How can I solve an ODE with changing variable over time ?

I want to solve a sytem of ODE, with the following paramiters and initioal conditions.

in the 4th equation of the ODE, Tset(t) is a variable which is changing over time, however in this code I have made it as an constant value over time and my code is working.

I have the values for Tset(t) as well as the corresponding time of these values in a mat file : (TsetTime, TsetValue)

how can I solve the ODE if the value of Tset (in the 4th equation of the ODE) is changing over time.

% Paramiters 
Xb         = 16;                              
Xw         = 0.4;                             
Rg         = 8.314;                           
pT         = 101325;                          
g          = 0.042;                          
mue        = 4e7;                             
NumBubbles = 2e11;                            
R0         = 5e-5;                            
Temp0       = 303;                          
n0         = 0;                           
C0         = 0;                             
q0         = 0.0015;                          
tt = 1/30;
nN2        = 4/3*pi*R0^3*(pT+2*g/R0)/Rg/Temp0; 
VD         = 1-R0.^3*4/3*pi*NumBubbles;      

init       = [R0; n0; C0;Temp0; q0];               


%sysytem of ODE

OdeSys = @(t,y) [
    1/4/mue*(3*Rg*y(4)/4/pi/y(1)^2*(y(2)+nN2)-pT*y(1)-2*g); 
    4*pi*(1.77e-9*Xw*y(4)/298)*y(1)*(y(3)-((pT/(100*(y(4)-273)+1200)*(1-(R0/y(1))^3)+2*g/(100*(y(4)-273)+1200)/y(1)*(1-(R0/y(1))^2))));
    Xb*y(5)-NumBubbles*4*pi*(1.77e-9*Xw*y(4)/298)*y(1)*(y(3)-((pT/(100*(y(4)-273)+1200)*(1-(R0/y(1))^3)+2*g/(100*(y(4)-273)+1200)/y(1)*(1-(R0/y(1))^2))));                    % dc_CO2/dt -> CO2 concentration in (liquid) dough
    tt*(Tset(t) - y(4));
    0                                                       
];


[T,S] = ode45(OdeSys, [0 3000], init);

%Plot the results
figure('Position', [0 0 1600 500]);
for i = 1:4
    subplot(1,4,i);
    plot(T,S(:,i))
    xlim([0, T(end)]); grid on; box off
    xlabel('time $/s$','interpreter','Latex');
    ylabel('value $/units$','interpreter','Latex');
    title(titles{i},'interpreter','latex');
end


% this function is used to make Tset(t) constatnt over time, however I want
% to change this with TsetValue at TsetTime

function Ts = Tset(t)
    Ts = 303;
    
end


%load  TsetTime
%load  TsetValue

Answer 1

[Stephen23]

Replace your Tset function with this:

P = 'absolute or relative path to where the mat file is saved';
F = 'name of the mat file';
S = load(fullfile(P,F));
Tset = @(t) interp1(S.TsetTime, S.TsetValue,t);