How to I plot Laplace transfer function characteristics using the symbolic toolbox?

Question

Rogier Reerink 2020-5-19

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评论： Andrew Krill 2022-6-19

Hi there,

I'd like to be able to use the symbolic toolbox for plotting the amplitude and phase response of a transfer function in the Laplace domain. Reason is because I find symbolic functions to keep my work neat and easily readable.

I've tried plotting the transfer functions' amp and phase characteristics using the following piece of code. Transfer function H describes a simple passive RC low pass filter where R*C = 0.001 in Vx = Vy + R*C*Vy*s.

syms s;
H = 1/(0.001*s+1);
figure; fplot(abs(H), [0 100000]);
figure; fplot(angle(H), [0 100000]);

I would expect the phase shift between Vy and Vx to go from 0 to -pi/2 (or -90 deg), as in the bode plot below:

bode([0 1], [0.001 1]);

However, when plotting the angle with fplot I see no phase shift:

fplot(angle(H), [0 100000]);

I'd be glad if anyone could explain to me why bode and fplot give different results.

Thanks in advance!

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Answer 1

Star Strider 2020-5-19

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在 MATLAB Online 中打开

Here, ‘s’ needs to be complex:

syms s;
H = 1/(0.001*1j*s+1);
figure; fplot(20*log10(abs(H)), [0 100000]);
% set(gca, 'XScale','log')
figure; fplot(angle(H), [0 100000]);
% set(gca, 'XScale','log')

For some reason, setting the 'XScale' to 'log' (so that it matches the bode plot) fails for fplot plots. I will experiment with that and post back if I can figure out a way to get it to work.

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Star Strider 2020-5-19

As always, my pleasure!

Symbolic variables are ‘complex’ by definition, however by defaault the imaginary parts are equal to 0, making them real. I set ‘s’ to be purely imaginary in my code.

I also had no problems creating logarithmic x-axis (and y-axis) scaling, however I could not get it to work correctly when I converted ‘H’ to decibels and plotted the y-axis linearly after the transformation to dB, with logarithmic x-axis scaling. That is what I wanted to do, and could not.

Andrew Krill 2022-6-19