Offset-free MPC control

[Alessio98]

Hello everyone,

I am designing an MPC controller in Matlab/Simulink and I was actually able to make it work.

Now I would like to bring the tracking error to zero by implementing an integral action, and I have to do it via the "full increment velocity form" technique. In my head this should be an easy task: after augmenting the state properly, I just need to modify the scheme so that, in the cost function, u_ref is replaced by u(k-1).

However this solution does not work, so I suppose I am missing something.
Can anybody please help me?

 

[Alessio98]

I have also tried a different solution, that is: instead of replacing u_ref, I adapted the MPC so that its optimization variable is delta_u instead of u. I guess that in the unconstrained case I shouldn't need to do other modifications.

However, this solution does not work neither.