how to perform excel goal seek in Matlab?

I have a equation to find a missing variable 'If'

all the other values are fixed/known other than that of another variable 'Ib', to which i assign an initial value and i want to find the actual/optimum value using goal seek.

the conditions are

vap = 250-tb;

h = vap - If -Ib; %h = 0 (this will be the target value in goal seek)(vap = If+Ib);

h = vap - If -Ib;

solving for (goalseek)h = y (where y = 0), (varying)Ib = 39.32214

which gives If = 35.67756

Answer 1

[Joe Vinciguerra]

Simply rearrange the equations to solve for I_b when h=0, then calculate teh resulting I_f.

EC_n = 1.7;
EC_in = 1;
tbal = 175;
EC_f = 0.4;
EC_b = 6; 
% I_b = 20; %(initialisation)
R = 0.2;
DP = 0.1;
% I_f = ((EC_n.*(tbal+I_b+DP+R))-(EC_in.*tbal)-(EC_b.*I_b))/(EC_f-EC_n);
% y = 0;
% vap = 250-tbal;
% h = vap - I_f -I_b;
% solving for (goalseek )h = y (where y = 0), (varying)I_b = 39.32214 
% which gives I_f = 35.67756

% rearrange the equations to solve for I_b:
% h = vap - I_f -I_b;
% 0 = vap - I_f -I_b;
% 0 = 250 - tbal - (EC_n*tbal + EC_n*I_b + EC_n*DP + EC_n*R - EC_in*tbal - EC_b*I_b) / (EC_f-EC_n) - I_b;
% I_b*EC_f - I_b*EC_n + EC_n*tbal + EC_n*I_b + EC_n*DP + EC_n*R - EC_in*tbal - EC_b*I_b = (250 - tbal)*(EC_f-EC_n);
% I_b*EC_f - I_b*EC_n + EC_n*I_b - EC_b*I_b = (250 - tbal)*(EC_f-EC_n) - EC_n*tbal - EC_n*DP - EC_n*R + EC_in*tbal;
% I_b(EC_f - EC_n + EC_n - EC_b) = (250 - tbal)*(EC_f-EC_n) - EC_n*tbal - EC_n*DP - EC_n*R + EC_in*tbal 
I_b = ((250 - tbal)*(EC_f-EC_n) - EC_n*tbal - EC_n*DP - EC_n*R + EC_in*tbal )/(EC_f - EC_n + EC_n - EC_b)

I_b = 39.3768

% solve for I_f:
I_f = ((EC_n.*(tbal+I_b+DP+R))-(EC_in.*tbal)-(EC_b.*I_b))/(EC_f-EC_n

I_f = 35.6232

[Joe Vinciguerra]

That doesn't matter for the problem that was presented.

% a bunch of random input data:
n = 10;
EC_n = [1.7 * 2*rand(1, n)];
EC_in = [1 * 2*rand(1, n)];
tbal = [175 * 2*rand(1, n)];
EC_f = [0.4 * 2*rand(1, n)];
EC_b = [6 * 2*rand(1, n)]; 
R = [0.2 * 2*rand(1, n)];
DP = [0.1 * 2*rand(1, n)];

% solve for I_b and I_f:
for i = 1:n
    I_b(i) = ((250 - tbal(i))*(EC_f(i)-EC_n(i)) - EC_n(i)*tbal(i)- EC_n(i)*DP(i) - EC_n(i)*R(i) + EC_in(i)*tbal(i))/(EC_f(i) - EC_n(i) + EC_n(i) - EC_b(i));
    I_f(i) = ((EC_n(i).*(tbal(i)+I_b(i)+DP(i)+R(i)))-(EC_in(i).*tbal(i))-(EC_b(i).*I_b(i)))/(EC_f(i)-EC_n(i));
end

Answer 2

[Cris LaPierre]

If you have the optimization toolbox, I suggest using the Optimization Live Editor Task (Problem based) to solve this. You could do this programatically, but this allows you to use a user interface to set up the problem. If you are new to this, it can be a bit overwhelming at first, so I'll walk you through it.

Begin by opening a live script and defining all your constants.

EC_n = 1.7;
EC_in = 1;
tbal = 175;
EC_f = 0.4;
EC_b = 6; 
R = 0.2;
DP = 0.1;
vap = 250-tbal;

Then, add the Optimize Live Editor Task and select Problem Based. Once that opens, add I_b and I_f as optimization variables (these are the ones whose values change).

For Define problem, select Solve equations.

Enter 2 equations:

1. the equation for h: vap-I_f-I_b = 0
2. and the equation for I_f: I_f = (EC_n.*(tbal+I_b+DP+R)-EC_in.*tbal-EC_b.*I_b)/(EC_f-EC_n)

Finally, click Solve problem. The results are captured in the structure solution, and are also displayed in the task output.

EquationProblem :

Solve for:

I_b, I_f

equation1:

-I_f - I_b == -75

equation2:

I_f - 3.3077*I_b == -94.6231

Solving problem using lsqlin.

solution = struct with fields:

I_b: 39.3768

I_f: 35.6232

reasonSolverStopped =

EquationSolved

objectiveValue = struct with fields:

equation1: 0

equation2: -1.4211e-14

Once solved, you can export the live task to code, which looks like this.

% Create optimization variables
I_b6 = optimvar("I_b");
I_f6 = optimvar("I_f");

% Set initial starting point for the solver
initialPoint6.I_b = repmat(20,size(I_b6));
initialPoint6.I_f = zeros(size(I_f6));

% Create problem
problem = eqnproblem;

% Define problem equations
problem.Equations.equation1 = vap - I_f6 -I_b6 == 0;
problem.Equations.equation2 = I_f6 == (EC_n.*(tbal+I_b6+DP+R)-EC_in.*tbal-EC_b.*I_b6)/(EC_f-EC_n);

% Display problem information
show(problem);

  EquationProblem : 

	Solve for:
       I_b, I_f


 equation1:
       -I_f - I_b == -75

 equation2:
       I_f - 3.3077*I_b == -94.6231

% Solve problem
[solution,objectiveValue,reasonSolverStopped] = solve(problem,initialPoint6);

Solving problem using lsqlin.

% Display results
solution

solution = struct with fields:
    I_b: 39.3768
    I_f: 35.6232

reasonSolverStopped

reasonSolverStopped = 
    EquationSolved

objectiveValue

objectiveValue = struct with fields:
    equation1: 0
    equation2: -1.4211e-14

% Clear variables
clearvars I_b6 I_f6 initialPoint6 reasonSolverStopped objectiveValue

And you can access the final values like this:

solution.I_b

ans = 39.3768

solution.I_f

ans = 35.6232

[Harsh Harsh]

Thank you for this answer, but the issue is that in my model, the constants are actually variables.

EC_n , EC_in , tbal , EC_f , EC_b , R , DP , vap keep changing every iteration

[Cris LaPierre]

That's not a problem. Now you know what to do. Any variables that change must be defined as an optimization variable. I think the rest of the problem stays the same.

As an aside, it was my observation that, when using goal seek in Excel, none of the other variables actually changed value, so the results I came up with in MATLAB matched the results in Excel.