# How to obtain model parameters by fitting experimental data to the monod model. monod model.

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O'Brien Ikart on 30 Jul 2021
Commented: Alex Sha on 31 Jul 2021
t= [0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 48]
x= [15, 18.3, 22, 23.4, 23.8, 24.1, 24.5, 24.8, 24.87, 24.9, 24.95, 25, 25]
S= [49.7, 28, 26.1, 18.1, 13.7, 10.1, 4.1, 1.2, 0.3, 0.08, 0.05, 0.05, 0.05 ]
P= [0, 5.2, 8.1, 9.3, 10.5, 12.3, 12.8, 13.2, 13.6, 13.8, 13.9, 13.95, 13.95]
I used initial guess values of umax, ks, y1 and y2 as 0.5, 55, 5 and 1.4 respectively. dx/dt= umax*s*x/(ks + s); ds/dt= -y1*umax*s*x/(ks + s) dp/dt= y2*umax*s*x/(ks +s). I used the code provided by star strider on a similar question but I keep getting errors, I also have to fit the data to other fermentation models. Also can simulink be used for the fitting?
O'Brien Ikart on 30 Jul 2021
I tried using that code to numerically integrate the models from 0 to 48 with the guess values for the model parameters. I kept getting errors.... I have to fit the model to the experimental parameters. It was easier to numerically integrate the models using simulink but I dunno how to do the fitting on either Matlab or simulink.
O'Brien Ikart on 30 Jul 2021
Really new to Matlab and simulink

Alex Sha on 31 Jul 2021
Refer to the results below:
Root of Mean Square Error (RMSE): 1.50437634361661
Sum of Squared Residual: 81.4733345963976
Correlation Coef. (R): 0.97672011839718
R-Square: 0.9539821896818
Parameter Best Estimate
-------------------- -------------
umax -0.0619295716977556
ks -88.5509341201568
y1 4.65073776898894
y2 1.33836136350295
O'Brien Ikart on 31 Jul 2021
Thanks @Alex Sha..... But the values of umax and ks are supposed to non- negative
Alex Sha on 31 Jul 2021
If you want all parameters to be positive without upper bound limition, the result will be a bit strange as below:
Root of Mean Square Error (RMSE): 1.70454457017103
Sum of Squared Residual: 104.596998901184
Correlation Coef. (R): 0.976253765588915
R-Square: 0.953071414826535
Parameter Best Estimate
-------------------- -------------
y1 4.78475504434034
y2 1.35947688117111
umax 515071175352863
ks 5.10885251418351E17