Modeling concentration using ODE

I'm trying to model a dye concentration but I cannot make to run and I'm stuck. It gives an error but it will not tell what is wrong. Can any one help thanks?

clear all; 
data = load('test_data.dat');

Error using load
Unable to find file or directory 'test_data.dat'.

time  = size(data,1);
u = data(:,2);
tspan = [1:1:time];
y0  = data(1,3);

f  = -0.25; 
g  = 0.25; 
T = 10.0; 

[t,y]=ode45(@model,tspan,y0,f,g,T,U);

plot(t, y(:,end), '*-b', 'LineWidth', 1);


function dydt = model(t,y,f,g,T,u)
if t-1 <= T
    u = 0;
else
    t_back = t-T;
    n = floor(t_back); u =(n);
end
dydt = f*y + g*u;
return;
end

[Image Analyst]

Well we're also stuck. I formatted your post as code but you forgot to attach 'test_data.dat' so we're stuck. We'll check back later for it, after you read this:

TUTORIAL: How to ask a question (on Answers) and get a fast answer

[Stark Volt]

thank you sorry for that, and thank you for reformatting my post

[Image Analyst]

What is option? It says it's not defined. If I use options instead of option, I just get more errors.

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
imtool close all;  % Close all imtool figures if you have the Image Processing Toolbox.
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format short g;
format compact;
fontSize = 20;

%(the .mlx file)
%Dye concentration
clear all; 
data = load('test_data.dat');

time  = size(data,1);	% simulation time
input = data(:,2);		% measured top concentration
rslt  = data(:,3);      % measured bottom concentration

tspan = [1:1:time]; % time variable
inc  = data(1,3);  % initial bottom concentration

%model parameters
fparameter  = -0.25; 
gparameter  = 0.25; 
delay = 10.0; 

options = odeset('RelTol', 1e-3);
[t,y]=ode45(@model,tspan,inc,option);

plot(tspan, obsv, '-b', 'LineWidth', 0.5); hold on; 
plot(tspan, input, '-g', 'LineWidth', 0.5);
plot(t, y(:,end), '-.m', 'LineWidth', 1);
legend('rslt', 'input');
xlabel('time(second)'); ylabel('Concentration');
grid;

%Predefined function (the .m file)
function dydt = model(t,y,parameter,input)
% MODEL ordinary differential equation (ODE) model:
%          dy/dt = f*y(t) + g*u(t-T)
dxdt = 0;%return variables
if t-1 <= parameter(3) %delay the initial concentration
    u_input = 0;
else
    t_back = t-parameter(3);
    n = floor(t_back); u_input = input(n);
end
dydt = f*y(t) + g*u(t-T)
return;
end

[Stark Volt]

I don't know if it is good to put the option when i read the ode45 you can set a range of error. But you can remove it. Thank you

[Star Strider]

@Stark Volt — Do you want to estimate parameters of the model using the data?

This can be relatively straightforward, however the system of differential equations must be defined in terms of the parameters. It is not obvious to me what those are.

.

[Stark Volt]

Hi @Star Strider that is what i'm trying to do. So by reading those help and mathlab knowledge and finishing mathlab onramp i come up to that code base on my understanding. Thank you,

[Star Strider]

I cannot understand what you are doing well enough to attempt an actual answer.

See Coefficient estimation for a system of coupled ODEs for an illustration of an approach that works. (There are several others as well, all using the same essential approach.)

Put your system in that sort of format, and use your data. If you have problems with it, post back here and I will do my best to get your code to work correctly.

.

[Stark Volt]

hello @ Star rider, after I did go through the link you provided which made me read other mathlab knowlegde and documentation so I revise the code that I posted but it I still can't figure out what is wrong. Here are the error poping up thanks.

Not enough input arguments.

Error in cstr_model (line 19)

n = floor(t_back); u= u(n);

Error in odefcncleanup>@(t,y)oldFcn(t,y,inputArgs{:}) (line 11)

newFcn = @(t,y) oldFcn(t,y,inputArgs{:});

Error in ode45 (line 299)

f2 = odeFcn_main(t2, y2);

Error in hw3 (line 33)

[t, x] = ode45(@cstr_model,tspan, y0,f,g,T,u);

**so in the this error newFcn = @(t,y) oldFcn(t,y,inputArgs{:}); what does this mean inputArgs{:}? thank you.

[Star Strider]

Please provide a symbolic (preferably LaTeX) version of the differential equation system you’re working with, and the parameters you want to estimate. If you have a PDF of a paper describing what you want to do, that would be even better. (Attach / upload the PDF, not a link to it, because thery’re usually behind a paywall, preventing me from accessing them if I don’t subscribe to the journal.)

Also, putting if blocks in the differential equation function is going to cause problems. Numerical differential equation integration functions don’t do well when integrating across the discontinuities that the if blocks cause.

I don’t understand the reason ‘parameter’ is nowhere represented in the differential equation.

I’ll do my best to see if I can get the differential equation (or system of them) to work with my code and your data.

.

Answer 1

[Sulaymon Eshkabilov]

You had better use this data importing fcn:

data = readmatrix('test_data.dat');

Make sure that the data file (test_data.dat) is present in your current directory or change to the directory where the data file (test_data.dat) is residing.