Disturbance Models for Offset-Free Model-Predictive Control

Model predicti®e control algorithms achie®e offset-free control objecti®es by adding integrating disturbances to the process model. The purpose of these additional disturbances is to lump the plant-model mismatch andror unmodeled disturbances. Its effecti®eness has been pro®en for particular square cases only. For systems with a number of ( ) ( ) measured ®ariables p greater than the number of manipulated ®ariables m , it is clear that any controller can track without offset at most m controlled ®ariables. One may think that m integrating disturbances are sufficient to guarantee offset-free control in the m controlled ®ariables. We show this idea is incorrect and present general conditions that allow zero steady-state offset. In particular, a number of integrating disturbances equal to the number of measured ®ariables are shown to be sufficient to guarantee zero offset in the controlled ®ariables. These results apply to square and nonsquare, open-loop stable, integrating and unstable systems.