Disturbance models for offset‐free model‐predictive control

Gabriele Pannocchia, James B. Rawlings

AIChE Journal · 2003 · 597 citations · 27 references

Concepts

TL;DR

Model predictive control achieves offset‑free control by adding integrating disturbances that absorb plant‑model mismatch, but this has only been proven for square cases, and for systems where measured variables exceed manipulated variables, at most m variables can be offset‑free, leading to the misconception that m disturbances suffice. The paper demonstrates that the assumption of m disturbances is wrong and derives general conditions for zero steady‑state offset. The authors prove that using as many integrating disturbances as measured variables guarantees zero offset in all controlled variables, a result that holds for both square and nonsquare, stable and unstable systems.

Abstract

Abstract Model predictive control algorithms achieve offset‐free control objectives by adding integrating disturbances to the process model. The purpose of these additional disturbances is to lump the plant‐model mismatch and/or unmodeled disturbances. Its effectiveness has been proven for particular square cases only. For systems with a number of measured variables (p) greater than the number of manipulated variables (m), it is clear that any controller can track without offset at most m controlled variables. One may think that m integrating disturbances are sufficient to guarantee offset‐free control in the m controlled variables. 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 variables are shown to be sufficient to guarantee zero offset in the controlled variables. These results apply to square and nonsquare, open‐loop stable, integrating and unstable systems.

References

27