Offset free tracking for a nonlinear model predictive system.

I'm trying to write a matlab script for an offset free tracking problem for a nonlinear model predictive control. The system I have chosen for the task is the three tank system. My observer design is as follows:

A =[-0.01562 -0.01562 0; -0.01562 -0.01562 -0.01562;0 -0.01562 -0.01562];
B = [704.9; 0;0];
C =[0 0 1];
D = 0;
L=place(A',C',[-10 -15 -20])';
eig(A-L*C)
eig(A)
x=[0.01;0.01;0.01]; % initial state
xhat=[0.002;0.002;0.002]; % initial estimate
XX=x;
XXhat=xhat;
T=15;
UU=3e-5*ones(1,T); % input signal
for k=1:T,
    u=UU(k);
    y(k)=C*x+D*u;
    yhat(k)=C*xhat+D*u;
    x=A*x+B*u;
    error(k+1)=(y(k)-yhat(k));
    XX=[XX,x];
    XXhat=[XXhat,xhat];
end

The objective function that I want to minimise is as follows:

[Q,R,P]=getQR();
J = 0;
xk=x;
for ct=1:N-1
    uk = u(ct);
    ex_dot=obs();
    J = J + uk'*R*uk + (xk(1)-h1(ct))'*Q*(xk(1)-h1(ct))+(xk(2)-h2(ct))'*Q*(xk(2)-h2(ct))+(xk(3)-h3(ct))'*Q*(xk(3)-h3(ct))+(h1(N)-ex_dot(1))'*Q*(h1(N)-ex_dot(1))+(h2(N)-ex_dot(5))'*Q*(h2(N)-ex_dot(5))+(h3(N)-ex_dot(9))'*Q*h3(N)-(ex_dot(9));
    xk1=rungeKutta(0,xk,uk,Ts);
    xk=xk1;

There is steady state error when I compile my entire script. I mainly need help with figuring out what is wrong with the observer design and if there is any example that I can go through to get a better idea. As matlab doesn't provide any exaple for any disturbance observer or such for nonlinear model predictive control.

I would really appreciate you help with the code that I have posted or if you could point me towards some resources.

Answer 1

[dorka astra]

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