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Simulation, Parameter Estimation and Optimization
of an Industrial-Scale Evaporation System
Ines Mynttinen, Erich Runge, and Pu Li
Technische Universitat Ilmenau, Helmholtzplatz 5, 98693 Ilmenau, Germany
{
ines.mynttinen,erich.runge,pu.li
}
@tu-ilmenau.de
Abstract.
Design and operation of complex industrial systems can be improved
based on simulation and optimization using physical process models. However,
this endeavor is particularly challenging for hybrid systems, where in addition
to the continuous evolution described by differential algebraic equations the dy-
namic process shows instantaneous switches between different operating modes.
In this study, we consider parameter estimation for an industrial evaporation sys-
tem with discrete mode switches due to phase transitions. Simulation results of
the hybrid evaporator model are compared with those of a smooth evaporator
model. A smoothing approach is applied in order to modify the hybrid model
such that the discrete transitions are integrated into the system of differential
algebraic equations. This leads to exclusively smooth trajectories, making the
model suitable for parameter estimation to be solved by means of gradient-based
optimization methods. The dependence of the parameter estimation results on the
smoothing parameter is investigated.
Keywords:
Parameter estimation, Nonlinear dynamic optimization, Large-scale
hybrid systems.
1
Introduction
Simulation and optimization based on physical models are state-of-the-art tools in de-
sign and operation of complex industrial systems. Optimization problems result from
many tasks such as parameter estimation, data validation, safety verification and model
predictive control. The underlying model is given by the dynamic equations of the
process under consideration and possibly additional equality and inequality constraints
resulting, e.g., from safety specifications. The objective function depends on the
particular task. Several powerful methods and computer codes are available for opti-
mization problems which include only continuous system models expressed as a set of
differential algebraic equations (DAEs). Unfortunately, in many processes occurring in,
e.g., chemical industries, power plants and oil refineries, continuous and discrete state
dynamics are coupled strongly. Such systems with mixed continuous and discrete dy-
namics are called hybrid systems. The discrete dynamics can result from instantaneous
autonomous or from controlled (externally triggered) transitions from one operating
regime to another. In the time periods between these transition points, the state vari-
ables of the system evolve continuously according to the DAEs of the respective op-
eration mode. The trajectories of the state variables are in general non-smooth or even
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