Extracting an intermediate vector from ode45

Hello,

I have done search in the forum and found how to exract a variable from a ODE45 function. I'm trying to do the same, though, I'm not able to do it. I need some help on this. s, u and z variables they are suposed to be arrays but I dont know why I can only extract a single value from them. How can I take the whole array from them?

close all;
clc;

%% CONTEXT
% create an observer that estimates x2 while sliding variable and x1,x2
% tends to 0

%   x1'=x2                  x1(0)=x10
%   x2'= u + f(x1,x2,t)     x2(0)=x20
%   y = x1

% injection term (sliding mode observer)
% v = x1' = x2 = -r1*sign(z1)

% auxiliar sliding variable is the error estimation
% z1= x1s - x1

%% INIT
t0=0;
tfinal= 8;


% solving the ode
tspan  = linspace(t0, tfinal, 8e4);
x0     = [1 -2 0 0];
[t, x] = ode45(@(t,x) smc_obsv(t,x), tspan, x0);

%
[~, s,u,z] = smc_obsv(t, x);


%% plotting the solution
figure()
plot(t,x(:,3),'k', 'LineWidth',2)
set(gca,'FontSize',12)
hold on
plot(t,x(:,4),'r', 'LineWidth',2)
grid on
title("speed stimation")
xlabel('time(s)','fontweight','bold','FontSize',12)
ylabel('x2 and x2s ','fontweight','bold','FontSize',12)
legend('x2','x2s')
minPlot = min(x(:,4));
maxPlot = max(x(:,4));
ylim([minPlot, maxPlot]);



figure()
plot(t,s,'k', 'LineWidth',2)
set(gca,'FontSize',12)
grid on
title("Sliding variable")
xlabel('time(s)','fontweight','bold','FontSize',12)
ylabel('s','fontweight','bold','FontSize',12)
legend('sigma')
minPlot = min(sp);
maxPlot = max(sp);
ylim([minPlot, maxPlot]);


figure()
plot(t,x1(1:end-1),'k', 'LineWidth',2)
hold on 
plot(t,x2s(1:end-1),'r', 'LineWidth',2)
set(gca,'FontSize',12)
grid on
title("x1 and x2 trough time")
xlabel('x1 and x2s','fontweight','bold','FontSize',12)
ylabel('t','fontweight','bold','FontSize',12)
legend('x1','x2')
xlim([0 8])


%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% describing the ode
function [xdot,s,u,z] = smc_obsv(t, x)
    xdot    = zeros(4, length(t));	
    
    % parameters
    f       = sin(2*t);                     % disturbance
    
    c       = 1.5;                          %
    r       = 2;                            % criterion: r > max(f)
    s       = c*x(1) + x(4);                % sliding surface
    
    u       = - r*tanh(s/0.001) - c*x(4);   % control input
    
    r1      = 10;                           % high gain
    z       = x(3) - x(1);                  % estimation error
     
    v1      = - r1*tanh(z/0.001);           % rate of xhat_1
    LPF     = 1/0.01;                       % adapatation rate
    v2      = (v1 - x(4))*LPF;              % rate of xhat_2
    
    xdot(1) = x(2);
    xdot(2) = f + u;
    xdot(3) = v1;
    xdot(4) = v2;
    
end

Answer 1

[Torsten]

Use

s = zeros(numel(t),1);
u = s;
z = s;
for i = 1:numel(t)
  [~, s(i),u(i),z(i)] = smc_obsv(t(i), x(i,:));
end

instead of

[~, s,u,z] = smc_obsv(t, x);

[Mikel]

Thank you!