A reduced-basis discretization method for chemical vapor deposition reactor simulation

Chemical Engineering Science

2015

We focus on shaping the long-term spatiotemporal dynamics of transport-reaction processes which can be described by semi-linear partial differential equations (PDEs). The dynamic shaping problem is addressed via error dynamics regulation between the governing PDE and a target PDE which describes the desired spatiotemporal behavior. A model order reduction methodology is utilized to construct the required reduced order models (ROMs) for governing and target dynamics via Galerkin's method. We subtract the governing from the target ROMs to obtain reduced offset dynamics error. Then an output feedback sliding mode control structure is synthesized to stabilize the reduced error dynamics and correspondingly synchronize the system and the target spatiotemporal behaviors. A Luenberger-type dynamic observer is applied to estimate the states of the governing ROM required by the sliding mode controller. The proposed approach is applied to address the thermal spatiotemporal dynamic shaping problem in a tubular chemical reactor.

Section: Model Order Reduction Via Galerkin's Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic shaping of transport–reaction processes with a combined sliding mode controller and Luenberger-type dynamic observer design

Chemical Engineering Science

2015

“… for heating rod and catalytic packed‐bed reactor examples, Refs . for chemical vapor deposition process and Ref . for plasma discharge reactor).…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

APOD‐based control of linear distributed parameter systems under sensor/controller communication bandwidth limitations

2014

AIChE Journal

The synthesis of a model-based control structure for general linear dissipative distributed parameter systems (DPSs) is explored in this manuscript. Discrete-time distributed state measurements (called process snapshots) are used by a continuous-time regulator to stabilize the process. The main objective of this article is to identify a criterion to minimize the communication bandwidth between sensors and controller (snapshots acquisition frequency) using linear systems analysis and still achieve closed-loop stability. This objective is addressed by adding a modeling layer to the regulator. Theoretically, DPSs can be well described by low dimensional ordinary differential equation models when represented in functional spaces; practically, the model accuracy hinges on finding basis functions for these spaces. Adaptive proper orthogonal decomposition is used to identify statistically important basis functions and establish locally accurate reduced order models which are then used in controller design. The proposed approach is successfully applied toward thermal regulation in a tubular chemical reactor.

“…Important processes in chemical and advanced material industry often couple complex transport phenomena with chemical reactions, such as reactive distillation in petrochemical industry, lithographic processes in semiconductor manufacturing, chemical vapor deposition processes, plasma discharge reactors, and tin float bath process in glass production [1,18,39,61]. In recent years, research in the field of process control has focused on the synthesis of control structures for these transport-reaction processes.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, research in the field of process control has focused on the synthesis of control structures for these transport-reaction processes. The spatially distributed and nonlinear nature of the associated system dynamics make the control problem nontrivial [1,15,18,38,44,52,53,58]. The significant diffusion transport of the species leads to a mathematical description of dissipative partial differential equations (PDEs) whose long term and dominant behavior can be represented by finite number of the process spatial profiles [56] because the characteristic spectrum of the spatial differential operator of such PDEs can be decomposed to a finite-dimensional slow and an infinite-dimensional fast and stable parts [18].…”

Section: Introductionmentioning

confidence: 99%

Design of APOD-based switching dynamic observers and output feedback control for a class of nonlinear distributed parameter systems

Chemical Engineering Science

2015

The output feedback control problem for a class of nonlinear distributed parameter systems with limited number of continuous measurement sensors that describes a wide range of physico-chemical systems is investigated using adaptive proper orthogonal decomposition (APOD) method. Specifically, APOD is used to initiate and recursively revise locally valid reduced order models (ROMs) that approximate the dominant dynamic behavior of such physico-chemical systems. The controller is designed based on ROMs by combining a robust state controller with an APOD-based nonlinear Luenberger-type switching dynamic observer of the system states to reduce measurement sensors requirements. The important static observer requirements on the number of measurement sensors (that must be supernumerary to the ROM dimension) and their location is circumvented by synthesizing dynamic observers. Three different approaches are introduced to recursively compute the dynamic observer gains at the ROM revisions. The stability of the closed-loop system is proven via Lyapunov and hybrid system stability arguments without invoking the separation principle between control and observation. The proposed method is successfully used to regulate a physico-chemical system that can be described in the form of the Kuramoto-Sivashinsky equation when the process exhibits significant nonlinear behavior.