Geometric output tracking of nonlinear distributed parameter systems via adaptive model reduction

Davood Babaei Pourkargar, Antonios Armaou

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We focus on the output tracking problem of distributed parameter systems (DPSs) which can be described by a set of nonlinear dissipative partial differential equations (PDEs). The infinite-dimensional modal representation of such systems in appropriate subspaces can be decomposed to finite-dimensional slow and probably unstable, and infinite-dimensional fast and stable subsystems. Taking advantage of this decomposition, adaptive model reduction techniques and specifically adaptive proper orthogonal decomposition (APOD) can be used for the recursive construction of locally accurate low dimensional reduced order models (ROMs). The proposed geometric APOD-based control structure is the combination of a nonlinear Luenberger-like geometric dynamic observer and a globally linearizing controller (GLC) designed for tracking the desired output. The proposed geometric control approach is successfully illustrated on the output tracking of target thermal dynamics for a catalytic reactor. Specifically, the geometric output tracking strategy is used to reduce the hot spot temperature and manage the thermal energy distribution through reactor length during process evolution with limited number of actuators and sensors.

Original languageEnglish (US)
Pages (from-to)418-427
Number of pages10
JournalChemical Engineering Science
Volume116
DOIs
StatePublished - Sep 6 2014

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Distributed Parameter Systems
Model Reduction
Decomposition
Orthogonal Decomposition
Output
Reactor
Thermal energy
Partial differential equations
Reduced Order Model
Energy Distribution
Actuators
Hot Spot
Observer
Actuator
Controllers
Subsystem
Partial differential equation
Unstable
Sensors
Subspace

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Chemical Engineering(all)
  • Industrial and Manufacturing Engineering

Cite this

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abstract = "We focus on the output tracking problem of distributed parameter systems (DPSs) which can be described by a set of nonlinear dissipative partial differential equations (PDEs). The infinite-dimensional modal representation of such systems in appropriate subspaces can be decomposed to finite-dimensional slow and probably unstable, and infinite-dimensional fast and stable subsystems. Taking advantage of this decomposition, adaptive model reduction techniques and specifically adaptive proper orthogonal decomposition (APOD) can be used for the recursive construction of locally accurate low dimensional reduced order models (ROMs). The proposed geometric APOD-based control structure is the combination of a nonlinear Luenberger-like geometric dynamic observer and a globally linearizing controller (GLC) designed for tracking the desired output. The proposed geometric control approach is successfully illustrated on the output tracking of target thermal dynamics for a catalytic reactor. Specifically, the geometric output tracking strategy is used to reduce the hot spot temperature and manage the thermal energy distribution through reactor length during process evolution with limited number of actuators and sensors.",
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Geometric output tracking of nonlinear distributed parameter systems via adaptive model reduction. / Pourkargar, Davood Babaei; Armaou, Antonios.

In: Chemical Engineering Science, Vol. 116, 06.09.2014, p. 418-427.

Research output: Contribution to journalArticle

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