trastri asked . 2020-12-16

Euler method with state space model

s=tf('s');
pt2 = s/((s+0.1)*(s+4));
SYS = ss(pt2);

A = SYS.A; 
B = SYS.B; 
C = SYS.C;
D = SYS.D;

I created a linspaced timevector t_i that is equally distributed over all my discrete points. To make it easier to read I extracted some values of the real data:

% ax = traj.ax(1:10);
% you can use this vector of accelerations if you want
ax = [-0.7412; -0.749 ;-0.7525;-0.7508;-0.7443;-0.7331;-0.7178;-0.699;-0.6779;-0.6540];

t_i = linspace(1, 5, 10);
h = diff(t_i(1:2));  % calc step size

x = t_i(1) : h : t_i(end);  % the range of x - not sure about this 

y = zeros(length(x),2);  % allocate the result y 
u= ax; %make clear that ax is the input  

Now I want to solve Eulers method as state space model:

for i=1:10-1
    
    dx = A*x(i) + B*u(i);
    x_k1 = x_k + dx*h; %x_k1 is x_k+1 
    x_k = x_k1;
    % y should be a scalar output in my case, since I want to get weighted accelerations as output - but I can only compile if I put the (i,:) right now.
    y(i,:) = C*x_k;
    
end

matlab , ,matlab coder , control system