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Related to Matlab Step Comment

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Namjin Park
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 ??

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Accepted Answer

David Wilson
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

  1 Comment

Namjin Park
Namjin Park on 27 Aug 2019
Thanks for reply Wilson !
realy appritiate you,
Actually my transfer model is for MIMO system,
So i curious about steady - state error,
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?/..
Thanks for reading Wilson !

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