State Space observer Result

Hello everyone,

I have a question about the state space observer, I have programmed a state space space observer using Matlab function block but the result is odd. So if anyone can help I would appreciate it

this is the result of the state estimation.

[Sam Chak]

Hi @Hamidou Youness

I think this has nothing to do with the MATLAB function block.

Most likely you have designed a state observer that destabilized the system.

Without showing your work and design, it's very difficult to provide assistance.

[Hamidou Youness]

Hi @Sam Chak

this is what I have done until now.

Answer 1

[Sam Chak]

Hi @Hamidou Youness

Thanks for adding more info. However, if you are looking for assistance, it is preferred that you share your work or part of your work, rather than relying people to extract data from the pictures. Anyhow, check this out. Your system is both controllable and observable. Now, the observed-state feedback control system is stable. Hope this answer helps!

% state matrix
A = [0 0 1 0; ...
     0 0 0 1; ...
     0 1.962 0 0; ...
     0 5.886 0 0]

% input matrix
B = [0; 0; 0; 0.1]

% output matrix
C = [1 0 0 0]

% desired poles for computing the controller gain matrix K
pc = [-0.5+i -0.5-i -0.75 -1];
K = place(A, B ,pc)

% desired poles for computing the observer gain matrix L
po = [-5+i -5-i -5.5 -6]
L = place(A', C', po)'

% the observed-state feedback control system
sys = ss([A-B*K B*K; zeros(4, 4) A-L*C], eye(8), eye(8), eye(8));

t = 0:0.01:12;
z = initial(sys, [1; 0; 0.5; 0; 0.5; 0; 0.25; 0], t);
x1 = [1 0 0 0 0 0 0 0]*z';  % system states, x
x2 = [0 1 0 0 0 0 0 0]*z';
x3 = [0 0 1 0 0 0 0 0]*z';
x4 = [0 0 0 1 0 0 0 0]*z';
e1 = [0 0 0 0 1 0 0 0]*z';  % error states, e
e2 = [0 0 0 0 0 1 0 0]*z';
e3 = [0 0 0 0 0 0 1 0]*z';
e4 = [0 0 0 0 0 0 0 1]*z';

plot(t, x1, t, x2, t, x3, t, x4, t, e1, t, e2, t, e3, t, e4)

Results: