using fmincon to optimize function including simultaneous equations
显示 更早的评论
My optmization goal is equation (14) to maximize U cell
The code has 3 m.file(s)
1)
function [x,fval]=main
% 4 X's
x0=[0.207;0.00003288;0.592;0.004];
lb=[0.1656;0.000026304;0.4736;0.0032];
ub=[0.2484;0.000039456;0.7104;0.0048];
%linear constrain
A=[];B=[];
Aeq=[];Beq=[];
[x,fval]=fmincon(@objfunc,x0,A,B,Aeq,Beq,lb,ub,@confunc);
end
2)
function f=objfunc(x)
F=96485.4;a=0.051;b=0.663;R=8.3144;T=303;Va=0.000055;Vc=0.000055;XIn=0;
AcIn=1.56;OIn=0.3125;Am=0.0005;Fx=10;Yac=0.05;Kdec=0.000833;Ca=400;
Cc=500;Qa=0.0000225;Qc=0.0111;
q1=x(1)*exp((a*F*q3)/(R*T))*(q5*q7/(x(3)+q5)); %eq1
q2=-x(2)*(q6/(x(4)*q6))*exp(((b-1)*F*q4)/(R*T)); %eq2
0=Qa*(AcIn-q5)-(Am*q1); %eq3
0=(Qa*((XIn-q7)/Fx))+(Am*Yac*q1)-(Va*Kdec*q7); %eq4
0=Qc(OIn-q6)+q2*Am; %eq5
0=(3600*q8)-(8*F*q1);%eq6
0=(3600*q8)-(4*F*q2);%eq7 %
U0=0.77;dm=0.0001778;dcell=0.022;kaq=5;km=17;
f=U0-q3+q4-(((dm/km)+(dcell/kaq))*q8);
end
3)
function [c,ceq]=confunc(x)
F=96485.4;a=0.051;b=0.663;R=8.3144;T=303;Va=0.000055;Vc=0.000055;XIn=0;
AcIn=1.56;OIn=0.3125;Am=0.0005;Fx=10;Yac=0.05;Kdec=0.000833;Ca=400;
Cc=500;Qa=0.0000225;Qc=0.0111;
ceq=[Qa*(AcIn-q5)-(Am*q1);(Qa*((XIn-q7)/Fx))+(Am*Yac*q1)-(Va*Kdec*q7);Qc(OIn-q6)+q2*Am;(3600*q8)-(8*F*q1);(3600*q8)-(4*F*q2)];
c=[];
end
Can anyone enlighten me on what I might made wrong
2 个评论
John D'Errico
2020-3-5
Note that you cannot use fmincon to force the parameters to be integers. You seem to have indicated that in your problem statement, but it is not clear.
Husam Mahmoud
2020-3-5
回答（2 个）
These lines are illegal in Matlab. You cannot put a literal number like 0 on the left hand side of an '=', except when working with symbolic equations, which would not be appropriate here.
0=Qa*(AcIn-q5)-(Am*q1); %eq3
0=(Qa*((XIn-q7)/Fx))+(Am*Yac*q1)-(Va*Kdec*q7); %eq4
0=Qc(OIn-q6)+q2*Am; %eq5
0=(3600*q8)-(8*F*q1);%eq6
0=(3600*q8)-(4*F*q2);%eq7 %
If these are meant to represent equations that your solution must satisfy, they should go in confunc as additional equality constraints.
1 个评论
Husam Mahmoud
2020-3-5
编辑：Husam Mahmoud
2020-3-5
Walter Roberson
2020-3-5
1 个投票
You do not have simultaneous variables. You have a system of differential equations that are functions of time, but you are attempting to optimize as if the system was timeless.
You appear to working on chemical reactions. It might hypothetically make sense to optimize steady state, and it might hypothetically make sense to optimize over a limited time, but either way you would need to give time for the system to evolve with an ode solver, which you are not doing at all.
3 个评论
Husam Mahmoud
2020-3-5
Walter Roberson
2020-3-5
Is the idea that when you reach the steady state, the function stops changing, so its derivative becomes 0, so the left side of the differential equations become 0?
If so then you should probably use fsolve() on the system of expressions.
Husam Mahmoud
2020-3-5
编辑：Husam Mahmoud
2020-3-5
类别
在 帮助中心 和 File Exchange 中查找有关 Choose a Solver 的更多信息
产品
2020-3-4
2020-3-5
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
