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Add clocked variables in DAE-chapter.
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Just the minimal so that they don't look totally forgotten.
Closes #2286
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HansOlsson committed Dec 15, 2020
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Expand Up @@ -144,6 +144,8 @@ \chapter{Modelica DAE Representation}\label{modelica-dae-representation}
end loop
\end{lstlisting}

Clocked variables are handled similarly as $z$ and $m$ (depending on type), but using \lstinline!previous! instead of \lstinline!pre! and only solved in the first iteration of the event-loop.

Solving \eqref{eq:hydrid-dae} for the unknowns is non-trivial, because this set of equations contains not only \lstinline!Real!, but also discrete-valued unknowns.
Usually, in a first step these equations are sorted and in many cases the discrete-valued unknowns $m$ can be just computed by a forward evaluation sequence.
In some cases, there remain systems of equations involving $m$ due to cyclic dependencies with $y$ and $z$ (e.g.\ for ideal diodes, Coulomb friction elements), and specialized algorithms have to be used to solve them.
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