How can I pass a piecewise-defined function to Simulink?

I'm building a Simulink model in which I have to solve 3 coupled differential equations. In one of these, I need to use a function f(x) whose form isn't known: I just know its values at some points (the values of this function are written in a file produced by another program); that is, I have quite a big number of couples (x, y(x)). I wouldn't like to fit these points with a polynomial funtion and pass the coefficients valued to a 'polyval' block; on the contrary, I'd like to use a linear interpolation among the various points, because, in this case, it is probably way more faithful to the true behaviour of the function (suppose for instance that the function has some sharp edges: a polynomial would fit well those values only if it is a very high degree polynomial). I wrote down the code to perform this interpolation in MATLAB, but then I don't know how to pass this function to Simulink.

My code is the following:

    fopen(filename, 'r');
    formatSpec = '%f %f';
    sizeA = [Inf 2];
    A = fscanf(filename, formatSpec, sizeA);
    fclose(filename);

    y_p=A[:,2];
    x_p=A[:,1];
    syms x;

    if (x<x_p(1))
        f(x)=y_p(1)+(x-x_p(1))*((y_p(2)-y_p(1))/(x_p(2)-x_p(1)));

    elseif (x>x_p(length))
        f(x)=y_p(length(x_p))+(x-x_p(length(x_p)))*((y_p(length(x_p))-y_p(length(x_p)))/(x_p(length(x_p))-x_p(length(x_p)-1)));

    else
        for i=1:(length(x_p)-1)
            if ((x>x_p(i))&&(x<x_p(i+1)))
                f(x)=(y_p(i))+((y_p(i+1)-y_p(i))/(x_p(i+1)-x_p(i)))*(x-x_p(i));

            elseif (x==x_p(i))
                f(x)=y_p(i);
            end
        end

    end

Should I use the S-function block? The problem is, if I call this code through the S-function block in Simulink, I fear it's going to take too much time to open, copy the values in memory and close the file, resulting in a long simulation time. Is there a way I can manage to save "permanently" in memory the values read from the data file?

I obviously welcome other ideas!

Thanks in advance.

Answer 1

[Sebastian Castro]

Is your file changing during simulation, or can you just read it at the beginning of simulation?

If it's the latter, you can keep the code that loads the file and gives you the x_p and y_p vectors. If you want, you can put this in a Model Callback so it does it automatically as you open/simulate the model.

Then, you can use these vectors as the breakpoints and table data for a 1-D Lookup Table block. One of the available methods in the block is linear interpolation.

If you have to open, read, and close the file during simulation, that changes things. The easiest thing to do would be to use the same code above inside a MATLAB Function block. There are some more restrictions regarding that, but I won't get into them unless you think you have to resort to this approach (that is, if your file changes mid-simulation).

- Sebastian

[Filippo Bartolozzi]

Thanks, Sebastian! I'll try.