📄 level2.htm
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<TITLE>FDC help: Level 2</TITLE>
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<H2>Level 2 of the system <I><FONT FACE="Arial","Helvetica","Sans Serif">Beaver</FONT></I>: '<I><FONT FACE="Arial","Helvetica","Sans Serif">Beaver dynamics and output equations</FONT></I>'</H2>
The actual model of the 'Beaver' dynamics, consisting of twelve state and many output equations, is contained in level 2 of the system <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Beaver</FONT></I>. This is therefore the main level of the system, which clearly visualizes the modular structure of the aircraft model. The full name of this subsystem is <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Beaver dynamics and output equations</FONT></I>, but it will be denoted as <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Level 2</FONT></I> here. Since S<SMALL>IMULINK</SMALL> does not accept vector signals to be sent through <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Inport</FONT></I> and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Outport</FONT></I> blocks within the first level of a graphical system, it was necessary to include an additional I/O level with <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Mux</FONT></I>, <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Demux</FONT></I>, <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Inport</FONT></I>, and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Outport</FONT></I> blocks as well. This additional level was shortly denoted as <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="level1.htm">Level 1</A></FONT></I>. Of course, this is a serious limitation of S<SMALL>IMULINK</SMALL>, and it is hoped that this problem will be solved in future versions of that program.
<H3>Subsystems in <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Level 2</FONT></I></H3>
<I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Level 2</FONT></I> contains the following subsystems (masked subsystems are denoted by {M}):<BR><BR>
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<TR><TD ALIGN=LEFT><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="adgrp.htm">Airdata Group</A></FONT></I>
</TD></TR>
<TR><TD><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="aerogrp.htm">Aerodynamics Group (Beaver)</A></FONT></I></TD></TR>
<TR><TD><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="enggrp.htm">Engine Group (Beaver)</A></FONT></I>
</TD></TR>
<TR><TD><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="gravity.htm">Gravity</A></FONT></I></TD><TD ALIGN=CENTER>{M}</TD></TR>
<TR><TD><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="fwind.htm">Fwind</A></FONT></I></TD><TD ALIGN=CENTER>{M}</TD></TR>
<TR><TD><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="fmsort.htm">FMsort</A></FONT></I></TD><TD ALIGN=CENTER>{M}</TD></TR>
<TR><TD><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="eqmotion.htm">Aircraft Equations of Motion (Beaver)</A></FONT></I></TD><TD ALIGN=CENTER>{M}</TD></TR>
<TR><TD><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="moreouts.htm">Additional Outputs</A></FONT></I></TD></TR>
<TR><TD><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="hlpfcn.htm">Hlpfcn</A></FONT></I></TD><TD ALIGN=CENTER>{M}</TD></TR>
</TABLE><BR>
In those cases where the name of a subsystem has been enhanced with the extension '(Beaver)', the subsystem contains aircraft-dependent elements (currently configured for the 'Beaver' aircraft). The masked subsystem blocks only contain a small set of equations, whereas the other subsystem blocks contain more masked
or unmasked subsystems. In order to review the internal structure of the masked subsystems, it is necessary to unmask these systems first. Help-texts are available for all subsystem blocks.
<H3>Structure of <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Level 2</FONT></I></H3>
The system should be 'read' from top to bottom and from left to right. The upper-left subsystem is the block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Airdata Group</FONT></I>. Some of the results of this block are needed by others, for computing 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><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">FMsort</FONT></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><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Aircraft Equations of Motion</FONT></I> and <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Additional Outputs</FONT></I>, which use the main results from the other blocks.<BR><BR>
Since the subsystem <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Additional Outputs</FONT></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).<BR><BR>
In general, all (masked) subsystems use results from other blocks which are located on their left side, and the outputs of all subsystems are send to other blocks, located on their right side, if necessary. The different subsystems also have different vertical positions, in order to be able to connect their outputs to the <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Outport</FONT></I> blocks on the far right side in this second level of <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Beaver</FONT></I>.<BR><BR>
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><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Hlpfcn</FONT></I>, which contains a number of frequently used sines and cosines. The block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Hlpfcn</FONT></I> is the only one which uses an input vector that enters the block on the right side and an output vector which leaves the block on the left side.
<H3>Inputs to <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Level 2</FONT></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><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Level 2</FONT></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>
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. See also the <A HREF="colors.htm">color definitions</A> for the block-diagrams of the FDC toolbox (in particular the system <A HREF="beaver.htm"><I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">Beaver</FONT></I></A>).
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