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#: ../../source/behavior/equations/electrical.rst:4
msgid "An Electrical Example"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:6
msgid ""
"Let us return now to an engineering context.  For readers who are more "
"familiar with electrical systems, consider the following circuit:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:17
msgid "Low-Pass RLC Filter"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:19
msgid ""
"Suppose we want to solve for: :math:`V`, :math:`i_L`, :math:`i_R` and "
":math:`i_C`.  To solve for each of the currents :math:`i_L`, :math:`i_R` and"
" :math:`i_C`, we can use the equations associated with inductors, resistors "
"and capacitors, respectively:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:29
msgid "where :math:`V_b` is the battery voltage."
msgstr ""

#: ../../source/behavior/equations/electrical.rst:31
msgid ""
"Since we have only 3 equations, but 4 variables, we need one additional "
"equation.  That additional equation is going to be Kirchoff's current law:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:37
msgid ""
"Now that we have determined the equations and variables for this problem, we"
" will create a basic model (including physical types) by translating the "
"equations directly into Modelica.  But in a later section on :ref"
":`electrical-components` we will return to this same circuit and demonstrate"
" how to create models by dragging, dropping and connecting models that "
"really look like the circuit components in our :ref:`low-pass-rlc`."
msgstr ""

#: ../../source/behavior/equations/electrical.rst:45
msgid ""
"But for now, we will build a model composed simply of variables and "
"equations.  Such a model could be written as follows:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:52
msgid ""
"Let's go through this example bit by bit and reinforce the meaning of the "
"various statements.  Let's start at the top:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:59
msgid ""
"Here we see that the name of the model is ``RLC1``.  Furthermore, a "
"description of this model has been included, namely ``\"A resistor-inductor-"
"capacitor circuit model\"``.  Next, we introduce a few physical types that "
"we will need:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:68
msgid ""
"Each of these lines introduces a physical type that specializes the built-in"
" ``Real`` type by associating it with a particular physical unit.  Then, we "
"declare all of the ``parameter`` variables in our problem:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:77
msgid ""
"These ``parameter`` variables represent various physical characteristics (in"
" this case, voltage, inductance, resistance and capacitance, respectively)."
"  The last variables we need to define are the ones we wish to solve for, "
"*i.e.*,"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:86
msgid ""
"Now that all the variables have been declared, we add an ``equation`` "
"section to the model that specifies the equations to use when generating "
"solutions for this model:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:94
msgid ""
"Finally, we close the model by creating an ``end`` statement that includes "
"the ``model`` name (*i.e.*, ``RLC1`` in this case):"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:103
msgid ""
"One thing that distinguishes this example from the previous examples is the "
"fact that it contains more equations.  As with the ``NewtonCooling`` "
"example, we have some equations with expressions on both the left and right "
"hand sides.  We also have a mix of differential equation (ones that include "
"the derivative of a variable) and others that are simply algebraic "
"equations."
msgstr ""

#: ../../source/behavior/equations/electrical.rst:110
msgid ""
"This further emphasizes the point that in Modelica it is not necessary to "
"put the system of equations into the so-called \"explicit state-space form\""
" required in some modeling environments.  We could, of course, rearrange the"
" equations into a more explicit form like this:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:120
msgid ""
"But the important point is that with Modelica, we do not need to perform "
"such manipulations.  Instead, we are free to write the equations in whatever"
" form we chose."
msgstr ""

#: ../../source/behavior/equations/electrical.rst:124
msgid ""
"Ultimately, these equations will probably need to be manipulated into a form"
" like explicit state-space form.  But if such manipulations are necessary, "
"it will be the responsibility of the Modelica compiler, not the model "
"developer, to perform these manipulations.  This eliminates the need for the"
" model developer to deal with this tedious, time consuming and error prone "
"task."
msgstr ""

#: ../../source/behavior/equations/electrical.rst:131
msgid ""
"The ability to keep equations in their \"textbook form\" is important "
"because, as we will show in later sections, we eventually want to get to the"
" point where these equations are \"captured\" in individual components "
"models.  In those cases, we won't know (when we create the component model) "
"exactly what variable each equation will be used to solve for.  Making such "
"manipulations the responsibility of the Modelica compiler not only makes the"
" model development faster and easier, but it dramatically improves the "
"**reusability** of the models."
msgstr ""

#: ../../source/behavior/equations/electrical.rst:141
msgid "The following figure shows the dynamic response of the ``RLC1`` model:"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:0
msgid "Expanding on these electrical examples"
msgstr ""

#: ../../source/behavior/equations/electrical.rst:148
msgid ""
"As mentioned in the :ref:`preface`, the structure of this book allows us to "
"explore a more hypermedia based approach in which readers are encouraged to "
"process the material that is most aligned with their goals and interests.  "
"The next chapter will present a model whose equations are derived from a "
"mechanical system.  If you would prefer instead to see this electrical "
"example extended to include more complex behavior, you may want to skip "
"ahead to the :ref:`switched-rlc` example."
msgstr ""

#: ../../source/behavior/equations/electrical.rst:101
msgid "state-space form"
msgstr ""
