How to find the Transfer function of a Simulink output plot?

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Atefeh
Atefeh 2023-9-28
评论： Atefeh 2023-12-14
Hello My friends
I have a lot of figures and I want to find the transfer functions as I=Imax cos(ωt+ϴ) and V=Vmax cos(ωt+ϴ)
here is the values of V and I
Can you Advise?
I attached one of my plots.
I really appreciate your assistance.

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Sam Chak
Sam Chak 2023-9-28
Ran in:
Hi @Atefeh
Think you want to apply the curve-fitting method to fit the sinusoidal model to the time-series data.
load('V_I.mat')
Vtime = Vabc3.Time;
Vdat1 = Vabc3.Data(:,1);
ta = Vtime(1:1001);
Va = Vdat1(1:1001);
tb = Vtime(1002:2100);
Vb = Vdat1(1002:2100);
tc = Vtime(2101:3001);
Vc = Vdat1(2101:3001);
figure(1)
plot(Vtime, Vdat1), ylim([-1.5 1.5]), grid on
xlabel('Time (seconds)'), ylabel('V_{abc}')
[Vafit, gof1] = fit(ta, Va, 'sin1')
Vafit =
General model Sin1: Vafit(x) = a1*sin(b1*x+c1) Coefficients (with 95% confidence bounds): a1 = 0.998 (0.998, 0.998) b1 = 314.2 (314.2, 314.2) c1 = 1.031 (1.031, 1.031)
gof1 = struct with fields:
sse: 4.5659e-13 rsquare: 1.0000 dfe: 998 adjrsquare: 1.0000 rmse: 2.1389e-08
figure(2)
plot(Vafit, ta, Va), ylim([-1.5 1.5]), grid on
xlabel('Time (seconds)'), ylabel('V_{a}')
[Vbfit, gof1] = fit(tb, Vb, 'sin1')
Vbfit =
General model Sin1: Vbfit(x) = a1*sin(b1*x+c1) Coefficients (with 95% confidence bounds): a1 = 0.1984 (0.1983, 0.1985) b1 = 314.2 (314.1, 314.2) c1 = 7.268 (7.266, 7.27)
gof1 = struct with fields:
sse: 8.6937e-04 rsquare: 1.0000 dfe: 1096 adjrsquare: 1.0000 rmse: 8.9063e-04
figure(3)
plot(Vbfit, tb, Vb), ylim([-0.3 0.3]), grid on
xlabel('Time (seconds)'), ylabel('V_{b}')
[Vcfit, gof1] = fit(tc, Vc, 'sin1')
Vcfit =
General model Sin1: Vcfit(x) = a1*sin(b1*x+c1) Coefficients (with 95% confidence bounds): a1 = 0.9971 (0.9958, 0.9984) b1 = 314.2 (314.1, 314.2) c1 = 7.304 (7.291, 7.317)
gof1 = struct with fields:
sse: 0.1770 rsquare: 0.9996 dfe: 898 adjrsquare: 0.9996 rmse: 0.0140
figure(4)
plot(Vcfit, tc, Vc), ylim([-1.5 1.5]), grid on
xlabel('Time (seconds)'), ylabel('V_{c}')
  3 个评论
显示 1更早的评论
Sam Chak
Sam Chak 2023-11-2
Hi @Atefeh
Do you mean a single mathematical function that describes all 3 sine waves?

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更多回答（2 个）

Sam Chak
Sam Chak 2023-11-2
Ran in:
Hi @Atefeh
I'm not an expert, but I have friends who are, and one of them said this is possible with this math function:
where
, and .
If you find the proposed math function useful, don't forget voting 👍 for the answer.
load('V_I.mat')
Vtime = Vabc3.Time;
Vdat1 = Vabc3.Data(:,1);
ta = Vtime(1:1001);
Va = Vdat1(1:1001);
tb = Vtime(1002:2100);
Vb = Vdat1(1002:2100);
tc = Vtime(2101:3001);
Vc = Vdat1(2101:3001);
subplot(211)
plot(Vtime, Vdat1, 'color', '#528AFA'), ylim([-1.5 1.5]), grid on
title('Plot from Data')
xlabel('Time (seconds)'), ylabel('V_{abc}')
[Vafit, gof1] = fit(ta, Va, 'sin1');
vaAmp = Vafit.a1; vaFreq = Vafit.b1; vaPhi = Vafit.c1;
[Vbfit, gof1] = fit(tb, Vb, 'sin1');
vbAmp = Vbfit.a1; vbFreq = Vbfit.b1; vbPhi = Vbfit.c1;
[Vcfit, gof1] = fit(tc, Vc, 'sin1');
vcAmp = Vcfit.a1; vcFreq = Vcfit.b1; vcPhi = Vcfit.c1;
t = linspace(0, 0.3, 3001);
t1 = 0.1;
t2 = 0.21;
Vaf = vaAmp*sin(vaFreq*t + vaPhi);
Vbf = vbAmp*sin(vbFreq*t + vbPhi);
Vcf = vcAmp*sin(vcFreq*t + vcPhi);
fun1 = sign(t - t1).*(Vaf/4 - Vbf/4); % sigma1
fun2 = Vaf/4 + Vbf/4 + Vcf/2 - fun1;
fun3 = Vaf/4 + Vbf/4 - Vcf/2 - fun1;
f = fun2 - sign(t - t2).*fun3; % <-- this math function
subplot(212)
plot(t, f, 'color', '#FA477A'), ylim([-1.5 1.5]), grid on
title('Plot using Math function')
xlabel('Time (seconds)'), ylabel('V')
  4 个评论
显示 2更早的评论
Atefeh
Atefeh 2023-12-13
Dear Sam
Would you mind telling me the reference of the attached formulas?
Sam Chak
Sam Chak 2023-12-14
Hi @Atefeh
The provided signum-based formula does describe the behavior of the piecewise function. However, I find it unnecessary to cite the formula, as it involves a clever but unintuitive manipulation of the sign functions to separate the sub-functions at different intervals in the domain.
Moreover, I have provided a more intuitively understandable formula in my Answer below. If you still wish to cite, consider referencing the special function used in the formulation, acknowledging the mathematical properties of that function.

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Sam Chak
Sam Chak 2023-12-14
Ran in:
Hi @Atefeh
Given the piecewise function defined for
I propose a more intuitively understandable Heaviside-based formula, which I affectionately refer to as the Piecewise Function Put Together (PFPT) formula:
with .
In this formulation, the 1st term represents throughout the entire range of x. The 2nd term is activated by the Heaviside step function when x equals , plotting and canceling out from ​ onwards. Upon reaching , the Heaviside function triggers the 3rd term, plotting and canceling out from onwards.
If you appreciate the explanation of the PFPT formula, don't forget to vote 👍 for the answer as a token of appreciation.
load('V_I.mat')
Vtime = Vabc3.Time;
Vdat1 = Vabc3.Data(:,1);
ta = Vtime(1:1001);
Va = Vdat1(1:1001);
tb = Vtime(1002:2100);
Vb = Vdat1(1002:2100);
tc = Vtime(2101:3001);
Vc = Vdat1(2101:3001);
subplot(211)
plot(Vtime, Vdat1, 'color', '#528AFA'), ylim([-1.5 1.5]), grid on
title('Plot from Data')
xlabel('Time (seconds)'), ylabel('V_{abc}')
[Vafit, gof1] = fit(ta, Va, 'sin1');
vaAmp = Vafit.a1; vaFreq = Vafit.b1; vaPhi = Vafit.c1;
[Vbfit, gof1] = fit(tb, Vb, 'sin1');
vbAmp = Vbfit.a1; vbFreq = Vbfit.b1; vbPhi = Vbfit.c1;
[Vcfit, gof1] = fit(tc, Vc, 'sin1');
vcAmp = Vcfit.a1; vcFreq = Vcfit.b1; vcPhi = Vcfit.c1;
t = linspace(0, 0.3, 3001);
t1 = 0.1;
t2 = 0.21;
Vaf = vaAmp*sin(vaFreq*t + vaPhi); % f1, function at the 1st interval, t < t1
Vbf = vbAmp*sin(vbFreq*t + vbPhi); % f2, function at the 2nd interval, t1 < t < t2
Vcf = vcAmp*sin(vcFreq*t + vcPhi); % f3, function at the 3rd interval, t2 < t
%% Old Piecewise Function formula
% fun1 = sign(t - t1).*(Vaf/4 - Vbf/4); % sigma1
% fun2 = Vaf/4 + Vbf/4 + Vcf/2 - fun1;
% fun3 = Vaf/4 + Vbf/4 - Vcf/2 - fun1;
% fold = fun2 - sign(t - t2).*fun3; % <-- this math function
%% New Piecewise Function Put Together (PFPT) formula
fnew = Vaf + (Vbf - Vaf).*heaviside(t - t1) + (Vcf - Vbf).*heaviside(t - t2);
subplot(212)
plot(t, fnew, 'color', '#FA477A'), ylim([-1.5 1.5]), grid on
title('Plot using PFPT formula')
xlabel('Time (seconds)'), ylabel('V')

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