📄 level2.htm
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FDC help: Level 2
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<h2>
Level 2 of the system <i>Beaver</i>: '<i>Beaver dynamics and output
equations</i>'
</h2>
<p>The actual dynamic model of the 'Beaver' aircraft, consisting of twelve
state and many output equations, is contained in level 2 of the system <i>Beaver</i> (or its subsystem equivalents). This level clearly visualizes the modular structure of the aircraft model. The full
name of this subsystem is <i>Beaver dynamics and output equations</i>, but
it will be denoted as <i>Level 2</i> here.</p>
<p>Since earlier versions of Simulink did not accept
vector signals to be sent through <i>Inport</i> and <i>Outport</i> blocks
in the first level of a graphical system, an additional I/O level with <i>Mux</i>, <i>Demux</i>, <i>Inport</i>, and <i>Outport</i> blocks was included in the model; this additional level has been shortly denoted as <i><a href="level1.htm">Level 1</a></i>. Nowadays, this additional I/O level is not really required anymore; it is planned to change this solution in future versions of the FDC toolbox.</p>
<h3>
Subsystems in <i>Level 2</i>
</h3>
<i>Level 2</i> contains the following subsystems (masked subsystems are
denoted by {M}):<br>
<br>
<div align="center">
<table>
<tr>
<td align="LEFT">
<i><a href="adgrp.htm">Airdata Group</a></i>
</td>
</tr>
<tr>
<td>
<i><a href="aerogrp.htm">Aerodynamics Group (Beaver)</a></i>
</td>
</tr>
<tr>
<td>
<i><a href="enggrp.htm">Engine Group (Beaver)</a></i>
</td>
</tr>
<tr>
<td>
<i><a href="gravity.htm">Gravity</a></i>
</td>
<td align="CENTER">
{M}
</td>
</tr>
<tr>
<td>
<i><a href="fwind.htm">Fwind</a></i>
</td>
<td align="CENTER">
{M}
</td>
</tr>
<tr>
<td>
<i><a href="fmsort.htm">FMsort</a></i>
</td>
<td align="CENTER">
{M}
</td>
</tr>
<tr>
<td>
<i><a href="eqmotion.htm">Aircraft Equations of Motion
(Beaver)</a></i>
</td>
<td align="CENTER">
{M}
</td>
</tr>
<tr>
<td>
<i><a href="moreouts.htm">Additional Outputs</a></i>
</td>
</tr>
<tr>
<td>
<i><a href="hlpfcn.htm">Hlpfcn</a></i>
</td>
<td align="CENTER">
{M}
</td>
</tr>
</table>
</div>
<p>Subsystems that are denoted with the
extension '(Beaver)' contain aircraft-dependent
elements (currently configured for the 'Beaver' aircraft). All masked blocks and the light-blue colored subsystems have been linked to a blocklibrary.</p>
<h3>
Structure of <i>Level 2</i>
</h3>
<p>The system should be 'read' from top to bottom and from left to
right. The upper-left subsystem is the block <i>Airdata Group</i>. Some of
the results of this block are needed by other subsystems, e.g. for the determination of forces and
moments, which is why those blocks have been shifted further rightwards and
downwards. The different contributions to the external forces and moments
are added and sorted in the block <i>FMsort</i>, so this block is located
on the lower right side of the forces and moments blocks. One step further
right and downwards are the subsystems <i>Aircraft Equations of Motion</i>
and <i>Additional Outputs</i>, which use the main results from the other
blocks.</p>
<p>Since the subsystem <i>Additional Outputs</i> also needs time-derivatives
of the state variables, a 'feedback loop' of <i>xdot</i> has been included in
the blockdiagram. This does not result in an algebraic loop, because the
Ordinary Differential Equations for the twelve states of the aircraft are
in no way involved in this loop (the outputs are called
'additional' because they don't represent interim results for
the solution of the state equations themselves).</p>
<p>In general, all (masked) subsystems use results from other blocks which
are located on their left side, and their outputs are sent
to blocks on their right-hand side, if necessary. Their vertical position makes it possible to
connect their outputs to the <i>Outport</i> blocks on the far right side in
this second level of <i>Beaver</i>.</p>
<p>The only exceptions to this 'rule' are the ('artificial')
feedback loops of the state vector <i>x</i>, its time-derivative
<i>xdot</i>, and the outputvector <i>yhlp</i> from the block <i>Hlpfcn</i>,
which contains a number of frequently used sines and cosines.</p>
<h3>
Inputs to <i>Level 2</i>
</h3>
<pre>
uaero = [deltae deltaa deltar deltaf]' (aerodynamic inputs)
uprop = [n pz]' (engine inputs)
uwind = [uw vw ww uwdot vwdot wwdot]' (atmospheric disturban-
ces; wind & turbulence)
</pre>
<h3>
Outputs from <i>Level 2</i>
</h3>
<pre>
x = [V alpha beta p q r psi theta phi xe ye H]' (states)
xdot = dx/dt (time-derivatives of states)
ybvel = [u v w]' (body-axes velocity components)
yuvw = [udot vdot wdot]' (time-derivatives of u, v, and w)
ydl = [pb/2V qc/V rb/2V]' (dimensionless rotational veloci-
ties along aircraft's body-axes)
yfp = [gamma fpa chi Phi]' (flightpath variables)
ypow = [dpt P]' (engine power (-related) outputs)
yacc = [Ax Ay Az axk ayk azk]' (accelerations and specific
forces in aircraft's c.g.)
Caero = [CXa CYa CZa Cla Cma Cna]' (aerodyn. force & moment
coefficients)
Cprop = [CXp CYp CZp Clp Cmp Cnp]' (engine force & moment
coefficients)
FMaero= [Xa Ya Za La Ma Na]' (aerodyn. forces & moments)
FMprop= [Xp Yp Zp Lp Mp Np]' (engine forces & moments)
Fgrav = [Xgr Ygr Zgr]' (gravity forces)
Fwind = [Xw Yw Zw]' (forces due to wind & turbulence)
yatm = [rho ps T mu g]' (atmosphere variables)
yad1 = [a M qdyn]' (airdata variables)
yad2 = [qc Ve Vc]' (more airdata variables)
yad3 = [Tt Re Rc]' (more airdata variables)
</pre>
<p>See the lists of <a href="inputs.htm">input</a> and <a href=
"outputs.htm">output</a> variables for the exact definitions of these
variables. Also, please take a look at the <a href="colors.htm">color definitions</a> for the
block-diagrams of the FDC toolbox.</p>
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