how to convert tranfer function into a polynomial function?

Question

H 2023-3-12

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回答： Sam Chak 2023-3-12

I have got an transfer function which is having a relative degree of 4 or higher. I want to find out the gain for root locus based design for a given dominant pole. for the Transfer function I have got i need to substitute the value of s. for that i need to convert Transfer function into a polynomial so that i can use substitution operation.

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H 2023-3-12

also is there a way to convert transfer function to polynomial or symbolic?

H 2023-3-12

i have an open loop transfer function C*P= 1.656e09 s^4 + 2.751e12 s^3 + 1.196e15 s^2 + 4.445e16 s + 4.433e15

------------------------------------------------------------------------------------

25 s^7 + 75982 s^6 + 8.552e07 s^5 + 4.409e10 s^4 + 1.057e13 s^3 + 1.049e15 s^2

+ 2.797e16 s

i am finding the closed loop Transfer function =CP/(1+CP) but the matlab is not solving it properly

like I am getting 4.14e10 s^11 + 1.946e14 s^10 + 3.805e17 s^9 + 4.003e20 s^8 + 2.445e23 s^7

+ 8.735e25 s^6 + 1.754e28 s^5 + 1.802e30 s^4 + 8.014e31 s^3 + 1.248e33 s^2

+ 1.24e32 s

---------------------------------------------------------------------------------------

625 s^14 + 3.799e06 s^13 + 1.005e10 s^12 + 1.524e13 s^11 + 1.474e16 s^10 + 9.58e18 s^9

+ 4.313e21 s^8 + 1.36e24 s^7 + 2.964e26 s^6 + 4.218e28 s^5 + 3.494e30 s^4

+ 1.388e32 s^3 + 2.031e33 s^2 + 1.24e32 s

instead of 1.656e09 s^4 + 2.751e12 s^3 + 1.196e15 s^2 + 4.445e16 s + 4.433e15

-----------------------------------------------------------------------------------

25 s^7 + 75982 s^6 + 8.552e07 s^5 + 4.574e10 s^4 + 1.332e13 s^3 + 2.245e15 s^2

+ 7.243e16 s + 4.433e15.??

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Answer 1

Sam Chak 2023-3-12

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Hi @H

I think you use the minreal() and tfdata() function.

s = tf('s');
ncp = 1.656e09*s^4 + 2.751e12*s^3 + 1.196e15*s^2 + 4.445e16*s + 4.433e15;
dcp = 25*s^7 + 75982*s^6 + 8.552e07*s^5 + 4.409e10*s^4 + 1.057e13*s^3 + 1.049e15*s^2 + 2.797e16*s;
G   = ncp/dcp;
Gcl = feedback(G, 1)
Gcl =
 
                    1.656e09 s^4 + 2.751e12 s^3 + 1.196e15 s^2 + 4.445e16 s + 4.433e15
  ------------------------------------------------------------------------------------------------------
  25 s^7 + 75982 s^6 + 8.552e07 s^5 + 4.575e10 s^4 + 1.332e13 s^3 + 2.245e15 s^2 + 7.242e16 s + 4.433e15
 
Continuous-time transfer function.
Gcl = minreal(Gcl)
Gcl =
 
                  6.624e07 s^4 + 1.1e11 s^3 + 4.784e13 s^2 + 1.778e15 s + 1.773e14
  ------------------------------------------------------------------------------------------------
  s^7 + 3039 s^6 + 3.421e06 s^5 + 1.83e09 s^4 + 5.328e11 s^3 + 8.98e13 s^2 + 2.897e15 s + 1.773e14
 
Continuous-time transfer function.
[num,den] = tfdata(Gcl, 'v')
num = 1×8
1.0e+15 *

         0         0         0    0.0000    0.0001    0.0478    1.7780    0.1773
den = 1×8
1.0e+15 *

    0.0000    0.0000    0.0000    0.0000    0.0005    0.0898    2.8968    0.1773