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Multi term power series fitting with MATLAB

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Hy,
I would like to do parameter-identification of a DC motor.
The estimation is based on the attached pdf file.
I would like to fit mullti term power series (built-in function is only able to estimate with maximum 2 term) to the data, which also attached with time domain.
The equation is the following:
equation.jpg
The motor parameters can be calculated from these constants as described in the pdf.
Do you have an idea how to calculate these constants?
Sincerely,
Gergely Hunyady

Answers (1)

Star Strider
Star Strider on 29 Jan 2020
Try this:
D = load('NoLoadSpeed.mat');
T = load('Time.mat');
NLS = D.MotorSpeed_NoLoad; % Column Vector
t = T.Time; % Column Vector
pdv = 2:9; % Power & Denominator Vector
DM = t.^pdv./cumprod(pdv); % Design Matrix
BetaVct = DM \ NLS;
NLSfit = DM * BetaVct; % Fit Regression
figure
plot(t, NLS, '.')
hold on
plot(t, NLSfit, '-r')
hold off
grid
xlabel('Time')
ylabel('MotorSpeed_NoLoad')
legend('Data', 'Fit', 'Location','E')
The ‘pdv’ vector can only go to 9 before the design matrix loses rank. This produces 8 β coefficients (the ‘BetaVec’ vector).

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