Problem with system of non linear equation

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Giuseppe 2014-10-25

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https://ww2.mathworks.cn/matlabcentral/answers/160065-problem-with-system-of-non-linear-equation

回答： Giuseppe 2014-10-26

Hi Guys, i'm Giuseppe and i would have some advice in order to solve the problem of my code.

i need to create a function that solve this stupid equation system:

where all the terms are known, except x, y and z that represent the solutions that i'm trying to calculate.

the function should be able to accept all well-known terms, and give out x, y, z.

i tried to use fsolve, but it doesn't work..

can someone help me? thanks in Advance!

greetings, Giuseppe

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Zoltán Csáti 2014-10-25

What do you mean under fsolve does not work? Doesn't it give you the solution or you can not use it?

Giuseppe 2014-10-26

编辑：Giuseppe 2014-10-26

在 MATLAB Online 中打开

Basically, i have two problems:

1) Using fsolve, i'm not able to give all the constant terms as input parameter! I tried to read about it on the Help page: there is a specific topic - how to pass extra parameters, but something should be wrong. Matlab say: "Error using ==> fminunc at 301 User supplied objective function must return a scalar value." (Sincerely, i'm not sure if that problems is related to "fisical code" that i implemented or is just a syntax error..)

2) So, firstly, i decide to try introducing all the constants in the body of function created. here, when i tried to solve it, it seemed to work but, when i try to change some values of constants, i obtain messages like: or Equation Solved (and i think it's ok) or Equation Solved, fvsolve stalled; or Solver stopped prematurely -fsolve stopped because it exceeded the function evaluation limit, options.MaxFunEvals = 500 (the selected value).

this is the code that i implemented :

function [funz] =solver(x) %Equilibrium Calculation Uf=0.65; % T_cell=600; %°C T_c=T_cell+273.15; %[K]

[K_ref K_wgs]=C_equilibrio(T_c); %NOTE: this is an external function..

%Mass flow - Fuel da DESIGN POINT CONFIG.xls Gfuel=100; %[mol/s] Biogas Flow rate

%Composizione % gas iniziale CH4=0.60; % H2=0; % CO2=0.4; % CO=0; % H2O=0; %

%Composizione molare gas iniziale m_CH4=CH4*Gfuel; %[mol/s] m_H2=H2*Gfuel; %[mol/s] m_H2Of=H2O*Gfuel; %[mol/s] m_CO2=CO2*Gfuel; %[mol/s] m_CO=CO*Gfuel; %[mol/s]

%SC - Steam to Carbon ratio SC=2.5; m_H2O=SC*m_CH4; %[mol/s]

n_tot=m_CH4+m_H2+m_H2O+m_CO2+m_CO; %[mol/s]

p_cell=1; %[bar];

funz=[K_ref-(p_cell^2)*((((m_CO+x(1)-x(2))/(n_tot+2*x(1)))*((m_H2+3*x(1)+x(2)-x(3))/(n_tot+2*x(1)))^3)/(((m_CH4-x(1))/(n_tot+2*x(1)))*((m_H2O-x(1)-x(2)+x(3))/(n_tot+2*x(1)))));

    K_wgs-(((m_H2+3*x(1)+x(2)-x(3))/(n_tot+2*x(1)))*((m_CO2+x(2))/(n_tot+2*x(1))))/(((m_CO+x(1)-x(2))/(n_tot+2*x(1)))*((m_H2O-x(1)-x(2)+x(3))/(n_tot+2*x(1))));
    x(3)-Uf*(3*x(1)+x(2)+m_H2)];

If you need other informations, please ask me and i'll answer back as soon is possilbe!"

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