unable to create state space observer

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Abdul Hamzah 2024-10-13

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https://ww2.mathworks.cn/matlabcentral/answers/2159385-unable-to-create-state-space-observer

评论： Umar 2024-10-14

Hello everyone, I am trying to make a state-space observer using this code :

% Parameters of the system
M = 1.0;   % Mass of the cart
m = 0.1;   % Mass of the pendulum
g = 9.81;  % Gravitational constant
l = 0.6;   % Length of the pendulum
%for state-space block on top
A_ = [0 1 0 0;
     0 0 -(m*g)/(M - m) 0;
     0 0 0 1;
     0 0 (g*M)/(l*(M - m)) 0];
B_ = [0;
     1/(M - m);
     0;
     -1/(l*(M - m))];
C_ = eye(4); % Identity matrix as all states can be observed
D_ = [0;0;0;0];     % No direct feedthrough
sys2=ss(A_,B_,C_,D_)
%sys_ctrl = compreal(sys2,"c");
%A_ctrl = sys_ctrl.A
%B_ctrl = sys_ctrl.B
%C_ctrl = sys_ctrl.C
%D_ctrl = sys_ctrl.D
p= [-2 -2.5 -3 -3.5];
K=place(A_,B_,p)
pol= eig(A_-B_*K)
op = [-5 -6 -7 -8];
%op = [-1;-1;-1;-1];
L_mat=place(A_',C_',op)'
%for state-space block on bottom
A_new = A-L_mat*C_;
B_new = [B,L_mat];
C_new=eye(4);
D_new = 0;
sys3=ss(A_new,B_new,C_new,D_new)

and I connect it to this model :

but somehow I am only able to produce this graph:

Do you know what is actually wrong with my code?? any response and help is really appreciated..

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Umar 2024-10-13

Hi @Abdul Hamzah,

After going through your comments,the code you provided for implementing a state-space observer appears to be fundamentally sound; however, there are a few areas to check that may be causing the unexpected output graph.

Observer Gain Matrix (L_mat): Ensure that the poles specified in the op variable are appropriate for your system dynamics. If the poles are too far from the origin, the observer may not converge properly.

State-Space Representation: Verify that the matrices A_new, B_new, C_new, and D_new are correctly defined. The observer's dynamics should be stable, and the dimensions of these matrices must align with the state-space model.

Simulink Model Configuration: Check the configuration of your Simulink model. Ensure that the input signals are correctly connected and that the simulation parameters (like time step and solver) are set appropriately.

Initial Conditions: If the initial conditions for the states are not set correctly, it may lead to unexpected behavior in the output.

Graph Settings: Lastly, ensure that the graph settings in Simulink are configured to display the desired outputs. Sometimes, the wrong signals may be plotted.

By addressing these points, you should be able to identify the issue and achieve the expected results from your state-space observer.

If problems persist, consider simplifying the model to isolate the issue further.

Hope this helps.

Sam Chak 2024-10-14

在 MATLAB Online 中打开

Hi @Aquatris,

Have you also observed that all states of the system are fully measurable, as indicated by the output matrix being an identity matrix? The linear system is controllable with a full-state feedback controller, which the OP (@Abdul Hamzah) designed using pole placement.

However, it is unclear which 4th-order system formula the OP used to "mathematically calculate" such closed-loop poles, resulting in the low-mass pendulum bob settling at around 4 seconds, which is deemed unrealistic.

% Parameters of the system

M = 1.0; % Mass of the cart

m = 0.1; % Mass of the pendulum

g = 9.81; % Gravitational constant

l = 0.6; % Length of the pendulum

%for state-space block on top

A = [0 1 0 0;

0 0 -(m*g)/(M - m) 0;

0 0 0 1;

0 0 (g*M)/(l*(M - m)) 0];

B = [0;

1/(M - m);

0;

-1/(l*(M - m))];

C = eye(4); % Identity matrix as all states can be observed

D = [0;0;0;0]; % No direct feedthrough

%% Desired closed-loop poles

p = [-2 -2.5 -3 -3.5];

%% Pole placement design of control gain matrix

K = place(A, B, p)

K = 1×4

-2.8899 -4.3899 -35.7089 -8.5739

%% Closed-loop system

sys = ss(A-B*K, B, C, D);

step(sys), grid on

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Answer 1

Umar 2024-10-13

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