Simulation of differential equations with multiple variables. What is wrong with my code? Monod-like kinetic, Biotechnology, Differential equations, ODE15s

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Biotechnewbie
Biotechnewbie 2015-3-6
评论： Anna Gardarsdottir 2021-2-2
My problem goes like this:
I have to simulate the following Equations
I would do this with a function summing up all the equatiobs and ODE15s.
The code of my function looks like this:
function [ f ] = dXdt( ~, x )
%% Variables%%
Cx = x(1);
cp = x(2);
mu = x(3);
c_s = x(4);
nu = x(5);
%% Constants%%
R=8.3144621; %kJ/(K*kmol)
Kcm=0.03; % 1/h
Kd0=1.836*10^(-3);% 1/h
Ks=60; % g/L
Ksp=50; % g/L
Kss= 500; % g/L
Kssp=620; % g/L
Pm= 70; % g/L
PIm= 70; % g/L
Cp0= 0; % g/L
Cs0= 220; % g/L
Cx0=0.2; % g/L
E=3.461*10^(4);% kJ/kmol
Ed=1.777*10^(5); % kJ/kmol
Ep=3.496*10^(4);
Y_x=0.41;
Y_p=0.42;
mu_m=0.414; %1/h
nu_m=3.974; %1/h
nu_0=2.511833179;
mu_0=0.241719745;
T=308.15; % K
%% Equations%%
dCxdt=mu*Cx-Kd0*Cx;
dCpdt=Cx*nu;
mu=mu_m*(c_s/(Ks+c_s+(c_s^2)/Kss))*(1-cp/Pm);
dc_sdt=(-1)*((1/Y_x)*dCxdt+(1/Y_p)*dCpdt+Kcm*Cx);
nu=nu_m*(c_s/(Ksp+c_s+(c_s^2)/Kssp))*(1-cp/PIm);
f=[dCxdt; dCpdt; mu; dc_sdt; nu];
end
When executing this function, using
[t,x]=ode15s(@dXdt,[0,72],[Cx0 Cp0 mu_0 Cs0 nu_0]);
I get a time error:
Warning: Failure at t=4.971802e+00. Unable to meet integration tolerances without reducing
the step size below the smallest value allowed (1.421085e-14) at time t.
> In ode15s at 731
But I can't spot the bug in my code, or the transcription/translation of the equations.
Or is this even the proper way to solve this?
If it works, the plots of t,cs ... should look like those on the right.
Thanks in advance for your help !

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采纳的回答

Torsten
Torsten 2015-3-9
The equations for mu and nu are algebraic equations, but at the moment you solve
dmu/dt=mu_m*(c_s/(Ks+c_s+(c_s^2)/Kss))*(1-cp/Pm);
dnu/dt=nu_m*(c_s/(Ksp+c_s+(c_s^2)/Kssp))*(1-cp/PIm);
Best wishes
Torsten.
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显示 2更早的评论
darova
darova 2021-2-2
HEre is what you should change
% dCxdt=mu*Cx-Kd0*Cx;
% dCpdt=Cx*nu;
% mu=mu_m*(c_s/(Ks+c_s+(c_s^2)/Kss))*(1-cp/Pm);
% dc_sdt=(-1)*((1/Y_x)*dCxdt+(1/Y_p)*dCpdt+Kcm*Cx);
% nu=nu_m*(c_s/(Ksp+c_s+(c_s^2)/Kssp))*(1-cp/PIm);
% f=[dCxdt; dCpdt; mu; dc_sdt; nu];
mu=mu_m*(c_s/(Ks+c_s+(c_s^2)/Kss))*(1-cp/Pm);
nu=nu_m*(c_s/(Ksp+c_s+(c_s^2)/Kssp))*(1-cp/PIm);
dCxdt=mu*Cx-Kd0*Cx;
dCpdt=Cx*nu;
dc_sdt=(-1)*((1/Y_x)*dCxdt+(1/Y_p)*dCpdt+Kcm*Cx);
f=[dCxdt; dCpdt; dc_sdt];
Remember about the ode45 call int main code

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