can anyone offer control of state space system using Iterative Learning Control in command window in MATALB

can anyone offer control of state space system using Iterative Learning Control in command window in MATALB

[Mark Sherstan]

Please provide more information such as transfer function, sampling time, initial conditions, etc... Does your system include a controller or is that factored into your state space?

[Walter Roberson]

When you say in the command window does that mean that it is not permitted to define true functions to assist? Or are you trying to distinguish from a Simulink solution ?

[Mohamed Eshag]

@mark sherstan

[Mohamed Eshag]

Walter Roberson: Yeah, to distinguish from a Simulink solution, and ususally I like to design a control system in command window better than simulink

Answer 1

[Mark Sherstan]

Here is an example that should push you in the correct direction. I havent completed it as I dont know what 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.

function [ ] = ILC()

%[Ad Bd Cd Dd] = ssdata(sys);
Ad = [0 1 0; 3 0 1; 0 1 0];
Bd = [1; 1; 3];
Cd = [1 1 1];
Dd = [0];
    
% Set Ts, initial condition x0, time range t, pure time delay n0, relative 
% degree r, and matrix size N 
Ts = 1;
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

[Mohamed Eshag]

Thanks Mr.Mark for your feedback. It will be usefull for me. please if you have good book in this area, could you send it yo me here ;( [e-mail]). because I have two types of disturbances in my system.

[mazin alseadi]

Dear Mohamed Eshag

Have you developed or did this codes to be worked successfuly ? if you did, so please could you kindly send me this files ?

with respect and appreciate