Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
255 If the order of approximations
M
is increased, the integral error is decreased notably. For example, for
= 3 M
and
= 4 M
the relative errors are equal to
6
= 4.8 10
−
∆ ⋅
and
6
= 1.1 10
−
∆ ⋅
, respectively. Note that the function
, z t
ϕ helps to detect
imperfection of the applied finite-dimensional model and gives one the possibility to develop new strategies for
model refinement [43].
VII. Conclusions and Outlook
In this paper, an adaptive control algorithm with parameter identification for trajectory tracking in
distributed heating systems has been proposed and discussed. This control strategy is based on the method
of integrodifferential relations, a variational approach, and the finite element technique. The principle scheme of
the adaptive control structure has been derived and its specific features have been considered in detail. A
verification of the proposed control laws is performed in numerical simulations taking into account the explicit
local and integral error estimates resulting directly from the MIDR.
In future work, the basic building blocks of the control strategy proposed in this paper will be applied to
more complex thermal systems. One of the goals is the use of model-based strategies for the control of the
temperature distribution in the interior of high- temperature SOFC fuel cell stacks after derivation of a
suitable control-oriented model. A corresponding test rig is currently being built up at the Chair of Mechatronics
of the University of Rostock. Finally, possibilities for the combination with stochastic state, parameter, and
disturbance estimation will be investigated to cope with the influence of measurement noise in a more
sophisticated way.
Acknowledgements
This work was supported by the Russian Foundation for Basic Research, project nos. 08-01-00234, 09-01-
00582, 10-01-00409 and the Leading Scientific Schools Grants NSh-3288.2010.1, NSh-64817.2010.1. This
project is furthermore supported by the German Research Foundation Deutsche Forschungsgemeinschaft DFG
under the grant number AS 1322-1.
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Authors’ information
1
Laboratory of Mechanics and Optimization of Structures, Institute for Problems in Mechanics of the Russian Academy of
Sciences, Pr. Vernadskogo 101-1, 119526 Moscow, Russia. E-mail:
saurinipmnet.ru
2
Laboratory of Mechanics of Controlled Systems, Institute for Problems in Mechanics of the Russian Academy of
Sciences, Pr. Vernadskogo 101-1, 119526 Moscow, Russia. E-mail:
kostinipmnet.ru
3
Chair of Mechatronics, University of Rostock, D-18059 Rostock, Germany.
E-mails: Andreas.Rauhuni-rostock.de
Harald.Aschemannuni-rostock.de
Vasily Vasilevich Saurin was born in Moscow
Region, Russia, on March 9, 1961. He received his diploma degree in aircraft strength from the
Moscow Institute of Physics and Technology, Moscow, Russia, in 1984 and his PhD degree
from the Kazan Aviation Institute, Kazan, Russia, in 1992.
He has published more than 70 papers in
international conferences and journals. His research interests are: modeling in mechanics, structural and shape optimization, variational
methods and numerical simulation for initial boundary value problems in physics.
Dr. Saurin is currently Senior Researcher of the Laboratory of Mechanics and Optimization of Structures, A. Ishlinsky Institute for
Problems in Mechanics of the Russian Academy of Sciences. In 2009 he was elected academician of the Russian Academy of Engineering.
Georgy Viktorovich Kostin was born in Rostov
Region, Russia, on October 13, 1965. He received his diploma degree in aircraft flight
dynamics and control from the Moscow Institute of Physics and Technology, Moscow, Russia, in
1988 and his PhD degree from the Keldysh Institute of Applied Mathematics of the Russian
Academy of Sciences, Moscow, Russia, in 1992.
He has published more than 70 papers in international conferences and journals. His research interests are: system dynamics, optimal control,
mechanics of solids, robotics, and modeling of structures. Dr. Kostin is currently Senior Researcher of the Laboratory of Control
Mechanical Systems at the A. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences. Since 2009 he has
been a Vice-Head of the Chair of Mechanics and Control Processes at the Moscow Institute of Physics and Technology State University.
Andreas Rauh was born in Munich, Germany,
on March 25, 1977. He received his diploma degree in electrical engineering and information
technology from the Technische Universität München, Munich, Germany, in 2001 and his
PhD degree Dr.-Ing. from the University of Ulm, Germany, in 2008.
He has published more than 50 publications in
international conferences and journals. His research interests are: state and parameter estimation for stochastic and set-valued uncertainties,
verified simulation of nonlinear uncertain systems, nonlinear, robust, and optimal control, interval methods for ordinary differential equations
as well as differential-algebraic systems. Dr. Rauh is currently with the Chair of Mechatronics, University of
Rostock, Germany, as post-doctoral researcher.
Harald Aschemann was born in Hildesheim,
Germany, on June 27, 1966. He received his diploma degree in mechanical engineering from
the University of Hanover, Germany, in 1994. After two years work in research and
development with a leading company in machine tools, where he worked on automated transfer
systems, he joined the Dept. of Measurement,
Control, and Microtechnology at the University of Ulm, Germany. He completed his Ph.D. Dr. Ing. on optimal trajectory planning and
trajectory control of an overhead travelling crane in 2001. From 2001 till 2006, he proceeded as Research Associate and lecturer at the same
department. Since 2006 Harald Aschemann has been a Full Professor and Head of
the Chair of Mechatronics at the University of Rostock, Germany. His research interests involve control-oriented modelling, identification,
nonlinear control, and simulation of mechatronic, robotic and thermofluidic systems.
Special Issue on Heat Transfer, February 2011
Manuscript received and revised January 2011, accepted February 2011 Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved
257
Simulation of Thermal Transfer Process in Cast Ingots at Electron Beam Melting and Refining
Katia Zh. Vutova, Elena G. Koleva, Georgi M. Mladenov
Abstract – Computer simulations of the heat transfer processes at electron beam melting and refining is a tool for better understanding and choice of optimal regimes of application of this
expensive modern technology. The heat exchange at different interfaces between the casting ingot and both the water-cooled crucible and the pulling mechanism is studied. Radiation and
evaporation losses from the top molten surface of drip cast ingots are also evaluated. Regression equations for the heat flows through the concrete boundary surfaces, as well as for the volume of
the molten metal pool have been created. They are considered as functions of the coefficients of the heat transfer and the width of the heat contact ring between the top part of the casting ingot
and the copper crucible. The response surface plots are obtained to visualize these dependences. They can be used for choosing proper process conditions and for the optimization of the heat
flows according to the process requirements. Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved.
Keywords:
Electron Beam, Heat Transfer, Crucible, Molten Pool, Cast Ingot
I. Introduction
