Why the transfer function involving exponential term comes out in matrix form? Not in usual polynomial form, in particular Net variable in below code

Question

Vaibhav Ajmera 2021-4-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/789659-why-the-transfer-function-involving-exponential-term-comes-out-in-matrix-form-not-in-usual-polynomi

回答： Abhinav Aravindan 2024-2-21

s=tf('s');
G=7.46*exp(-2.668*s)/( 1+2.562*s);
K=7.446;
T=2.5652;
L=2.668;
Lambda=0.089;
alpha=0.28;
C_=(1+T*s)*(1+alpha*T*s);
C_den=(1+Lambda*T*s)^2*1 ;
F=- (1+alpha*T*s)*exp(-L*s);
Net=C_/(C_den+F);

Its a snippet of How Net variable is visible

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Answer 1

Abhinav Aravindan 2024-2-21

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/789659-why-the-transfer-function-involving-exponential-term-comes-out-in-matrix-form-not-in-usual-polynomi#answer_1413278

"Net" results in an irrational expression and is therefore converted to a state-space model. The above transfer function can be modelled using Pade approximation. A similar query to yours is answered in the link below.

https://www.mathworks.com/matlabcentral/answers/246815

You can find the documentation for Pade approximation and “tf” here.

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

https://www.mathworks.com/help/control/ref/dynamicsystem.pade.html