Hi, Has anyone been able to implement ILC (using basis functions) in Matlab? Can someone please share the code of an example. Thank you very much.

Hi, Has anyone been able to implement ILC (using basis functions) in Matlab? Can someone please share the code of an example. Thank you very much.

Answer 1

[Mark Sherstan]

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Update:

Look at the following post for a more developed example:

https://www.mathworks.com/matlabcentral/answers/59641-implementation-of-iterative-learning-control-in-matlab-simulink

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Here is an example that should push you in the correct direction. I havent completed it as I dont know what your input signal is or your reference signal is or if you need to add noise, disturbances, pure time delay, etc... but it is basically complete. Refer to the comments to follow what is going on. You need to put in a discrete time transfer function (sys) and sampling time (Ts) into the function. Let me know if you have any further questions!

function [ ] = ILC(sys,Ts)

[Ad Bd Cd Dd] = ssdata(sys);

% Initial condition x0, time range t, pure time delay n0, relative 
% degree r, and matrix size N 
x0 = 0;
t = 0:Ts:60;
n0 = 0;
r = 1;
N = length(t);

% Define input vector U and reference J
U = [zeros(1,15) 10*ones(1,15) zeros(1,15) 10*ones(1,16)];
Rj = [zeros(1,15) 20*ones(1,15) zeros(1,15) 20*ones(1,16)]';

% G0 not formulated as initial condition is 0

% Formulate G
Gvec = zeros(N,1);
rvec = ((r-1):(N-n0-1))';

for ii = 1:length(rvec)
  ApowVec = Ad^rvec(ii);
  Gvec(ii) = Cd*ApowVec*Bd;
end

G = tril(toeplitz(Gvec));

% Set up ILC
jmax = 25;
l0 = 0.95;
q0 = 1;
L = l0 * eye(N,N);
Q = q0 * eye(N,N);
I = eye(N);
Uj = zeros(N,1); Ujold = Uj;
Ej = zeros(N,1); Ejold = Ej;
e2k = zeros(jmax,1);

% Run ILC and plot the response for each iteration
for ii = 1:jmax
  Uj = Q*Ujold + L*Ejold;
  Yj = G*Uj;
  Ej = Rj - Yj; Ej(1) = 0;
  Ejold = Ej;
  Ujold = Uj;
  plotter(ii,t,Ej,Yj,Uj,Rj,U)
  e2k(ii) = Ej'*Ej;
end

end



function [] = plotter(ii,t,Ej,Yj,Uj,Rj,U)
  figure(1)
  
  % Plot the error Ej of the current itteration
  subplot(1,3,1);
  plot(t,Ej,'LineWidth',1.5);
  title('Error, Ej','FontSize',16);
  ylabel('Error Response','FontSize',16);
  
  % Plot the input Uj of the current itteration
  subplot(1,3,2);
  plot(t,Uj,t,U,'-k','LineWidth',1.5);
  title({['Iteration: ', num2str(ii)],'Input, Uj'},'FontSize',16);
  xlabel('Time (s)','FontSize',16);
  ylabel('Input Response','FontSize',16);
  
  % Plot the output Yj of the current itteration
  subplot(1,3,3);
  plot(t,Yj,t,Rj,'-k','LineWidth',1.5);
  title('Output, Yj','FontSize',16);
  ylabel('Output Response','FontSize',16);
  pause(0.1);
  
end

[Hekma Sekandari]

Hi mark, thank u very much for your reply.

I have a question, what is G? and how did you calculate G in this way?

Did you use basis functions?

[Mark Sherstan]

G is basically a representation of your discrete time transfer function taken from its state space representation. The formulas look like this where G is a lower triangular Toeplitz matrix:

[Hekma Sekandari]

Thank u very much for your reply, i never saw this represantation of G.

Do you also use basis functions?

[Mark Sherstan]

I will flip through some of my notes but I am pretty sure I never used basis functions and only used variations of the formulas above (super vector notation). This presentation will give you some further contex located here (not my notes but similar equations and methodology).

[Hekma Sekandari]

Hi mark,

did you find something?

[Mark Sherstan]

I only covered super vector form, sorry sir.

[Hekma Sekandari]

No problem, thank u very much.

If you have more examples, please share :)

Answer 2

[TARUN KARAK]

hi, can any one tell me how to code for constraints handling using barrier method with ILC?