%%%
%%% Simulation of sampled data system
%%%

K = 0.01; %% try 0.05, 0.02, 0.01, 0.001
T  = 1;   %% Discrete time increments in seconds
dt = 1/1000; %% ``continuous'' time increments in seconds
NT = 30; %% Experiment duration in T periods

N_TICS = round(T*NT/dt); %% Tot n. of tics in exper.
alpha = exp(log(2)*dt);%% exponent of continous time system


%% Set up the arrays and plots that are necessary for the simulation
y = zeros(1,N_TICS);
t_tics = [1:N_TICS]*dt;
pt = zeros(1,NT); %% Array of pointers to data markers
y(1)=0; figure(1); clf;
title(['K=' num2str(K) ' T=' num2str(T)]);
hold on;
for TT = 1:NT,
    tti = (TT-1)*T/dt + [1:(1/dt)];
    pt(TT) = plot(t_tics(tti),y(tti),'.w','MarkerSize',5);
end;
hold off;

xs = zeros(1,NT); xs(3)=1; %% Sampled input
ys = zeros(1,NT); TT=1; ys(TT)=0; %% Sampled output

for tt=2:N_TICS, %% tt is is the `continuous' time tic
    e = xs(TT) - K*ys(TT); %% Error signal
    
    y(tt)=alpha*y(tt-1)+e; %% Output of continuous systems
    
    if mod((tt*dt),T)==0, %% If the time is equal to one of the discrete system's sampling times
        TT = (tt*dt)/T; %% sample number is it
        tti = (TT-1)*T/dt + [1:(1/dt)];  %% All the tics in the preceding period
        ys(TT) = y(tt);  %% Sample the output
        set(pt(TT),'YData',y(tti),'Color','b');
        pause(0.1);
    end;
    drawnow;
end;