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Talks and Poster Presentations (with Proceedings-Entry):

B. Heinzl, M. Rößler, A. Körner, G. Zauner, H. Ecker, F. Breitenecker:
"BCP - A Benchmark for Teaching Structural Dynamical Systems";
Talk: MATHMOD 2012 - 7th Vienna Conference on Mathematical Modelling, Wien; 2012-02-14 - 2012-02-17; in: "Preprints Mathmod 2012 Vienna - Full Paper Volume", F. Breitenecker, I. Troch (ed.); Argesim / Asim, 38 (2012), 254 - 255.



English abstract:
Introduction. Since 2000, the relatively old CSSL standard (Continuous System Simulation Language) for simulation
of continuous systems has become obsolete and new standards and techniques for system simulation are
arising. At modelling level, object-oriented modelling or component-based modelling has introduced a new era
for multi-domain modelling of physical systems (physical modelling). With Modelica [1] and with competitive
VHDL-AMS, modelling languages with a certain standard have emerged using component-based modelling with
acausal relations.
From a mathematical viewpoint, instead of classical explicit state space descriptions with an ODE system, physical
modelling techniques very often result in (semi-) implicit differential-algebraic equation systems (DAE). The
additional algebraic equations emerge new problems, which relate to the simulation level. As a consequence,
the simulator must either be capable of automatic symbolic ´extension´ of the system (index reduction) or the
model description has to be split into different models where algebraic conditions control switching between these
models, leading to handling a structural dynamic system and requiring features for state event handling [2].
Three case studies allow investigation of new approaches and modelling techniques for hybrid or structural dynamic
systems with emphasis on physical modelling techniques and state event modelling [3]. These examples are
also well suited to be used in education for teaching event handling, hybrid and structural dynamic systems.
Case Study 1: Bouncing Ball. The classical example of a ball bouncing on a surface allows various modelling
approaches and incorporates events. A first modelling approach for the bouncing ball dynamics recognizes two
different phases: the free falling phase (flying phase) with or without air resistance, and a ´timeless´ contact phase,
where the ball hits the ground and changes direction of movement. A more realistic model takes into account the
elasticity in the contact region by modelling the deformation with a spring-damper-element (Kelvin-Voigt model).
The contact phase in this case is not an isolated event anymore, it consumes time. Beginning and end of the contact
phase are controlled by state events.
Case Study 2: Switching RLC Circuit. The second case study defines an extension of a class-E amplifier
including a diode. It aims for investigation of modelling techniques and efficient calculation of switching elements
(i.e. time events and state events) and for physical modelling of circuits or similar methods. One switching element
is represented by a time-variant resistor, which switches continuously via a fast transition between high and low
resistance values. Modelling such a variable resistor seems to be a trivial task, although some variants are possible.
The chosen approach may have advantages or disadvantages in combination with event handling.
Switching in a circuit may also be designed by a diode as an active switch with dynamic behaviour. Simple diode
models mimic the dynamic behaviour as an ideal switch, possibly with threshold voltage, other (more realistic)
diode models use e.g. the Shockley equation defining nonlinear algebraic conditions.
Case Study 3: Rotating Pendulum with Free Flight Phase. The third example discusses an idealized rotating
pendulum on a rope with damping. It has to be distinguished between two different states: The rotation phase
where the mass is moving along a circular path and the flying phase where the rope is loose due to gravitation and
the mass is free falling. Additional state-dependent algebraic equations define switching conditions for transition
between the models. Since the two states have different numbers of degrees of freedom, i.e. the state space
dimension changes cyclically as the pendulum alters its state, this model represents a structural dynamic system.

Created from the Publication Database of the Vienna University of Technology.