Fitting multiple RC time constants

[KeithB]

I am putting this here since I am trying to find the best tool for the job.

I am trying to model a thermal response as a series of RC time constants.

The basic model is
Tc + r1*(1-exp(-t/(r1*c1))) + r2*(1-exp(-t/(r2*c2))) + r3*(1-exp(-t/(r3*c3))) ...
where in this case I go up to 10.

I have the Zth as a function of t. (t ranges from 1 E-10 to 100 seconds, and Zth ranges from .02 to 2.8 so it is a pretty "stiff" system.)

This was solved by the folks that did the original work for us, but I am trying to build some local capability. They have a 10 element (10 r's and 10 c's) that fit very well. But when I try to use Excel and its solver, it does not do very well.

So does anyone have a good idea for a tool/procedure?
I am really tempted to try the HP71 since I have the curve fitting pack...

I also have a Prime.