How to chose one form of transfer function from other forms

Hi,

I want to generate the transfer function of an induction motor by using its caracteristic matrix (A,B,C,D):

syst=ss(A,B,C,D)
[num,dem]=tfdata(syst)
h=tf(num,dem)

but I get 4 from of transfer function h because I have 2 inputs in my system :

h =

From input 1 to output...

60.54 s^3 + 1.003e04 s^2 + 4.953e08 s - 1.133e11

1: ------------------------------------------------------

s^4 + 318.4 s^3 + 8.206e06 s^2 - 3.742e09 s + 4.281e11

-6.605e07 s - 3.266e08

2: ------------------------------------------------------

s^4 + 318.4 s^3 + 8.206e06 s^2 - 3.742e09 s + 4.281e11

From input 2 to output...

6.605e07 s + 3.266e08

1: ------------------------------------------------------

s^4 + 318.4 s^3 + 8.206e06 s^2 - 3.742e09 s + 4.281e11

60.54 s^3 + 1.003e04 s^2 + 4.953e08 s - 1.133e11

2: ------------------------------------------------------

s^4 + 318.4 s^3 + 8.206e06 s^2 - 3.742e09 s + 4.281e11

Continuous-time transfer function.

I want to use this command :

sys=ss(tf(h))

but I need to choose one of these transfert functions.

Answer 1

[Paul]

You don't need to get the num and den explicitly using tfdata (unless you need them for some reason). To convert from ss to tf:

h = tf(syst)

h is a transfer function matrix that you can index into to pick what you want. For example, a state space realization for the transfer function from the first input to the second output is:

sys = ss(h(2,1))

[Abdelouahab IGHISSANE]

Thanks Paul

it worked, but I have an other ptoblem when I want to generate the estimated variables of state (yest,test,xest):

est=estim(syst,l)
t=0:0.01:6
[y,t,x]=step (syst,t);
xest0=[0.1;0.2;0.3;0.4];
[yest,test,xest]=lsim(est,[ones(size(t)) y],t,xest0);

error message:

Error using horzcat

Dimensions of arrays being concatenated are not consistent.

[Walter Roberson]

Your t has one row. If your system has multiple outputs, then step() of the system at t probably has more than one row.

Perhaps you should [ones(size(y)) y] or [ones(size(y,1),1) y]

[Paul]

Walter's solutions should work. One clarification: I believe that step always returns y with as many rows as in t, even for systems with a single output.

[Abdelouahab IGHISSANE]

Hi again

I used [ones(size(y)) y], yet I got an error:

[yest,test,xest]=lsim(est,[ones(size(y)) y],t,xest0);

error message:

Error using DynamicSystem/lsim (line 84)

When simulating the response to a specific input signal, the input data U must be a matrix of numeric values with at least two rows (samples) and without any NaN or Inf.

I tryed the other formula: [ones(size(y,1),1) y] but i got the following error message:

Error using horzcat

Dimensions of arrays being concatenated are not consistent.