Problem with kalman function for LQG

I am trying to implement and LQG regulator, but for some reason I get an error related to the "kalman" function. A snippet of my code is as follows:

sys=ss(A_ae_control,[B_ae_control(:,1) B_ae_control(:,2)],C_ae_control,0);
Qn=0.7;
Rn=0.01*eye(size(A_ae_control,1));
kest=kalman(sys,Qn,Rn);

The variable B_ae_control has 2 columns, with the first column corresponding to the control input and the second column corresponding to the random noise input. The code seems to run when I set Qn to be a 2x2 matrix, but I don't see why this should be the case since I have only one noise input. I get the following error message when I run the above code:

The "kalman" command could not compute a convergent Kalman estimator for this plant model and
covariance data. To remedy the problem:
1. Make sure that all unstable poles of A are observable through C (use MINREAL to check)
2. Modify the weights QN and RN to make [G 0;H I]*[Qn Nn;Nn' Rn]*[G 0;H I]' positive definite (use EIG
to check positivity)

I have tried checking the observability and controllability of the system but I am not sure what else to do. Any insight would be appreciated!

[William Alberg]

I think it should either be:

sys=ss(A_ae_control,B_ae_control(:,1),C_ae_control,0);
Qn=0.7;
Rn=0.01*eye(size(A_ae_control,1));
Qn_matrix = B_ae_control(:,2)*Qn*B_ae_control(:,2)'
kest=kalman(sys,Qn,Rn);

or

sys=ss(A_ae_control,[B_ae_control(:,1) B_ae_control(:,2)],C_ae_control,0);
Qn=0.7;
Rn=0.01*eye(size(A_ae_control,1));
Qn_matrix = [0,0;0,Qn]
kest=kalman(sys,Qn,Rn);

If you post your A,B and C matrices, then i can check

[Arhant Sethia]

Tried both methods and still no luck unfortunately. Please see attached my A, B and C matrix. Appreciate your help!

[Arhant Sethia]

The problem seems to be with the column of B corresponding to the noise input. For example, it works when I define this as a column of all ones. Any idea why this could be the case?

[William Alberg]

The following appears to work:

Qn = 0.7;
Rn = 0.01*eye(16);

sys = ss(A,B,C,0);
[kest,L,P] = kalman(sys,Qn,Rn)

"kalman" allows for specification on which column of B that is controlled

sys = ss(A,B,C,0);
[kest,L,P] = kalman(sys,Qn,Rn,0,1:16,1);

"1:16" is related to the sensors - Essentielly stating that all sensors are measureing (atleast if i understand correctly)

"1" is related to input, and states that column 1 is known. column 2 is then treated as unknown

[Arhant Sethia]

What did you set as Qn and Rn? For some reason I still get the convergence error when I run it. Just to clarify did you use the whole B matrix that I sent or just the first column? Thanks

[William Alberg]

I edited my previus response some time after i posted it to include the Qn and Rn, i guess you didn't see it

The B matrix is both columns.

My complete test code is below:

clc;clear;close all

A = load('A_ae_control');
A = A.A_ae_control;
B = load('B_ae_control');
B = B.B_ae_control;
C = load('C_ae_control');
C = C.C_ae_control;
D = 0;

Qn = 0.7;
Rn = 0.01*eye(16);

sys = ss(A,B,C,0);
[kest,L,P] = kalman(sys,Qn,Rn,0,1:16,1);

[Arhant Sethia]

Thanks for this. That is very strange because when I run the exact same code on my computer, it still gives me a convergence issue (the error which I mentioned in my original post). It worked smoothly for you when you ran it?

[Arhant Sethia]

If it makes any difference, I'm using the 2017 version?

[William Alberg]

Im using the 2020a version

[William Alberg]

I installed matlab 2017a, and i can't make it work either.

I also tried the lqe, care and icare commands, but they all seem to hit the same problem.

[Arhant Sethia]

Installed 2020a and it seems to work. Thanks for all your help!