Good day guys. How do I write a Matlab program that will integrate a nonlinear system over one sample period?

I am trying to write a function that integrates a nonlinear model over one sample period. My outputs are next states (x1k1, x2k1). My inputs contain among others current states (x1k, x2k). I want to use the "int" command in matlab but, I am not getting it right. Below is my code.

function [x1k1,x2k1]=integr_S(x1k,x2k,uk,V,k1p,k2p,ca0,cb0,T)
% Calculates the next-state concentrations of the reactor given the
% input
syms ca0 x1k x2k k1p k2p cb0 uk V
fint1=(((ca0-x1k)*uk/V)-k1p*x1k);
fint2=(((cb0-x2k)*uk/V)-k2p*x2k);
x1k1=x1k+integral(fint1,t, 0, 1);
x2k1=x1k+integral(fint2,t 0, 1);

Please help.

Thanks

[Star Strider]

You apparently want to integrate with respect to ‘t’, however ‘t’ is not a variable in the functions you want to integrate.

You can use the integral function (or int for symbolic functions) to integrate other functions, however neither of the variables you want to integrate are defined as functions. Also, you immediately declare the arguments to your symbolic expressions as symbolic variables. This overwrites whatever the values of those variables are passed as arguments to your function.

Foir example:

x = 20;
syms x t 
y = x^t

produces:

y =
x^t

If you want to integrate vectors or matrices, use the trapz (or cumtrapz) function.

[Torsten]

Since there is no variable t in the expressions for fint1 and fint2,

x1k1 = x1k + fint1
x2k1 = x2k + fint2

[ojonugwa adukwu]

Thanks so much to both of you. Torsen looks like a simple answer. What if my range of integration is from 0:2 and not 0:1 as show above? Star strider, I appear not to know what are symbolic variables. Sorry, I am still low in MATLAB. Reagrads

[Torsten]

There is no longer an integration.

x1k1 = x1k + (((ca0-x1k)*uk/V)-k1p*x1k);
x2k1 = x2k + (((cb0-x2k)*uk/V)-k2p*x2k);

[Star Strider]

Symbolic variables are the ones you declare with this syms call:

syms ca0 x1k x2k k1p k2p cb0 uk V

‘What if my range of integration is from 0:2 and not 0:1 as show above?’

Define ‘fint1’ and ‘fint2’ as functions of ‘t’, then supply the appropriate integration limits to the integral function.

[ojonugwa adukwu]

Ok. Thanks. I just have to figure that out.

[Torsten]

If you have ordinary differential equations to solve (which I suspect)

dx1/dt = (ca0-x1)*u(t)/V - k1(t)*x1
dx2/dt = (cb0-x2)*u(t)/V - k2(t)*x2

use one of MATLAB's ODE integrators (e.g. ODE45).

[Star Strider]

If your function arguments are vectors (or matrices) that already functions of ‘t’, and you have the ‘t’ vector, you can use logical indexing (or the find function) to determine the values of ‘t’ between 0 and 2 or whatever other limits you choose. Then use trapz to do the integration.

Example (with ‘v’ the vector you want to integrate):

idx = (t >= 0) & (t <= 2);
vint = trapz(v(idx));

[ojonugwa adukwu]

When I made my function to depend on time as shown below, I got the error message after it.

syms t
fint1=(((ca0-x1k(t))*uk/V)-k1p*x1k(t));
fint2=(((cb0-x2k)*uk/V)-k2p*x2k(t)+k1p*x1k(t));
x1k1=x1k+int(fint1,0,1);
x2k1=x1k+int(fint2,0,1);

The error message is;

Error using sym/subsindex (line 732)

Invalid indexing or function definition. When defining a function, ensure that the arguments are

symbolic variables and the body of the function is a SYM expression. When indexing, the input must be

numeric, logical, or ':'.

What does MATLAB mean by symbolic variables and what is a SYS expression?

[Star Strider]

Try this:

syms ca0 x1k x2k k1p k2p cb0 uk V t x1k(t) x2k(t) 
fint1(t)=(((ca0-x1k(t))*uk/V)-k1p*x1k(t));
fint2(t)=(((cb0-x2k)*uk/V)-k2p*x2k(t)+k1p*x1k(t));
x1k1=x1k+int(fint1,t,0,1);
x2k1=x1k+int(fint2,t,0,1);

You need to define all the variables numerically to get a numeric result. Your numeric variables must either be defined after the syms call, or be omitted from the syms call.

For an extended discussion of symbolic variables, see: Symbolic Computations in MATLAB (link).

[ojonugwa adukwu]

Great. I give it a try again