MPC: using State-Space model generated from detrended data

Greetings,

Generating a model, through the System Id. Toolbox, from treated data (detrended) results in a good fit, but when such model is subjected to the untreated inputs it returns the plant correct behaviour minus an offset.

Nevertheless, using this model in a MPC project resulted in satisfactory control despite the obvious plant-model mismatch. What am I missing here ?

Does this satisfactory control results from the fact that the cost function computes the optimal input increments instead of just inputs ? Is this the result of some kind of feedback action presented in the predictive algorithm used in the MPC toolbox and I am loosing feedforward action ? Can I make the model generated from detrended data fit the untreated data ?

thanks in advance