How can I write a code that works like MS Excel "Goal seak"?

I'm working on a thermodynamic problem, and i have to find a pressure value that solves:

Value of η and are known, are function of that is the value i'm looking for.

in particular:

s9_1s = s8 ; %known
x9_1 = 0.98;
h9_1s = XSteam('h_ps',p9_1,s9_1s); % as you can see h values that are functions in wich p9_1 (that is the objective) is a parameter.
x9_1s = XSteam('x_ps',p9_1,s9_1s);
h9_1 = XSteam('h_px',p9_1,x9_1);

The problem is that i can't write in a explicit form, because of the function XSteam, so i'm not able to use Fsolve or similar.

Can anyone give me some help?

Answer 1

[Alan Stevens]

What about fzero? Your code could be structured like

p90 = ... % put initial guess here
p9_1 = fzero(@(p) fn(p, XSteam), p90);

function Z = fn(p9_1, XSteam)

        s9_1s = s8 ; %known
        x9_1 = 0.98;
        eta = ...   
        h8 = ...
        h9_1s = XSteam('h_ps',p9_1,s9_1s); 
        x9_1s = XSteam('x_ps',p9_1,s9_1s);
        h9_1 = XSteam('h_px',p9_1,x9_1);
        
        Z = (h8 - h9_1)/(h8 - h9_1s) - eta;

end

View doc fzero for details on exact syntax etc of fzero.

[Luca Vergani]

I don't uderstand, even reading the doc, how to use fzero, because the dipendence h(p) trough XSteam is not explicitable.

In order to make the problem more clear, I've wrote an if cycle that does the same thing I want to to with fzero of similar:

p9_1_vect = [p_cond:1e-03:p8];
    err1 = [];
    s9_1s = s8 ;
    x9_1 = 0.98;

    for (ii = 1:length(p9_1_vect))
        p9_1 = p9_1_vect(ii);
        h9_1s = XSteam('h_ps',p9_1,s9_1s);
        x9_1s = XSteam('x_ps',p9_1,s9_1s);
        h9_1 = XSteam('h_px',p9_1,x9_1);
        err1(ii) = abs((h8 - h9_1) / (h8 - h9_1s) - eta_ST_98);
    end

    [e1, index1] = min(err1);
    p9_1 = p9_1_vect(index1);
    h9_1s = XSteam('h_ps',p9_1,s9_1s);
    x9_1s = XSteam('x_ps',p9_1,s9_1s);
    h9_1 = XSteam('h_px',p9_1,x9_1);
    s9_1 = XSteam('s_ph',p9_1,h9_1);

The code works, but is far to be good because is not obtimazed and takes way too much time to work.

I'm basically searching for some built-in function that could make that more efficient...

[Alan Stevens]

The correct syntax for calling my fn function from fzero is

p9_1 = fzero(@(p) fn(p,@XSteam,s8), p90);

and the function line should be

function Z = fn(p9_1, XSteam,s8)

[Luca Vergani]

It finally works!!

Thanks thanks thanks both for the patience and for the answer.

Best regards.

LV