Matlab Transfer function multiple single s terms

Question

Aaron Frost 2023-2-20

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1915880-matlab-transfer-function-multiple-single-s-terms

评论： Paul 2023-2-22

采纳的回答： Sulaymon Eshkabilov

IMG_3598.jpg

在 MATLAB Online 中打开

How can modify this script in order to get the transfer function shown in the picutre. Thanks.

C1 = 0.000000000150;
C2 = 0.000000000470;
R1 = 10000;
R2 = 180000;
R3 = 2700;
R4 = 56000;
A = 1/(C1*R2);
B = 1/(C2*R2);
C = (1/(C1*R1))*(1-G);
D = 1/(C1*C2*R1*R2);
G = (R3+R4)/R3;
%{
Numerator = {[G 0 0] };
Denominator = {[1 0] [A] [B] [C] [0 D]};
T = tf(Numerator, Denominator)
%}
T = tf([G 0 0], {[1] [A] [B] [C] [0 D]})

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Answer 1

Sulaymon Eshkabilov 2023-2-20

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1915880-matlab-transfer-function-multiple-single-s-terms#answer_1175880

在 MATLAB Online 中打开

Here it is:

C1 = 0.000000000150;
C2 = 0.000000000470;
R1 = 10000;
R2 = 180000;
R3 = 2700;
R4 = 56000;
G = (R3+R4)/R3;
A = 1/(C1*R2);
B = 1/(C2*R2);
C = (1/(C1*R1))*(1-G);
D = 1/(C1*C2*R1*R2);
%{
Numerator = {[G 0 0] };
Denominator = {[1 0] [A] [B] [C] [0 D]};
T = tf(Numerator, Denominator)
%}
T = tf([G 0 0], [1 (A+B+C) -D])
T =
 
          21.74 s^2
  --------------------------
  s^2 - 1.378e07 s - 7.88e09
 
Continuous-time transfer function.

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Answer 2

Walter Roberson 2023-2-20

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1915880-matlab-transfer-function-multiple-single-s-terms#answer_1175875

在 MATLAB Online 中打开

syms G C_1 R_2 C_2 R_1 s R_3 R_4

G = (R_3 + R_4)/R_3

G =

vratio = G*s^2/ ( s^2 + s * (1/(C_1*R_2) + 1/(C_2*R_2) + 1/(C_1*R_1)*(1-G)) + 1/(C_1*C_2*R_1*R_2) )

vratio =

vex = expand(vratio);

[N, D] = numden(vex)

N =

D =

Nc = collect(N, s);

Dc = collect(D, s);

vpretty = Nc/Dc

vpretty =

NCs = coeffs(Nc, s, 'all')

NCs =

DCs = coeffs(Dc, s, 'all')

DCs =

C1 = 0.000000000150;

C2 = 0.000000000470;

R1 = 10000;

R2 = 180000;

R3 = 2700;

R4 = 56000;

NC = double(subs(NCs, [C_1, C_2, R_1, R_2, R_3, R_4], [C1, C2, R1, R2, R3, R4]));

DC = double(subs(DCs, [C_1, C_2, R_1, R_2, R_3, R_4], [C1, C2, R1, R2, R3, R4]));

leading = DC(1);

NC = NC ./ leading;

DC = DC ./ leading;

sys = tf(NC, DC)

sys = 21.74 s^2 -------------------------- s^2 - 1.378e07 s + 7.88e09 Continuous-time transfer function.

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Walter Roberson 2023-2-21

Note that the reason to solve symbolically is to construct a general form that multiple sets of resister and capacitor values could be substituted into. After calculating NCs and DCs you could use matlabFunction() to create functions that would accept numeric inputs and calculate the coefficients.

Paul 2023-2-22

在 MATLAB Online 中打开

But the CST can handle this directly without too much complication, even if the desire is to have a general expression

s = tf('s');
G = @(R_3,R_4) ((R_3 + R_4)/R_3);
vratio = @(C_1,C_2,R_1,R_2,R_3,R_4) G(R_3,R_4)*s^2/ ( s^2 + s * (1/(C_1*R_2) + 1/(C_2*R_2) + 1/(C_1*R_1)*(1-G(R_3,R_4))) + 1/(C_1*C_2*R_1*R_2) );
C1 = 0.000000000150;
C2 = 0.000000000470;
R1 = 10000;
R2 = 180000;
R3 = 2700;
R4 = 56000;
vratio(C1,C2,R1,R2,R3,R4)
ans =
 
          21.74 s^2
  --------------------------
  s^2 - 1.378e07 s + 7.88e09
 
Continuous-time transfer function.

Unrelated comment, but I have my suspicions about the expression for vratio in the question. I thought that circuits composed of just (positive) resistors and (positive) capacitors can't be unstable, whereas vratio clearly is.

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