K matrix for MIMO

Hello!

Can anyone explain how i can define the K matrix for state feedback control if i have a MIMO system? I have found the 3 desirable poles. If we had a SISO system then K would be a vector of a 1x3 but now that my B matrix is 3x3 how can i find the other ks in order to get a K matrix that is 3x3 so i can get the sysk = (A - B*K,B,C,D)?

Thank you in advance..

Answer 1

[Shivam Gothi]

Hello @Ilias,

As per my understanding, you are trying to find the gain matrix [K] for a MIMO system.

The dimentions of [B*K] matrix must be [3 x 3]. For a MIMO system, the size of [B] matrix specified by you is 3 x 3. This means that the size of [K] matrix is also [3 x 3].

The [K] matrix is decided in such a way that the poles of matrix [A-BK] lies on the left hand plane (in case of continuous time system) and within unit circle (in case of discrete time system).

Therefore, in order to find an appropriate gain matrix [K] for state feedback control, you must find desirable pole location.

As mentioned in the question, you already have the desired poles location.

Therefore in order to find the gain matrix [K], you can use the below given MATLAB function. It will give the gain matrix which will place the poles of [A-BK] matrix at desirable location

K = place(A,B,p) places the desired closed-loop poles p by computing a state-feedback gain matrix K. Refer to the documentation: https://www.mathworks.com/help/control/ref/place.html

I hope it helps !