How do I convert descriptor state-space to transfer function?

Question

Justin Burzachiello 2021-7-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/870248-how-do-i-convert-descriptor-state-space-to-transfer-function

评论： Star Strider 2021-7-4

采纳的回答： Star Strider

在 MATLAB Online 中打开

Hello. I have a state-space forumla of the form

.

I'd like to have MATLAB convert this into its respective transfer function for me. I plan on encoding

sys = dss(A,B,C,D,E)

However, I looked on the page for transfer functions through tf, and I am unable to find how to convert from this dss to tf. Is there a direct way to encode it? Yes, I know that I can just do it by hand and encode the result myself. I'd just like to know if MATLAB can do it, and if so, how.

https://www.mathworks.com/help/control/ref/dss.html

https://www.mathworks.com/help/control/ref/tf.html

Thank you

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Answer 1

Star Strider 2021-7-2

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/870248-how-do-i-convert-descriptor-state-space-to-transfer-function#answer_738633

在 MATLAB Online 中打开

This seems to work:

A = [1 2; 3 4];
B = [5; 6];
C = [7 8; 9 10];
D = 0;
E = [11 12; 13 14];
ss_sys = dss(A,B,C,D,E)
ss_sys =
 
  A = 
       x1  x2
   x1   1   2
   x2   3   4
 
  B = 
       u1
   x1   5
   x2   6
 
  C = 
       x1  x2
   y1   7   8
   y2   9  10
 
  D = 
       u1
   y1   0
   y2   0
 
  E = 
       x1  x2
   x1  11  12
   x2  13  14
 
Continuous-time state-space model.
tf_sys = tf(ss_sys)
tf_sys =
 
  From input to output...
          3 s - 8
   1:  -------------
       s^2 - 2 s + 1
 
          4 s - 9
   2:  -------------
       s^2 - 2 s + 1
 
Continuous-time transfer function.

.

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Justin Burzachiello 2021-7-4

Also, do you by any chance know what to do if sparse A,B,C,D,E matrices are so large that I recieve a "unable to convert the model to a transfer function because of overflow" error when using this method?

This is a bit off-topic, so I asked this in a new question, but I thought that I might as well ask here.