How do I create a transfer function of a high order

Question

DAL 2023-2-7

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https://ww2.mathworks.cn/matlabcentral/answers/1908320-how-do-i-create-a-transfer-function-of-a-high-order

回答： Sam Chak 2023-2-8

I am trying to write a high order transfer function in matlab that i need to approximate and reduce to a lower order transfer function. My question is, how do i write a transfer function that has multiplication in between in the denominator:

Looks like this:

G(s) = (14.14s^2 + 318.2s + 707) / (s^2 +20s+101)*(100*s+1)*(0.2*s^2 + 1.2*s+1)

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Answer 1

Sulaymon Eshkabilov 2023-2-7

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https://ww2.mathworks.cn/matlabcentral/answers/1908320-how-do-i-create-a-transfer-function-of-a-high-order#answer_1165920

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It can be done this way:

s = tf('s');

G = (14.14*s^2 + 318.2*s + 707) / ((s^2 +20*s+101)*(100*s+1)*(0.2*s^2 + 1.2*s+1))

G = 14.14 s^2 + 318.2 s + 707 --------------------------------------------------------------- 20 s^5 + 520.2 s^4 + 4525 s^3 + 1.417e04 s^2 + 1.024e04 s + 101 Continuous-time transfer function.

% Simulate and get step response of this TF:

step(G)

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Answer 2

Sam Chak 2023-2-8

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https://ww2.mathworks.cn/matlabcentral/answers/1908320-how-do-i-create-a-transfer-function-of-a-high-order#answer_1166325

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Hi @DAL

Here is an alternative approach that should produce the same result.

Note that num, p3, and den are vectors of polynomial coefficients.

num = [14.14 318.2 707]             % numerator
num = 1×3
   14.1400  318.2000  707.0000
p3  = conv([1 20 101], [100 1]);    % obtain a 3rd-order polynomial via Convolution
den = conv(p3, [0.2 1.2 1])         % denominator
den = 1×6
1.0e+04 *

    0.0020    0.0520    0.4525    1.4165    1.0241    0.0101
G   = tf(num, den)                  % transfer function
G =
 
                     14.14 s^2 + 318.2 s + 707
  ---------------------------------------------------------------
  20 s^5 + 520.2 s^4 + 4525 s^3 + 1.417e04 s^2 + 1.024e04 s + 101
 
Continuous-time transfer function.