Related to Matlab Step Comment

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 ??

Answer 1

[David Wilson]

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]

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 !