how to use fsolve with more equation

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chirag patel
chirag patel 2019-9-21
评论： Walter Roberson 2019-9-23
function F = fullfun(S_c,S_d,Ru,T,mu_s0,mu_w0,F,lambda_0,alpha,C_c,C_d,V_cp,r_am,r_cm,b_d,sigma_d,sigma_c,N_cp,h_r,sigma)
F = [T_s+(4*10^(-6)*S_d^(2))-(4*10^(-5)*S_d)-0.96;
T_w+(4*10^(-5)*S_c^(2))+(1.9*10^(-2)*S_c)-11.2;
L_s-(min(2*10^(-12)*S_d^(2)-3*10^(-10)*S_d+...
6*10^(-8),2*10^(-12)*S_c^(2)-3*10^(-10)*S_c+6*10^(-8)));
L_w-(5*10^(-4)*S_c^(-0.416));
mu_sc-(mu_s0+Ru*T*log(S_c/1000));
mu_sd-(mu_s0+Ru*T*log(S_d/1000));
mu_wc-(mu_w0+Ru*T*log((1000-S_c)/1000));
mu_wd-(mu_w0+Ru*T*log((1000-S_d)/1000));
E_m-(T_s/F*(mu_sc-mu_sd)+T_w/F*(mu_wc-mu_wd));
E_am-E_m;
E_cm-E_m;
lambda_c-lambda_0+alpha*sqrt(C_c);
lambda_d-lambda_0+alpha*sqrt(C_d);
lambda_r-((lambda_c + lambda_d)/2);
C_r-((C_c+C_d)/2);
k-(lambda_r * C_r);
I-((V_cp-E_am-E_cm)/(r_am+r_cm+b_d/(sigma_d*lambda_d*C_d)+(b_c/(sigma_c*lambda_c*C_c))+...
r_cm/N_cp+2*h_r/(sigma*k*N_cp)));
J_s-(T_s*I/F - L_s*(C_c-C_d));
J_w-(T_w*I/F + L_w*Ru*T*(C_c-C_d)*10^(-5)*2);

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回答（2 个）

Walter Roberson
Walter Roberson 2019-9-21
Bundle all of the variables into a single vector for the purposes of fsolve. You can unbundle them inside the function.
vars20init = vector of 20 initial values
sol = fsolve(@fullfun, vars20init)
function result = fullfun(vars20)
tcell = num2cell(vars20);
[S_c,S_d,Ru,T,mu_s0,mu_w0,F,lambda_0,alpha,C_c,C_d,V_cp,r_am,r_cm,b_d,sigma_d,sigma_c,N_cp,h_r,sigma] = tcell{:};
result = [T_s+(4*10^(-6)*S_d^(2))-(4*10^(-5)*S_d)-0.96;
T_w+(4*10^(-5)*S_c^(2))+(1.9*10^(-2)*S_c)-11.2;
L_s-(min(2*10^(-12)*S_d^(2)-3*10^(-10)*S_d+...
6*10^(-8),2*10^(-12)*S_c^(2)-3*10^(-10)*S_c+6*10^(-8)));
L_w-(5*10^(-4)*S_c^(-0.416));
mu_sc-(mu_s0+Ru*T*log(S_c/1000));
mu_sd-(mu_s0+Ru*T*log(S_d/1000));
mu_wc-(mu_w0+Ru*T*log((1000-S_c)/1000));
mu_wd-(mu_w0+Ru*T*log((1000-S_d)/1000));
E_m-(T_s/F*(mu_sc-mu_sd)+T_w/F*(mu_wc-mu_wd));
E_am-E_m;
E_cm-E_m;
lambda_c-lambda_0+alpha*sqrt(C_c);
lambda_d-lambda_0+alpha*sqrt(C_d);
lambda_r-((lambda_c + lambda_d)/2);
C_r-((C_c+C_d)/2);
k-(lambda_r * C_r);
I-((V_cp-E_am-E_cm)/(r_am+r_cm+b_d/(sigma_d*lambda_d*C_d)+(b_c/(sigma_c*lambda_c*C_c))+...
r_cm/N_cp+2*h_r/(sigma*k*N_cp)));
J_s-(T_s*I/F - L_s*(C_c-C_d));
J_w-(T_w*I/F + L_w*Ru*T*(C_c-C_d)*10^(-5)*2);]
end
I notice you use F as both input and output. That is unlikely to be a good idea when you are calling fsolve with the function.
  2 个评论
chirag patel
chirag patel 2019-9-22
编辑：chirag patel 2019-9-22
in m main i have used this :
vars20init = [S_c,S_d,Ru,T,mu_s0,mu_w0,F,lambda_0,alpha,C_c,C_d,V_cp,r_am,r_cm,b_d,sigma_d,sigma_c,N_cp,h_r,sigma];
sol = fsolve(@fullfun, vars20init)
when i use I got following Error :
Unrecognized function or variable 'T_s'.
Error in fullfun (line 4)
result = [T_s+(4*10^(-6)*S_d^(2))-(4*10^(-5)*S_d)-0.96;
Error in fsolve (line 248)
fuser = feval(funfcn{3},x,varargin{:});
Error in main (line 14)
sol = fsolve(@fullfun, vars20init)
Caused by:
Failure in initial objective function evaluation. FSOLVE cannot continue.
Walter Roberson
Walter Roberson 2019-9-22
You use T_s in your function, but it is not a parameter to the function. Where do you want your code to find T_s from?

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chirag patel
chirag patel 2019-9-23
I understand your question and modify code as follows :
vars20init = [70,70,1.2875e+03,1.2875e+03,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
sol = fsolve(@fullfun, vars20init)
function result = fullfun(vars20)
tcell = num2cell(vars20);
[S_c,S_d,C_c,C_d,T_w,T_s,L_s,L_w,mu_sc,mu_sd,mu_wc,mu_wd,E_m,E_am,E_cm,lambda_c,lambda_d,lambda_r,k,C_r,I,J_s,J_w] = tcell{:};
result = [T_s+(4*10^(-6)*S_d^(2))-(4*10^(-5)*S_d)-0.96;
T_w+(4*10^(-5)*S_c^(2))+(1.9*10^(-2)*S_c)-11.2;
L_s-(min(2*10^(-12)*S_d^(2)-3*10^(-10)*S_d+...
6*10^(-8),2*10^(-12)*S_c^(2)-3*10^(-10)*S_c+6*10^(-8)));
L_w-(5*10^(-4)*S_c^(-0.416));
mu_sc-(-732*10^3+8.314*298.15*log(S_c/1000));
mu_sd-(-732*10^3+8.314*298.15*log(S_d/1000));
mu_wc-(-237*10^3+8.314*298.15*log((1000-S_c)/1000));
mu_wd-(-237*10^3+8.314*298.15*log((1000-S_d)/1000));
E_m-(T_s/96485*(mu_sc-mu_sd)+T_w/96485*(mu_wc-mu_wd));
E_am-E_m;
E_cm-E_m;
lambda_c-0.012639+2.444*10^-4*sqrt(C_c);
lambda_d-0.012639+2.444*10^-4*sqrt(C_d);
lambda_r-((lambda_c + lambda_d)/2);
C_r-((C_c+C_d)/2);
k-(lambda_r * C_r);
I-((0.56-E_am-E_cm)/(3.5*10^(-4)+3.5*10^(-4)+5*10^(-04)/(0.64*lambda_d*C_d)+(5*10^(-4)/(0.64*lambda_c*C_c))+...
3.5*10^(-4)/1+2*5*10^(-04)/(0.64*k*1)));
J_s-(T_s*I/96485 - L_s*(C_c-C_d));
J_w-(T_w*I/96485 + L_w*8.314*298.15*(C_c-C_d)*10^(-5)*2);];
end
run but got answer as follows :
Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm
instead.
> In fsolve (line 316)
In main (line 14)
Equation solved, solver stalled.
fsolve stopped because the relative size of the current step is less than the
value of the step size tolerance and the vector of function values
is near zero as measured by the value of the function tolerance.
<stopping criteria details>
sol =
1.0e+05 *
Columns 1 through 6
0.3139 - 0.0019i 0.8325 - 0.0078i 0.0086 + 0.0000i 0.0086 + 0.0000i -0.4001 + 0.0047i -0.2772 + 0.0052i
Columns 7 through 12
0.0000 - 0.0000i 0.0000 + 0.0000i -7.2346 - 0.0001i -7.2104 - 0.0002i -2.2854 + 0.0777i -2.2607 + 0.0776i
Columns 13 through 18
0.0172 - 0.0003i 0.0172 - 0.0003i 0.0172 - 0.0003i 0.0000 - 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i
Columns 19 through 23
-0.0000 - 0.0000i 0.0086 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i
>>
  3 个评论
显示 1更早的评论
chirag patel
chirag patel 2019-9-23
Atualyy i want to solve following using fsolve :
function [S_c,S_d,mdot_c,mdot_d,I,J_s,J_w,energy_kWhpm3,power]=algo(S_c,S_d,Ru,T,mu_s0,mu_w0,F,lambda_0,...
alpha,C_c,C_d,V_cp,r_am,r_cm,b_c,b_d,sigma_d,sigma_c,N_cp,h_r,sigma,dA,...
mdot_c,mdot_d,ndot_sc,ndot_sd,N,MW_s,MW_w,rho_w,A_cp,mdot_cin,mdot_din)
for i=1:N
T_s(i) = -4*10^(-6)*S_d(i)^(2)+4*10^(-5)*S_d(i)+0.96;
T_w(i) = -4*10^(-5)*S_c(i)^(2)-1.9*10^(-2)*S_c(i)+11.2;
L_s(i) = min(2*10^(-12)*S_d(i)^(2)-3*10^(-10)*S_d(i)+...
6*10^(-8),2*10^(-12)*S_c(i)^(2)-3*10^(-10)*S_c(i)+6*10^(-8));
L_s(i) = 2*10^(-12)*S_d(i)^(2)-3*10^(-10)*S_d(i)+6*10^(-8);
L_w(i) = 5*S_c(i)^(-0.416)*10^(-4);
mu_sc(i) = mu_s0+Ru*T*log(S_c(i)/1000); mu_sd(i) = mu_s0+Ru*T*log(S_d(i)/1000);
mu_wc(i) = mu_w0+Ru*T*log((1000-S_c(i))/1000); mu_wd(i) = mu_w0+Ru*T*log((1000-S_d(i))/1000);
E_m(i) = T_s(i)/F*(mu_sc(i)-mu_sd(i))+T_w(i)/F*(mu_wc(i)-mu_wd(i));
E_am(i) = E_m(i)/2; E_cm(i) = E_m(i)/2;
lambda_c = lambda_0-alpha*sqrt(C_c(i));
lambda_d = lambda_0-alpha*sqrt(C_d(i));
lambda_r = (lambda_c + lambda_d)/2; C_r = (C_c(i)+C_d(i))/2;
k = lambda_r * C_r;
I(i) = (V_cp-E_am(i)-E_cm(i))/(r_am(i)+r_cm(i)+b_d/(sigma_d*...
lambda_d*C_d(i))+(b_c/(sigma_c*lambda_c*C_c(i)))+...
r_cm(i)/N_cp+2*h_r/(sigma*k*N_cp));
J_s(i) = T_s(i)*I(i)/F - L_s(i)*(C_c(i)-C_d(i));
J_w(i) = T_w(i)*I(i)/F + L_w(i)*Ru*T*(C_c(i)-C_d(i))*10^(-5)*2;
ndot_sc(i+1) = ndot_sc(i) + dA*J_s(i);
ndot_sd(i+1) = ndot_sd(i) - dA*J_s(i);
mdot_c(i+1) = mdot_c(i)+(J_s(i)*dA*MW_s+J_w(i)*dA*MW_w);
mdot_d(i+1) = mdot_d(i)-(J_s(i)*dA*MW_s+J_w(i)*dA*MW_w);
S_c(i+1) = ndot_sc(i+1)*1000*MW_s/mdot_c(i+1);
S_d(i+1) = ndot_sd(i+1)*1000*MW_s/mdot_d(i+1);
rho_c(i+1) = (1000+S_c(i+1))/1000*rho_w; % S_c(i+1)/1000*rho_nacl+
rho_d(i+1) = (1000+S_d(i+1))/1000*rho_w; % S_d(i+1)/1000*rho_nacl+
C_c(i+1) = S_c(i+1)*rho_c(i+1)/(1000*MW_s);
C_d(i+1) = S_d(i+1)*rho_d(i+1)/(1000*MW_s);
end
Walter Roberson
Walter Roberson 2019-9-23
Okay, go ahead. Follow the same strategy as before: all inputs should go into a single vector, and when you get the vector output from the solver, break it up into meaningful variables. Inside the function to be solved, expect everything as a single input, and break the values out into meaningful variables (this is what the num2cell and {:} is for)

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