How to calculate the norm of the transfer function in frequency domain?

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Cola 2022-3-13

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评论： William Rose 2022-3-14

To calculate the norm of the transfer function by substituting s=jω is troublesome, especially for some complicated transfer functions. Is there a way to calculate the norm directly? Thanks!

For example, transfer funciton:

Substituting s=jω，

then,

Thus we can plot the figure in frequency domain,

Matlab code:

omega=0:0.01:10;

G1_N=0.25e-2 .* omega .^ 2 + 0.1e1;

G1_D=((2 .* omega) - 0.15e0 .* (omega .^ 3)) .^ 2 + (0.1e1 + 0.5e-2 .* (omega .^ 4) - (omega .^ 2)) .^ 2;

G1=sqrt(G1_N ./ G1_D);

plot(omega,G1)

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采纳的回答

William Rose 2022-3-13

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@Cola,

You don't need to multiply the function by its complex conjugate to get a purely real denominator. Just divide complex numerator by the complex denominator, to get a new complex number, and take the abs() of it.

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Cola 2022-3-14

编辑：Cola 2022-3-14

@William Rose Thank you so much.

William Rose 2022-3-14

@Cola, you're welcome, and good luck with your work.

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Paul 2022-3-13

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在 MATLAB Online 中打开

Check out

doc tf

to learn how to create a transfer function (tf) object. Once you have G(s) defined as a tf object use bode() to compute its magnitude (and phase if desired)

doc bode

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Paul 2022-3-13

Actually, I was thinking of the Control System Toolbox. I'm not famiiar with the System ID toolbox.

If just wanting to use base Matlab, I'd probably use polyval().

Cola 2022-3-14

编辑：Cola 2022-3-14

@Paul @William Rose Thanks to you. And we also can use the order 'freqs' to calculate the norm.

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