# How to get RC circuit parameter for equivalent circuit diagram from measurement Graph?

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Alps on 31 Aug 2021
Commented: Alps on 16 Sep 2021
Hallo MathWorks community,
I am trying to model the RC equivalent Circuit of fuse from thermal Cauer-Model as shown below, according to time Constant theory here, Temperature (T) reches to stedy-state in 5 Time Constant.
Thermal Cauer Model Temperature measurement Graph Time Constant I have measured Temperature for 45 Min and from that Graph, I need to get RC Parameters values for the Cauer Model.
Rth1 Cth1
Rth2 Cth2
Rth3 Cth3
Rth4 Cth4
Rth5 Cth5
How can I get these 5 RC pair values from the measurement of the Temperature Graph? Is there any script similar to this "Generate Parameter Data for Equivalent Circuit battery Block" Link: Generate Parameter Data for Equivalent Circuit Battery Block - MATLAB & Simulink - MathWorks Deutschland
Thank you so much in advance!
Alps

Yifeng Tang on 1 Sep 2021
Simscape user here. So first, I would build the thermal network using the thermal domain. It's just a few thermal resistance and thermal masses. With the thermal resistance and masses values (equivalent to R & C) unknown, I would then use the Parameter Estimator App in Simulink Design Optimization to estimate each of the parameters. I think there are 5 unknown parameters to figure out here, instead of 10, since each RC pair represent only one time constant and should scale with each other. As long as the 5 time constants are distinctive enough from each other, you should be able to obtain reasonable estimates this way. More on Parameter Estimation:
You can of course use electrical circuit model in Simscape and use the same parameter estimation method.
Alps on 16 Sep 2021
Here is my model, Electric resistance and Thermal model (Cauer Model of 5 RC pairs) both are dependent on each other.
Temperature will measure through temp sensor from model and that corresponds to the Experiment measurement Data.
[Error: Optimization started 16-Sep-2021 17:41:02
Estimation converged, 16-Sep-2021 17:42:39
The solver encountered 29 errors during the estimation. Details of the errors have been written to 'EvalErrors_14' in the Results workspace.
'XYZ' updated with estimated parameter values
Estimated experiment values written to 'Exp'
Estimation solver output:
Local minimum possible.
lsqnonlin stopped because the relative size of the current step is less than
the value of the step size tolerance.
Optimization stopped because the relative norm of the current step, 6.150860e-04, is less than options.StepTolerance = 1.000000e-03.]
In Result area: At the end of Estimation, this is how my Comparison looks like: I am attaching here the Model and also the Experiment Excel Data.
I am using here 5 RC pair (Total 10 unknowns), because it is a Cauer model and tau = R*C, so Thermal Resistance Rth and Thermal Capacitor Cth (since It is simscape model and Mass and Resistance is available). Otherwise, what should I use for Parameter 5 constant?
Thank you.
Alps

R2019a

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