# Optimisation problem in matlab

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wallflower 2021 年 6 月 21 日

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
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wallflower 2021 年 6 月 21 日
It is not a homework assignment. I am trying to reproduce a methology I've seen in a scientific paper.

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### 回答 (1 件)

Sergey Kasyanov 2021 年 6 月 21 日

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])';
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);
% 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)));
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Sergey Kasyanov 2021 年 6 月 24 日
I corrected code. There were some misprints.
Now it is working, but It is very sensitive to limits of Z_max and amount of ladder steps. Try, please. Does it working on your machine?

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R2019b

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