# Optimisation problem in matlab

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wallflower on 21 Jun 2021
Commented: Sergey Kasyanov on 13 Jul 2022
Hello guys,
So I have this scatte plot in the form of a measured impedance according to frequency Z(f), and I have an RL ladder circuit seen in the following figure
.
I need some help in writing an optimisation problem that will allow me to get the values of the parameters R_i L_i that will eventually give an equivalent impedance of the RL ladder similar to the one measured- Z(f) -.
Wallflower
##### 2 CommentsShowHide 1 older comment
wallflower on 21 Jun 2021
It is not a homework assignment. I am trying to reproduce a methology I've seen in a scientific paper.

Sergey Kasyanov on 21 Jun 2021
Edited: Torsten on 12 Jul 2022
Hello!
Try that:
% tune only next 2 lines
L = 5;% steps in ladder
Z_max = 1e2;% max Z for one R or Xl
% goal Z(w)
% w0 - array with measured angular frequences
% Z0 - array with measured impedances
% R0 - Rs_1.txt
% L0 - 2*Self_Energy_1.txt
w0 = (2.*pi.*[[1e-3,50,500],1e3:2e3:500e3])';
% Start inserted to make code work
R0 = rand(size(w0));
L0 = rand(size(w0));
% End inserted to make code work
Z0 = R0(:,1) + 1i*w0.*L0(:,1);
w0 = reshape(w0, 1, []);
Z0 = reshape(Z0, 1, []);
R = sym('R', [1,L+1]);
L = sym('L', [1,length(R)]);
w = sym('w');
par = @(a, b) 1/(1/a + 1/b);
h1 = @(a, i) R(i) + par(a, 1i*w*L(i));
Z = R(end);
for i = (length(R)-1):-1:1
Z = h1(Z, i);
end
% get lambda function for optimization
fun1 = matlabFunction(Z);
% do not look at that code
s = 'fun2 = @(vals, w) fun1(';
for i = 1:(length(R)*2 - 1)
s = [s, sprintf('vals(%i), ', i)];
end
s = [s, 'w);'];
eval(s);
% create optimization function
fun3 = @(vals) sum(abs(fun2(vals, w0) - Z0).^2);
% number of variables
N = length(symvar(Z)) - 1;
%the better way is to use more powerfull algorithms such as genetic algoritms which can stands
%against a huge amount of local min. There are a lot of algorithms that
%realized in matlab toolboxes. Try!
options = optimoptions('ga', 'Display', 'iter', 'PopulationSize', N*200, 'MaxGenerations', N*200);
res = ga(fun3, N, [], [], [], [], zeros(1, N), Z_max*[ones(1,floor(N/2))/2/pi, ones(1, ceil(N/2))], [], options);
Single objective optimization: 11 Variable(s) Options: CreationFcn: @gacreationuniform CrossoverFcn: @crossoverscattered SelectionFcn: @selectionstochunif MutationFcn: @mutationadaptfeasible Best Mean Stall Generation Func-count f(x) f(x) Generations 1 4400 2.953e+14 2.953e+14 0 2 6490 2.953e+14 2.953e+14 0 3 8580 2.953e+14 2.953e+14 0 4 10670 2.953e+14 2.953e+14 0 5 12760 2.953e+14 2.953e+14 0 6 14850 2.953e+14 2.953e+14 0 7 16940 2.953e+14 2.953e+14 0 8 19030 2.953e+14 2.953e+14 0 9 21120 2.953e+14 2.953e+14 0 10 23210 2.953e+14 2.953e+14 0 11 25300 2.953e+14 2.953e+14 0 12 27390 2.953e+14 2.953e+14 0 13 29480 2.953e+14 2.953e+14 0 14 31570 2.953e+14 2.953e+14 0 15 33660 2.953e+14 2.953e+14 0 16 35750 2.953e+14 2.953e+14 0 17 37840 2.953e+14 2.953e+14 0 18 39930 2.953e+14 2.953e+14 0 19 42020 2.953e+14 2.953e+14 0 20 44110 2.953e+14 2.953e+14 0 21 46200 2.953e+14 2.953e+14 0 22 48290 2.953e+14 2.953e+14 0 23 50380 2.953e+14 2.953e+14 0 24 52470 2.953e+14 2.953e+14 1 25 54560 2.953e+14 2.953e+14 0 26 56650 2.953e+14 2.953e+14 0 27 58740 2.953e+14 2.953e+14 0 28 60830 2.953e+14 2.953e+14 0 29 62920 2.953e+14 2.953e+14 0 30 65010 2.953e+14 2.953e+14 1 Best Mean Stall Generation Func-count f(x) f(x) Generations 31 67100 2.953e+14 2.953e+14 0 32 69190 2.953e+14 2.953e+14 1 33 71280 2.953e+14 2.953e+14 2 34 73370 2.953e+14 2.953e+14 0 35 75460 2.953e+14 2.953e+14 0 36 77550 2.953e+14 2.953e+14 0 37 79640 2.953e+14 2.953e+14 0 38 81730 2.953e+14 2.953e+14 0 39 83820 2.953e+14 2.953e+14 1 40 85910 2.953e+14 2.953e+14 2 41 88000 2.953e+14 2.953e+14 3 42 90090 2.953e+14 2.953e+14 0 43 92180 2.953e+14 2.953e+14 0 44 94270 2.953e+14 2.953e+14 0 45 96360 2.953e+14 2.953e+14 0 46 98450 2.953e+14 2.953e+14 1 47 100540 2.953e+14 2.953e+14 2 48 102630 2.953e+14 2.953e+14 3 49 104720 2.953e+14 2.953e+14 4 50 106810 2.953e+14 2.953e+14 0 51 108900 2.953e+14 2.953e+14 0 52 110990 2.953e+14 2.953e+14 0 53 113080 2.953e+14 2.953e+14 1 54 115170 2.953e+14 2.953e+14 0 55 117260 2.953e+14 2.953e+14 1 Optimization terminated: average change in the fitness value less than options.FunctionTolerance.
% first floor(N/2) of res - L(1), L(2), ...
% last ceil(N/2) of res - R(1), R(2), ...
%plot results
figure;plot(w0, abs(Z0), w0, abs(fun2(res,w0)));
figure;plot(w0, angle(Z0), w0, angle(fun2(res,w0)));
Sergey Kasyanov on 13 Jul 2022
Try to use that code with your w0 and Z0. Also you need function ladder_z in the file.
% tune only next 2 lines
L = 10;% steps in ladder
Z_max = 1e2;% max Z for one R or Xl
% w0 - array with measured angular frequences
% Z0 - array with measured impedances
% create data for testing
w0 = 2 * pi * logspace(-3, 2, 10);
z0 = [rand(1, L);rand(1, L)];
Z0 = [];
for i = 1:length(w0)
Z0(i) = ladder_z(z0(1, :) + z0(2, :) * 1i * w0(i));
end
% main code
h1 = @(vals, w) ladder_z(vals(1:fix(length(vals) / 2)) + 1i * w * vals(fix(length(vals) / 2) + 1:end));
h2 = @(vals) arrayfun(@(iw) h1(vals, iw), w0);
f = @(vals) sum(abs(h2(vals) - Z0).^2);
options = optimoptions('ga', 'Display', 'iter', 'PopulationSize', L*200, 'MaxGenerations', L*200, 'UseParallel', true);
res = ga(f, L * 2, [], [], [], [], zeros(1, 2 * L), Z_max*[ones(1, L), ones(1, L) / 2 / pi], [], options);
% check
figure;plot(w0, abs(Z0), w0, abs(h2(res)));

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