(0.25+0.5*z^(-1)+0.25*z^(-2));

m=2;

kr=1;

RCZ=(kr*QZ*z^(-199+m)/(1-QZ*z^(-199)));

PI=(w0^2*(Ts*z)/(z-1)+2*w0);

Grc=((1+RCZ)*PI);

U1Y2=((z-1)*Grc)/(z-1+Ts*Grc);

U1Y1=kc*(Grc*Ts)/(z-1+Ts*Grc);

Gbot3=(z*Grc-Grc+kc*Grc*Ts)/(z-1+Ts*Grc)