Simulating State Response with Disturbance via Multivariable Integral Control

I have a state space model with disturbance that I have to reduce the steady state error to zero. I am using the integral control method and seem to be getting stuck on the very end. I do not know if I am missing something or I do not know how to simulate my final product.

System:

A=[0 1;0 0];

B=[0;1];

Bw=[1;1]; %Disturbance added to make Ax+Bu+B_w*w

C=[1 0];

D=0;

Calculating the augmented system:

Abar=[A;-C];

zc=zeros(size(Abar,1),1);

Abar=[Abar,zc];

Bbar=[B;0];

Bwbar=[Bw,;0];

Brbar=[0;0;1];

Cbar=[C,0];

Finding the gain matrix K using LQR:

Q=eye(3);

R=1;

K = lqr(Abar,Bbar,Q,R);

Ana=[(Abar-Bbar*K)];

sys_Ka=ss(Ana,Bbar,Cbar,D) %This part seems to be correct, but the error value needs to be corrected to zero

Calculating the resultant feedback system:

AbarC=[A-B*K(1) -B*K(2); -C 0];

sys_F=ss(Abar,Bwbar,Cbar,AbarC)

The system (with disturbance and augmented matrices) should have zero steady state error for sys_F, but it doesn't. Doing it by hand, the sytem should be:

x_dot_bar=AbarC*(x v)+(Bw;0)u+(0;I)r

y=[C 0](x v)

I have the correct matrices (I would like to believe), but do not know how to plot the new system. I used lsim and ss for other models without disturbance.

So, I think I am making a mistake when plotting the final system, do not know how to convert the new system into the Ax+Bu form, or I am overlooking something. Attached is the correct plot of the system that I cannot simulate.

Any would would be greatly appreciated!