Plotting amplitude and phase spectrum

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chaneil james
chaneil james 2019년 10월 13일
We have been given the Response of a mechanical sensor (seismometer) where:
We were then given the original frequency, f, damping, h, and gain factor, G. With this we are meant to be able to plot the amplitude and phase spectrum against frequency. I have no idea where to start, and have been looking at coding for Fourier transformations and polynomials for ages. Could anyone suggest where to start?

답변 (1개)

Thiago Henrique Gomes Lobato
Thiago Henrique Gomes Lobato 2019년 10월 13일
This amplitude and phase spectrum plot of a transfer function is called the Bode plot , it is very well known and you may easily find some references online, this guy, for example, has some very nice tutorials about control engineering that may apply to your problem :https://www.youtube.com/watch?v=_eh1conN6YM&t=12s. In Matlab you have a tool to define the coefficients of your transfer function and then plot the result (as example of your equation):
% Parameters
G = 1;
h = 0.3;
w0 = 5;
% Generate the transfer function
numerator = [G,0,0];
denominator = [-1,-2*h*w0,w0^2];
sys = tf(numerator,denominator)
% Plot it
bode(sys)
grid
sys =
-s^2
--------------
s^2 + 3 s - 25
Continuous-time transfer function.
Untitled.png
I feel however about uneasy about your equation since it is not stable and I believe it should be a stable damped system. Maybe you had some typo erros? A more reasonable transfer function for a damped system would look like this
% Parameters
G = 1;
h = 0.3;
w0 = 5;
% Generate the transfer function
numerator = [w0^2*G];
denominator = [1,2*h*w0,w0^2];
sys = tf(numerator,denominator)
% Plot it
bode(sys)
grid
sys =
25
--------------
s^2 + 3 s + 25
Continuous-time transfer function.
Untitled.png

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