time dependent constant to solve 1st order ODE via ode45

I am able to solve my diff eq with ode45, however, I need one of my constants to change value once the output reaches a certain value. For context, this is to solve for the temperature in a simple energy balance for a stirred tank.

I need Tw to change to 15C once T reaches 34.7C

Code is as follows:

function diffeqs= ode_sys(t,var)

T=var(1);

dH=1200;
M=2300;
cp=4.2;
F=0.125;
Tw=20;
Tin=25;
U=3.4;
A=2.8;

diffeqs(1,1)=((F*cp*(Tin-T))+(F*cp*(Tin-T))+(F*dH)-(U*A*(T-Tw)))/(M*cp)

end 

***NEW SCRIPT***

tspan=[0:9000];
IC=(25); %initial Temp

[t,y]=ode45(@ode_sys,tspan,IC);

figure
plot(t,y,'-')
title('Temperature in CSTR')
xlabel('time/s')
ylabel('Temperature/C')

[Merwyn Pinto]

The temp reaches 34.7C when t>5000s if that helps. Every time i try to enter the code below, i get multiple errors

for t > 5000
    Tw=15;
end

Answer 1

[J. Alex Lee]

Seems like you just need Tw to be a function of T (of var(1)).

function diffeqs= ode_sys(t,var)
    
    T=var(1);
    
    dH=1200;
    M=2300;
    cp=4.2;
    F=0.125;
    % Tw=20;
    Tin=25;
    U=3.4;
    A=2.8;
    
    Tw = myfun(T)
    
    diffeqs(1,1)=((F*cp*(Tin-T))+(F*cp*(Tin-T))+(F*dH)-(U*A*(T-Tw)))/(M*cp)

end 

function Tw = myfun(T)
    % any functional form that you want, including a step function
    if T <= 34.7
        Tw = 20;
    else
        Tw = 15;
    end
end

I don't know if this "switch" type function is what you really want...should it be a smoother function? You can make the dependence on temperature in any functional form that you want, so just keep that in mind.

Also, I would recomment moving the constants outside of the odefun.

By the way time is not a reliable way to determine temperature..if you know when, then you don't really need to solve the ODE, do you?

[Merwyn Pinto]

I'm very much a beginner to Matlab so i'm not really sure what myfun means, but from a copy and paste i still can't get it to run unfortunately.

Just to clarify, I'm wanting Tw to remain at 15C after the very first time T reaches 34.7C

I've already solved the ODE via laplace but just wanted to become better at using matlab.

Thanks for the help

[J. Alex Lee]

By the way your system never seems to reach 34.7deg, so the switch will not affect your results.

Below will run, but I don't think the switch-liek function will give you what you want; demonstrated with a switch temperature of 33deg.

clc;
close all;
clear;

tspan=[0:9000];
IC=(25); %initial Temp

TwFunHndl = @TwFunConst;

[t,y]=ode45(@(t,Y)ode_sys(t,Y,TwFunHndl),tspan,IC);

figure; hold on;
plot(t,y,'-')
title('Temperature in CSTR')
xlabel('time/s')
ylabel('Temperature/C')

TwFunHndl = @TwFunSwitch;

[t,y]=ode45(@(t,Y)ode_sys(t,Y,TwFunHndl),tspan,IC);
plot(t,y,'--')


function diffeqs= ode_sys(t,var,TwFunHndl)

T=var(1);

dH=1200;
M=2300;
cp=4.2;
F=0.125;
% Tw=20;
Tin=25;
U=3.4;
A=2.8;

Tw = TwFunHndl(T);

diffeqs(1,1)=((F*cp*(Tin-T))+(F*cp*(Tin-T))+(F*dH)-(U*A*(T-Tw)))/(M*cp);

end

function Tw = TwFunSwitch(T)
% any functional form that you want, including a step function
if T <= 33 % 34.7
	Tw = 20;
else
	Tw = 15;
end
end

function Tw = TwFunConst(T)
% any functional form that you want, including a step function
Tw = 20;
end