Flipping a State Space Model so the input is now calculated from a previous output

I'm currenlty working on different ways to manipulate a common state space model.

If I run the following parameters:::::

u = -.012;
x = [0.0100000000000000;-0.0267035162502245];
A = [-20.2325181833801,-4.67364254028025;3.46393906420022,-22.4031616974973];
B = [94.7368421052632;67.0500000000000];
C = [1 0;0 1];
D = 0;
x_dot = A*x + B*u
u_new = (x_dot - A*x)/B

It outputs:::::

x_dot =
   -1.2144
   -0.1717

u_new =
   -0.0120         0
   -0.0085         0

u_new(1,1) lines up with the orignial input, but of course due to the matrix math there ends up being more information in the answer. Is it a problem if I ignor this information?

Answer 1

[Ameer Hamza]

The correct line is

u_new = B\(x_dot - A*x)

Matrix multiplication is not commutative. So you need to take care of the order of matrix multiplication.

[Michael Wyciechowski]

when I run

u_new = B/(x_dot - A*x)

i get

u_new =

  -83.3333         0
  -58.9792         0

which doesn't line up with my original input

[Ameer Hamza]

You used slash (/), whereas, in my answer, I used backslash (\). They are not same in MATLAB.

[Michael Wyciechowski]

thank you, that works

[Ameer Hamza]

I am glad to be of help!