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

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. Despit...

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Bibliographic Details
Published in:	Journal of process control Vol. 101; pp. 35 - 51
Main Authors:	Caspari, Adrian, Djelassi, Hatim, Mhamdi, Adel, Biegler, Lorenz T., Mitsos, Alexander
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.05.2021
Subjects:	Deterministic global optimization Offset-free nonlinear model predictive control Optimal disturbance modeling Plant model mismatch Semi-infinite programming Unknown disturbances Unknown disturbances Semi-infinite programming Plant model mismatch Optimal disturbance modeling Offset-free nonlinear model predictive control Deterministic global optimization
ISSN:	0959-1524, 1873-2771
Online Access:	Get full text
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Summary:	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. [Display omitted] •Generalized theory on offset-free NMPC.•First systematic approach for disturbance model generation.•Semi-infinite programming used for model generation.•Global optimization to guarantee system theoretical properties.•Three chemical engineering case studies.
ISSN:	0959-1524 1873-2771
DOI:	10.1016/j.jprocont.2021.03.005