Semi-infinite programming yields optimal disturbance model for offset-free nonlinear model predictive control

Abstract

Offset-free nonlinear model predictive control (NMPC) can eliminate the tracking offset associated with the presence of plant-model mismatch or other persistent disturbances by augmenting the plant model with disturbances and employing an observer to estimate both the states and disturbances. Despite their importance, a systematic approach for the generation of suitable disturbance models is not available.We propose an optimization-based method to generate disturbance models based on sufficient observability conditions and generalize the theory of offset-free NMPC by allowing for (i) more measured variables than controlled variables and (ii) unmeasured controlled variables. Based on the sufficient conditions, we formulate a generalized semi-infinite program, which we reformulate and solve as a simpler semi-infinite program using a discretization algorithm. The solution furnishes the optimal disturbance model, which maximizes the set of those state, manipulated variable, and disturbance realizations, for which a sufficient observability condition is satisfied. The disturbance model is generated offline and can be used online for offset-free NMPC.We apply the approach using three case studies ranging from small scale chemical reactor cases to a medium scale polymerization reactor case. The results demonstrate the validity and usefulness of the generalized theory and show that the model generation approach successfully finds suitable disturbance models for offset-free NMPC.