Determination of a PT1-element

Hello

I have a PT1-element and like to determine the parameters T and K. I’m able to measure the resulting y-values from the technical process. In the best case I mustn’t record a whole step response for analyzing. I tried this way:

http://www.mathworks.de/de/help/matlab/data_analysis/programmatic-fitting.html#f1-7306

with a model like this:

T=2; K=3; t=(0:0.1:10)';
y=K*(1-exp(-t/T));
X = [ones(size(t))  exp(-t)];
a=X\y;
y2=a(1)+a(2).*exp(-t);
plot(t,y,t,y2)

But with the result I can’t figure out the values of T and K.

y=2.7519-3.4315*exp(-t)

If I determine T=1, it’s easy because in my source equation “T” will be dropped:

y(t)=K*(1-exp(-t/T))

In all other cases I get this strange elements of “a”. Also this kind of fitting doesn’t seem to be ideal for my problem, like you can see in the plot. Is there a possibility to convert the upper result into a really fitting solution? If not, how can I adapt the backslash fitting to solve for T and K? I’ve read of other solutions in this assignment with usage of Statistics- or Optimization Toolbox, which I unfortunately cannot use.

I would be very happy about some advices

Felix