Multi term power series fitting with MATLAB

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:

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

Answer 1

[Star Strider]

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).