# Related to Matlab Step Comment

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Namjin Park on 27 Aug 2019
Edited: Namjin Park on 27 Aug 2019
Hello, I have some question about Step resoponse Comment,
once, I want to plot about open loop system only use Transfer function,
For example for 1/(s+3) sytem, when I plot,
G = tf(1, [1,3])
step(G)
then the Final value of step response is 0.333, So Steady - State error around 0.667
When calculate steadt-state error is fisrt ordher system, We use 1/(1+Kp),
So in this system, Kp = 1/3, So Ess have to be 0.75.
Why is that differenet ??

David Wilson on 27 Aug 2019
You are possibly confusing the closed loop response with the open loop. The closed loop gain is 1/4, so the error is 1-1/4 = 3/4.
>> Gcl = feedback(G,1);
>> step(Gcl)
>> dcgain(Gcl)
ans =
0.2500
Namjin Park on 27 Aug 2019
Edited: Namjin Park on 27 Aug 2019
realy appritiate you,
Actually my transfer model is for MIMO system,
following is my TF models,
L = [-22 9 3 10; 9 -25 9 7; 3 9 -15 3; 10 7 3 -20];
Co = diag(ones(1,N));
Co(N,N) = 99999;
Q_in = ones(1,N)';
[r,c] = size(Q_in);
Q_in(r,c) = 0;
A = Co\L;
B = Co\diag(Q_in);
C = diag(ones(1,N));
D = diag(zeros(1,N));
sys_mimo = ss(A,B,C,D);
TF = tf(sys_mimo);
step(TF)
This is building model for HVAC system,
So last Node is just outside temerature, that's why i subsitute 9999(Inf) in node 4,
by the way,
the important thing is just transfer function, when I plot step response,
I can get 4*4 step response,
see the transfer function,
From input 3 to output...
3 s^2 + 156 s + 0.04542
1: --------------------------------------------
s^4 + 62 s^3 + 1084 s^2 + 4542 s + 1.696e-15
9 s^2 + 225 s + 0.04542
2: --------------------------------------------
s^4 + 62 s^3 + 1084 s^2 + 4542 s + 1.696e-15
s^3 + 47 s^2 + 469 s + 0.04542
3: --------------------------------------------
s^4 + 62 s^3 + 1084 s^2 + 4542 s + 1.696e-15
3e-05 s^2 + 0.00234 s + 0.04542
4: --------------------------------------------
s^4 + 62 s^3 + 1084 s^2 + 4542 s + 1.696e-15
From input 3 to ouput is lke this,
Theoricaly, these steady-state error is around 0,
but in plot, there are big Ess,
i'm just wondering why there is big Ess Differnent with Control Thoery?/..