Frequency input to Transform Function

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Nerma Caluk 2022-8-12

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https://ww2.mathworks.cn/matlabcentral/answers/1778605-frequency-input-to-transform-function

回答： Paul 2022-8-13

I have developed set of transfer functions, with the final one being the acceleration. I have ran it successfully for an arbitary angular frequency range from 0.01 to 100 rad/s. Now I am trying to input a specific frequency response I have extracted using Fourier Transform, into the final Transfer function. I am not sure how to do this. I have tried using the function "freqresp", but I keep getting errors and weird graphs. Does anyone recommend any changes to the existing function or another function?

This is the code of the transfer functions and attempt signal input:

%%%%%Given Values

K_1 = 500000; % gain of the displacem transducer (V./m)

K_2 = 0.000016; % coil-magnet transfer function (m./s.^2)./V

K_3 = 31.6; % amplifier gain of the feedback output

omega_a = 0.0628; % output high pass cut-off angular frequency (rad./s)

omega_l = 8.72665; % output low pass cut-off angular frequency (rad./s)

f_l0 = 0.06667; % responant frequency of the pendulum (Hz)

h = 0.85; % damping constant

omega_d = 47.62; % demodulator low-pass cut-off angular frequency (rad./s)

omega_f = 0.000997; % feedback low-pass cut-off angular frequency (rad./s)

K = 208.4; % Conversion from V/(m/s^2) to DU/(m/s^2) [DU/V]

omega_f0 = 2*pi*f_l0;

%%%%Flat-Response Mode of the Long-Period Seismometer

% Transfer function of single-pole high-pass filter in the output amplifier

numerator_Fa = [1, 0];

denominator_Fa = [1, omega_a];

F_a = tf(numerator_Fa, denominator_Fa);

%Traner function of the feedback low-pass filter

numerator_Ff = [omega_f];

denominator_Ff = [1, omega_f];

F_f = tf(numerator_Ff, denominator_Ff);

% Tranfer function of the demodulator low-pass filter

numerator_Fd = [omega_d];

denominator_Fd = [1, omega_d];

F_d = tf(numerator_Fd, denominator_Fd);

% Transfer function of the seismometer for accleration

numerator_Sf = [1];

denominator_Sf = [1, 2*h*omega_f0, (omega_f0)^2];

S_f = tf(numerator_Sf, denominator_Sf);

% Transfer function of the feedback component of the seismometer

numerator_Fsf = K_1*S_f*F_d;

denominator_Fsf = 1 + K_1*K_2*S_f*F_d*F_f;

F_sf = numerator_Fsf/denominator_Fsf;

% Transfer function of 8-pole output low-pass anti-aliasing filter

numerator_Fla = [omega_l^2];

denominator_Fla = [1, 2*cos(pi/8)*omega_l,omega_l^2];

F_la = tf(numerator_Fla, denominator_Fla);

numerator_Flb = [omega_l^2];

denominator_Flb = [1, 2*cos((3*pi)/8)*omega_l,omega_l^2];

F_lb = tf(numerator_Flb, denominator_Flb);

F_l = [(F_la)^2] * [(F_lb)^2];

% Input of Frequnecy response (w) through the transfer functions

A_LPF_DU = K*K_3.*F_a*F_l*F_sf; % [DU/(m/s^2)]

s = j.*w;

[resp,freq] = freqresp(A_LPF_DU,s);

resp2 = abs(squeeze(resp))

figure (4)

loglog(freq,resp2)

xlabel('Frequency');

ylabel('Magnitude of Frequency Response');

Thank You!

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Answer 1

Paul 2022-8-13

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https://ww2.mathworks.cn/matlabcentral/answers/1778605-frequency-input-to-transform-function#answer_1025845

Hi Nerma,

Check freqresp. The second argument should be a real vector of frequencies (typically > 0). The multiplication by 1j is done inside the function.

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Frequency input to Transform Function

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