Abstract
Many industrial chemical processes are complex, multiphase and large scale
in nature. These processes are characterized by various nonlinear physiochemical
effects and fluid flows. Such processes often show coexistence of
fast and slow dynamics during their time evolutions. The increasing demand
for a flexible operation of a complex process, a pressing need to improve the
product quality, an increasing energy cost and tightening environmental regulations
make it rewarding to automate a large scale manufacturing process.
Mathematical tools used for process modeling, simulation and control are
useful to meet these challenges. Towards this purpose, development of process
models, either from the first principles (conservation laws) i.e. the rigorous
models or the inputoutput data based models constitute an important
step. Both types of models have their own advantages and pitfalls. Rigorous
process models can approximate the process behavior reasonably well. The
ability to extrapolate the rigorous process models and the physical interpretation
of their states make them more attractive for the automation purpose
over the inputoutput data based identified models. Therefore, the use of rigorous
process models and rigorous model based predictive control (RMPC)
for the purpose of online control and optimization of a process is very promising.
However, due to several limitations e.g. slow computation speed and
the high modeling efforts, it becomes difficult to employ the rigorous models
in practise. This thesis work aims to develop a methodology which will result
in smaller, less complex and computationally efficient process models from
the rigorous process models which can be used in real time for online control
and dynamic optimization of the industrial processes. Such methodology is
commonly referred to as a methodology of Model (order) Reduction. Model
order reduction aims at removing the model redundancy from the rigorous
process models.
The model order reduction methods that are investigated in this thesis,
are applied to two benchmark examples, an industrial glass manufacturing
process and a tubular reactor. The complex, nonlinear, multiphase fluid flow
that is observed in a glass manufacturing process offers multiple challenges to
any model reduction technique. Often, the rigorous first principle models of
these benchmark examples are implemented in a discretized form of partial
differential equations and their solutions are computed using the Computational
Fluid Dynamics (CFD) numerical tools. Although these models are
reliable representations of the underlying process, computation of their dynamic
solutions require a significant computation efforts in the form of CPU
power and simulation time.
The glass manufacturing process involves a large furnace whose walls
wear out due to the high process temperature and aggressive nature of the
molten glass. It is shown here that the wearing of a glass furnace walls result
in change of flow patterns of the molten glass inside the furnace. Therefore
it is also desired from the reduced order model to approximate the process
behavior under the influence of changes in the process parameters. In this
thesis the problem of change in flow patterns as result of changes in the
geometric parameter is treated as a bifurcation phenomenon. Such bifurcations
exhibited by the full order model are detected using a novel framework
of reduced order models and hybrid detection mechanisms. The reduced
order models are obtained using the methods explained in the subsequent
paragraphs.
The model reduction techniques investigated in this thesis are based on
the concept of Proper Orthogonal Decompositions (POD) of the process
measurements or the simulation data. The POD method of model reduction
involves spectral decomposition of system solutions and results into arranging
the spatiotemporal data in an order of increasing importance. The spectral
decomposition results into spatial and temporal patterns. Spatial patterns
are often known as POD basis while the temporal patterns are known as the
POD modal coefficients. Dominant spatiotemporal patterns are then chosen
to construct the most relevant lower dimensional subspace. The subsequent
step involves a Galerkin projection of the governing equations of a full order
first principle model on the resulting lower dimensional subspace.
This thesis can be viewed as a contribution towards developing the databased
nonlinear model reduction technique for large scale processes. The
major contribution of this thesis is presented in the form of two novel identification
based approaches to model order reduction. The methods proposed
here are based on the state information of a full order model and result into
linear and nonlinear reduced order models. Similar to the POD method
explained in the previous paragraph, the first step of the proposed identification
based methods involve spectral decomposition. The second step
is different and does not involve the Galerkin projection of the equation
residuals. Instead, the second step involves identification of reduced order
models to approximate the evolution of POD modal coefficients. Towards
this purpose, two different methods are presented. The first method involves
identification of locally valid linear models to represent the dynamic behavior
of the modal coefficients. Global behavior is then represented by ‘blending’
the local models. The second method involves direct identification of the
nonlinear models to represent dynamic evolution of the model coefficients.
In the first proposed model reduction method, the POD modal coefficients,
are treated as outputs of an unknown reduced order model that is to
be identified. Using the tools from the field of system identification, a blackbox
reduced order model is then identified as a linear map between the plant
inputs and the modal coefficients. Using this method, multiple local reduced
LTI models corresponding to various working points of the process are identified.
The working points cover the nonlinear operation range of the process
which describes the global process behavior. These reduced LTI models are
then blended into a single Reduced OrderLinear Parameter Varying (ROLPV)
model. The weighted blending is based on nonlinear splines whose
coefficients are estimated using the state information of the full order model.
Along with the process nonlinearity, the nonlinearity arising due to the wear
of the furnace wall is also approximated using the ROLPV modeling framework.
The second model reduction method that is proposed in this thesis allows
approximation of a full order nonlinear model by various (linear or nonlinear)
model structures. It is observed in this thesis, that, for certain class of full
order models, the POD modal coefficients can be viewed as the states of
the reduced order model. This knowledge is further used to approximate
the dynamic behavior of the POD modal coefficients. In particular, reduced
order nonlinear models in the form of tensorial (multivariable polynomial)
systems are identified. In the view of these nonlinear tensorial models, the
stability and dissipativity of these models is investigated.
During the identification of the reduced order models, the physical interpretation
of the states of the full order rigorous model is preserved. Due
to the smaller dimension and the reduced complexity, the reduced order
models are computationally very efficient. The smaller computation time
allows them to be used for online control and optimization of the process
plant. The possibility of inferring reduced order models from the state information
of a full order model alone i.e. the possibility to infer the reduced
order models in the absence of access to the governing equations of a full
order model (as observed for many commercial software packages) make the
methods presented here attractive. The resulting reduced order models need
further system theoretic analysis in order to estimate the model quality with
respect to their usage in an online controller setting.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  8 Feb 2010 
Place of Publication  Eindhoven 
Publisher  
Print ISBNs  9789038621548 
DOIs  
Publication status  Published  2010 