MATLAB: Solving nonlinear system of equations with different variables

electricalequationsMATLABnonlinear

Hello

I would like to solve a nonlinear system of equations. Im new to matlab and therefore i dont have enough experience to get this problem solved by myself.

i have googled around a bit but unfortunately didnt got the hint that i needed. Therefore i write now here in this community.

I hope someone can help me.

Here is my problem:

function F = root2d(x)
F(1) = (R1*(C2+C3) + R2*(C1+C2) + R3*C3*(1-1 / ( R5 / (R4+R5))))-0.24792;
F(2) = (R1*R2*(C1*C2 + C1*C3 +C2*C3)+R1*R3*C2*C3 +R2*R3*(C1+C2)*C3*(1-1 / ( R5 / (R4+R5)) ))-0.7807;
F(3) = (R1*C1*R2*C2*R3*C3)-0.0948;
F(4) = ((R1*C1*R2*C2*R3*C3)/ ( R5 / (R4+R5)) )-0.948;
end

I would like to find solutions for

R1, R2, R3, C1, C2, C3

R4 and R5 are known. R4 is 1 and R5 is 9.

How do i have to solve this system?

I have tried it that way:

fun = @root2d;
x0 = [1,1,1,1];
x = fsolve(fun,x0)
function F = root2d(x)
F(1) = (R1*(C2+C3) + R2*(C1+C2) + R3*C3*(1-1 / ( R5 / (R4+R5))))-0.24792;
F(2) = (R1*R2*(C1*C2 + C1*C3 +C2*C3)+R1*R3*C2*C3 +R2*R3*(C1+C2)*C3*(1-1 / ( R5 / (R4+R5)) ))-0.7807;
F(3) = (R1*C1*R2*C2*R3*C3)-0.0948;
F(4) = ((R1*C1*R2*C2*R3*C3)/ ( R5 / (R4+R5)) )-0.948;
end

but it tells me that it was not able to find any solutions.

Thanks in advance.

Regards

Best Answer

You have 4 equations that you want to solve for 6 variables. There will either be no solutions or an infinite number of solutions.

In your case, there are no solutions.

If you solve the first three equations for R1, R2, R3, you can do that by expressing R2 as the roots of a degree 6 polynomial, and then expressing R1 and R3 in terms of that; for example,

R1 = (4740 - 50000*C1^3*R2^3 + (-100000*C2*R2^3 + 12396*R2^2)*C1^2 + (-50000*C2^2*R2^3 + 12396*C2*R2^2 - 39035*R2)*C1)*`/`(50000*C1*C2^2*R2^2)

However, when you then substitute the R1, R2, R3 solutions into the fourth equation, you get out -316/375 instead of an equation in multiple variables. Your equations are rank deficient and inconsistent.

Related Solutions

MATLAB: What could be the issue if a global variable gets an error “Undefined function or variable ‘F_FEED’ ” when called from a function. The global variable is defined in the file from which the function is called.

Maybe you mean

function main
global F_FEED T0 P0 WEIGHT_cat R Ua F_G0 F_H2O0 F_N20 F_A0 F_AC0 F_AA0 F_FA0 F_T0;
F_FEED = 100;           %TOTAL FLOWRATE OF THE FEED (mol/s)
T0 = 650;          %INLET TEMPERATURE OF THE REACTOR (K)
P0 = 303975;    %INLET PRESSURE OF THE REACTOR (Pa)
WEIGHT_cat = 100;       %CATALYST WEIGHT (kg)
R = ToBeSpecified;       
Ua = ToBeSpecified;
Feed = zeros(8,1);
Feed(1) = 0.014*F_FEED;           %INLET FLOWRATE OF G (mol/s)
Feed(2) = 0.634*F_FEED;           %INLET FLOWRATE OF H2O (mol/s)
Feed(3) = 0.352*F_FEED;           %INLET FLOWRATE OF N2 (mol/s)
Feed(8) = T0; 
F_G0 = Feed(1);                 
F_H2O0 = Feed(2);              
F_N20 = Feed(3);                
F_A0 = Feed(4);               
F_AC0 = Feed(5);                
F_AA0 = Feed(6);                
F_FA0= Feed(7);                
F_T0 = F_FEED;
[W,F] = ode45(@Reactors , [0 WEIGHT_cat], Feed);
end
function dFdW = Reactors(t,F)
global F_FEED T0 P0 WEIGHT_cat R Ua F_G0 F_H2O0 F_N20 F_A0 F_AC0 F_AA0 F_FA0 F_T0;
dFdW = zeros(8,1);
%dFdW = [r_G]
%       [r_H2O]
%       [r_N2]
%       [r_O2]
%       [r_A]
%       [r_AC]
%       [r_AA]
%       [r_FA]
%       [T]     Temperature
%reaction
Hf_G = -577.9;                    %Heat of formation: G (kJ/mol)
Hf_H2O = -241.818;                %Heat of formation: H2O (kJ/mol)
Hf_N2 = 0;                        %Heat of formation: N2 (kJ/mol)
Hf_A = -65;                       %Heat of formation: A (kJ/mol)
Hf_AC = -370.06;                  %Heat of formation: AC (kJ/mol)
Hf_AA = -166.1;                   %Heat of formation: AA (kJ/mol)
Hf_FA = -108.6;                   %Heat of formation: FA (kJ/mol)
Cp_G = -35.3267443 + 0.645106658*F(8) - 0.00061741*F(8)^2 + 0.000000239229*F(8)^3;               %provide integrated form
Cp_H2O = 32.95266198 - 0.00391977*F(8) + 0.0000222314*F(8)^2 - 0.0000000104953*F(8)^3;
Cp_N2 = 28.883 -0.00157*F(8)+ 0.00000808*F(8)^2 -0.000000002871*F(8)^3;
Cp_A = -14.9617445 + 0.373240705*F(8) - 0.00034559*F(8)^2 + 0.000000129748*F(8)^3;
Cp_AC = -11.7479865 + 0.402868987*F(8) - 0.00031782*F(8)^2 + 0.000000109142*F(8)^3;
Cp_AA = -5.82005966 + 0.23787576*F(8) - 0.00017362*F(8)^2 + 0.0000000543415*F(8)^3;
Cp_FA = 19.10519375 + 0.048680586*F(8) + 0.00000878405*F(8)^2 - 0.0000000150776*F(8)^3;
integraldeltaCp_rxn_1 = 2*(32.95266198*(F(8)-298) - 0.5*0.00391977*(F(8)^2-298^2) + (1/3)*0.0000222314*(F(8)^3-298^3) - (1/4)*0.0000000104953*(F(8)^4-298^4)) + (-14.9617445*(F(8)-298) + 0.5*0.373240705*(F(8)^2-298^2) - (1/3)*0.00034559*(F(8)^3-298^3) + (1/4)*0.000000129748*(F(8)^4-298^4)) - ((-35.3267443*(F(8)-298) + 0.5*0.645106658*(F(8)^2-298^2) - (1/3)*0.00061741*(F(8)^3-298^3) + (1/4)*0.000000239229*(F(8)^4-298^4))); 
integraldeltaCp_rxn_2 = (32.95266198*(F(8)-298) - 0.5*0.00391977*(F(8)^2-298^2) + (1/3)*0.0000222314*(F(8)^3-298^3) - (1/4)*0.0000000104953*(F(8)^4-298^4) + (-11.7479865*(F(8)-298) + 0.5*0.402868987*(F(8)^2-298^2) - (1/3)*0.00031782*(F(8)^3-298^3) + (1/4)*0.000000109142*(F(8)^4-298^4)) - (32.95266198*(F(8)-298) - 0.5*0.00391977*(F(8)^2-298^2) + (1/3)*0.0000222314*(F(8)^3-298^3) - (1/4)*0.0000000104953*(F(8)^4-298^4)));
integraldeltaCp_rxn_3 = (32.95266198*(F(8)-298) - 0.5*0.00391977*(F(8)^2-298^2) + (1/3)*0.0000222314*(F(8)^3-298^3) - (1/4)*0.0000000104953*(F(8)^4-298^4) + (19.10519375*(F(8)-298) + 0.5*0.048680586*(F(8)^2-298^2) + (1/3)*0.00000878405*(F(8)^3-298^3) - (1/4)*0.0000000150776*(F(8)^4-298^4)) + (-5.82005966*(F(8)-298) + 0.5*0.23787576*(F(8)^2-298^2) - (1/3)*0.00017362*(F(8)^3-298^3) + (1/4)*0.0000000543415*(F(8)^4-298^4)) - (-35.3267443*(F(8)-298) + 0.5*0.645106658*(F(8)^2-298^2) - (1/3)*0.00061741*(F(8)^3-298^3) + (1/4)*0.000000239229*(F(8)^4-298^4)));
integraldeltaCp_rxn_4 = (32.95266198*(F(8)-298) - 0.5*0.00391977*(F(8)^2-298^2) + (1/3)*0.0000222314*(F(8)^3-298^3) - (1/4)*0.0000000104953*(F(8)^4-298^4) + (19.10519375*(F(8)-298) + 0.5*0.048680586*(F(8)^2-298^2) + (1/3)*0.00000878405*(F(8)^3-298^3) - (1/4)*0.0000000150776*(F(8)^4-298^4)) + (-5.82005966*(F(8)-298) + 0.5*0.23787576*(F(8)^2-298^2) - (1/3)*0.00017362*(F(8)^3-298^3) + (1/4)*0.0000000543415*(F(8)^4-298^4)) - (-35.3267443*(F(8)-298) + 0.5*0.645106658*(F(8)^2-298^2) - (1/3)*0.00061741*(F(8)^3-298^3) + (1/4)*0.000000239229*(F(8)^4-298^4)));
Hrxn_1 =  2*Hf_H2O + Hf_A - Hf_G + (integraldeltaCp_rxn_1);               %Heat of reaction: reaction 1
Hrxn_2 =  2*Hf_H2O + Hf_AC - Hf_G + (integraldeltaCp_rxn_2);              %Heat of reaction: reaction 2
Hrxn_3 =  Hf_H2O + Hf_AA + Hf_FA - Hf_G + (integraldeltaCp_rxn_3);        %Heat of reaction: reaction 3
Hrxn_4 =  Hf_H2O + Hf_AA + Hf_FA - Hf_G + (integraldeltaCp_rxn_4);        %Heat of reaction: reaction 4
%INITIAL CONCENTRATIONS  
VOLUMETRICFLOWRATEin = F_FEED*R*T0;                         %Initial volumetric flowrate into the reactor (m^3/s) (assuming ideal gas in)   NEGLECTING P/P0 to start...
C_G0 =      F_G0/VOLUMETRICFLOWRATEin;                      %Inital concentration of G
C_H2O0 =    F_H2O0/VOLUMETRICFLOWRATEin;                    %Inital concentration of H2O
C_N20 =     F_N20/VOLUMETRICFLOWRATEin;                     %Inital concentration of N2
C_A0 =  0;                                                  %Outlet concentration of A

C_AC0 = 0;                                                  %Outlet concentration of AC

C_AA0 = 0;                                                  %Outlet concentration of AA

C_FA0 = 0;                                                  %Outlet concentration of FA

C_T0 =      F_FEED/VOLUMETRICFLOWRATEin;                    %Initial total concentration
%FINAL Concentrations
F_T = F(1) + F(2) + F(3) + F(4) + F(5) + F(6) + F(7);       
C_G =   C_T0*(F(1)/F_T)*(T0/F(8));    %Outlet concentration of G              
C_H2O = C_T0*(F(2)/F_T)*(T0/F(8));      %Outlet concentration of H2O
C_N2 =  C_T0*(F(3)/F_T)*(T0/F(8));      %Outlet concentration of N2              NEGLECTING P/P0 to start...
C_A =   C_T0*(F(4)/F_T)*(T0/F(8));    %Outlet concentration of A
C_AC =  C_T0*(F(5)/F_T)*(T0/F(8));      %Outlet concentration of AC
C_AA =  C_T0*(F(6)/F_T)*(T0/F(8));      %Outlet concentration of AA
C_FA =  C_T0*(F(7)/F_T)*(T0/F(8));      %Outlet concentration of FA
%k-VALUES 
k1 = 23.3244*exp(-45007.1/(R*F(8)));           %Reaction rate constant k1 (m^3/kgcat*s)
k2 = 2528.8*exp(-79244.89/(R*F(8)));           %Reaction rate constant k2 (m^3/kgcat*s)
k3 = 2150.595*exp(-73702.78/(R*F(8)));         %Reaction rate constant k3 (m^3/kgcat*s)
k4 = 0.146768*exp(-24596.97/(R*F(8)));         %Reaction rate constant k4 (m^3/kgcat*s)
%reaction rates
r_1 = -k1*C_G;                                     %Rate of reaction 1
r_2 = -k2*C_G;                                     %Rate of reaction 2
r_3 = -k3*C_G;                                     %Rate of reaction 3
r_4 = -k4*C_G;                                     %Rate of reaction 4
r_G = -(k1+k2+k3+k4)*C_G;                  %Rate of formation of G
r_N2 = 0;                                  %Rate of formation of N2
r_H2O = k1*(C_G)^2+(k3+k4)*G_G;            %Rate of formation of H2O
r_A = k1*C_G;                              %Rate of formation of A
r_AC = k2*C_G;                             %Rate of formation of AC
r_AA = (k3+k4)*C_G;                        %Rate of formation of AA
r_FA = (k3+k4)*C_G;                        %Rate of formation of FA
%Differential Equations to Solve
dFdW(1) = (r_G);
dFdW(2) = (r_H2O);
dFdW(3) = (r_N2);
dFdW(4) = (r_A);
dFdW(5) = (r_AC);
dFdW(6) = (r_AA);
dFdW(7) = (r_FA);
dFdW(8) = (Ua(Ta-T0)+(-r_1)*(-Hrxn_1)+(-r_2)*(-Hrxn_2)+(-r_3)*(-Hrxn_3)+(-r_4)*(-Hrxn_4))/(F(1)*Cp_G + F(2)*Cp_H2O + F(3)*Cp_N2 + F(4)*Cp_A + F(5)*Cp_AC + F(6)*Cp_AA + F(7)*Cp_FA); %dTdW from pg 545 in Fogler;   
end

MATLAB: How to find coefficients of a polynomial , Given values of the function

t = [1; 2; 3; 4; 5];
y = [2.3; 4.8; 8.9; 16.9; 41.0]
M=[ones(5,1), t, t.^2, -y.*t, -y.*t.^2];
x=M\y;
c0=x(1); c1=x(2); c2=x(3); d1=x(4); d2=x(5);
% Check
f=@(t) (c0+c1*t+c2*t.^2)./(1+d1*t+d2*t.^2)
f(t)

Best Answer

Related Solutions

MATLAB: What could be the issue if a global variable gets an error “Undefined function or variable ‘F_FEED’ ” when called from a function. The global variable is defined in the file from which the function is called.

MATLAB: How to find coefficients of a polynomial , Given values of the function

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