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Question about the state space model SS
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Hi everyone
I have a question about the state space model. I have linearized my equations with Taylor at first order around a stationary point. If i consider my stationary point different from zero, I obtain the following model: x_dot = Ax+Bu+E and y = Cx+Du where E is the matrix that contains only known terms related to linearization constant. So my question is if there's a way to pass from this two equations to the state space model, cause I always used sys = ss(A,B,C,D), but this time I have also the matrix E.
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Answers (1)
Abhinav Aravindan
on 27 Feb 2024
Edited: Abhinav Aravindan
on 27 Feb 2024
A possible approach to model the above equations is to add an extra state to your system that represents the constant term. This state will have a derivative of 0 since it is constant.
The code snippet below illustrates this approach.
% State-space matrices (sample values)
A = [2 2 3; 1 2 1; 3 4 5];
B = [3; 4; 7];
C = [7 8 9];
D = 9;
E = [10; 11; 12];
% Number of states, inputs, and outputs
n = size(A, 1);
m = size(B, 2);
p = size(C, 1);
% Augment the A matrix with an extra column for E
A_new = [A, E; zeros(1, n), 0];
% Augment the B matrix with an extra row of zeros
B_new = [B; zeros(1, m)];
% Augment the C matrix with an extra column for effect of E on the output
C_new = [C, zeros(p, 1)];
% D matrix remains the same
D_new = D;
% Create the state-space model
sys = ss(A_new, B_new, C_new, D_new);
Output:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1629013/image.png)
Please find below similar queries to yours and relevant documentation for reference:
1 Comment
Sam Chak
on 27 Feb 2024
Hi @Abhinav Aravindan, it seems that you placed the E constants into the state matrix A. What will be the initial value of augmented state
?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1629048/image.png)
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