From 7d24d5dc25af90d75020b8d0236e5f865a87cf73 Mon Sep 17 00:00:00 2001 From: Henrik Tidefelt Date: Mon, 8 Jun 2020 01:01:37 +0200 Subject: [PATCH] Remove exaggerated emphasis with \textbf in equation/variable balance examples As it's clear from the context that these examples are all about these concepts anyway, it didn't seem motivated to make these terms stand out more with something like \emph. --- chapters/classes.tex | 59 +++++++++++++++----------------------------- 1 file changed, 20 insertions(+), 39 deletions(-) diff --git a/chapters/classes.tex b/chapters/classes.tex index a17f5f9bb..b32e1b7a6 100644 --- a/chapters/classes.tex +++ b/chapters/classes.tex @@ -1146,25 +1146,16 @@ \section{Balanced Models}\doublelabel{balanced-models} \end{align*} and 2 equations corresponding to the 2 flow-variables \lstinline!p.i! and \lstinline!n.i!. -These are 5 equations in 5 unknowns (\textbf{locally} -\textbf{balanced model}). A more detailed analysis would reveal that -this is \textbf{structurally non-singular}, i.e. that the hybrid DAE -will not contain a singularity independent of actual values. - -If the equation \lstinline!u = p.v - n.v! would be missing in the -Capacitor model, there would be 4 equations in 5 unknowns and the model -would be \textbf{locally} \textbf{unbalanced} and thus simulation models -in which this model is used would be usually structurally singular and -thus not solvable. - -If the equation \lstinline!u = p.v - n.v! would be replaced by the -equation \lstinline!u = 0! and the equation \lstinline!C*der(u) = p.i! would -be replaced by the equation \lstinline!C*der(u) = 0!, there would be 5 -equations in 5 unknowns (\textbf{locally} \textbf{balanced}), but the -equations would be \textbf{singular}, regardless of how the equations -corresponding to the flow-variables are constructed because the -information that \lstinline!u! is constant is given twice in a slightly -different form. +These are 5 equations in 5 unknowns (locally balanced model). A more detailed analysis would reveal that this is structurally non-singular, i.e. that +the hybrid DAE will not contain a singularity independent of actual values. + +If the equation \lstinline!u = p.v - n.v! would be missing in the \lstinline!Capacitor! model, there would be 4 equations in 5 unknowns and the model +would be locally unbalanced and thus simulation models in which this model is used would be usually structurally singular and thus not solvable. + +If the equation \lstinline!u = p.v - n.v! would be replaced by the equation \lstinline!u = 0! and the equation \lstinline!C*der(u) = p.i! would be +replaced by the equation \lstinline!C*der(u) = 0!, there would be 5 equations in 5 unknowns (locally balanced), but the equations would be singular, +regardless of how the equations corresponding to the flow-variables are constructed because the information that \lstinline!u! is constant is given twice +in a slightly different form. \end{example} \begin{example} @@ -1200,9 +1191,7 @@ \section{Balanced Models}\doublelabel{balanced-models} end Circuit; \end{lstlisting} -Since \lstinline!t! is partial we cannot check whether this is a -\textbf{globally balanced model}, but we can check that \lstinline!Circuit! -is \textbf{locally balanced}. +Since \lstinline!t! is partial we cannot check whether this is a globally balanced model, but we can check that \lstinline!Circuit! is locally balanced. Counting on model \lstinline!Circuit! results in the following balance sheet: @@ -1219,9 +1208,7 @@ \section{Balanced Models}\doublelabel{balanced-models} \end{align*} and 2 equation corresponding to the flow variables \lstinline!p.i!, \lstinline!n.i!. -In total we have 8 scalar unknowns and 8 scalar equations, i.e., a -\textbf{locally} \textbf{balanced model} (and this feature holds for any -models used for the replaceable component \lstinline!t!). +In total we have 8 scalar unknowns and 8 scalar equations, i.e., a locally balanced model (and this feature holds for any models used for the replaceable component \lstinline!t!). Some more analysis reveals that this local set of equations and unknowns is structurally non-singular. However, this does not provide @@ -1359,7 +1346,7 @@ \section{Balanced Models}\doublelabel{balanced-models} $2 + \text{\lstinline!nXi!}$ flow variables in the \lstinline!port! connector. \end{itemize} -Therefore, \lstinline!DynamicVolume! is a \textbf{locally balanced} model. +Therefore, \lstinline!DynamicVolume! is a locally balanced model. Note, when the \lstinline!DynamicVolume! is used and the \lstinline!Medium! model is redeclared to \lstinline!SimpleAir!, then a tool will try @@ -1410,19 +1397,13 @@ \section{Balanced Models}\doublelabel{balanced-models} $2 + \text{\lstinline!nXi!}$ flow variables in the \lstinline!port! connector. \end{itemize} -Therefore, \lstinline!FixedBoundary_pTX! is a \textbf{locally -balanced} model. The predefined boundary variables \lstinline!p! and \lstinline!Xi! -are provided via equations to the input arguments \lstinline!medium.p! -and \lstinline!medium.Xi!, in addition there is an equation for \lstinline!T! -in the same way -- even though \lstinline!T! is not an input. Depending -on the flow direction, either the specific enthalpy in the port -(\lstinline!port.h!) or h is used to compute the enthalpy flow rate -\lstinline!H_flow!. \lstinline!h! is provided as binding equation to the medium. With -the equation \lstinline!medium.T = T!, the specific enthalpy \lstinline!h! of the -reservoir is indirectly computed via the medium equations. Again, this -demonstrates, that an \lstinline!input! just defines the number of equations -have to be provided, but that it not necessarily defines the -computational causality. +Therefore, \lstinline!FixedBoundary_pTX! is a locally balanced model. The predefined boundary variables \lstinline!p! and \lstinline!Xi! are +provided via equations to the input arguments \lstinline!medium.p! and \lstinline!medium.Xi!, in addition there is an equation for \lstinline!T! +in the same way --- even though \lstinline!T! is not an input. Depending on the flow direction, either the specific enthalpy in the port +(\lstinline!port.h!) or \lstinline!h! is used to compute the enthalpy flow rate \lstinline!H_flow!. \lstinline!h! is provided as binding equation +to the medium. With the equation \lstinline!medium.T = T!, the specific enthalpy \lstinline!h! of the reservoir is indirectly computed via the +medium equations. Again, this demonstrates, that an \lstinline!input! just defines the number of equations have to be provided, but that it not +necessarily defines the computational causality. \end{example} \section{Predefined Types and Classes}\doublelabel{predefined-types-and-classes}