📄 xyhdot.htm
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<TITLE>FDC help: xyHdot</TITLE>
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<H2>Subsystem <I><FONT FACE="Arial","Helvetica","Sans Serif">xyHdot</FONT></I></H2>
<I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">xyHdot</FONT></I> is a masked S<SMALL>IMULINK</SMALL> subsystem which is contained in the sub-subsystem <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="12odes.htm">12 ODEs</A></FONT></I> of the subsystem <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="eqmotion.htm">Aircraft Equations of Motion (Beaver)</A></FONT></I>, within the S-function <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="beaver.htm">Beaver</A></FONT></I>. It computes time-derivatives of the coordinates <I>x<SUB>e</SUB></I> and <I>y<SUB>e</SUB></I> and the altitude <I>H</I>, being the last three state variables of the nonlinear aircraft model. The remaining nine differential equations are stored in the subsystems <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="vabdot.htm">Vabdot</A></FONT></I>, <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="pqrdot.htm">pqrdot</A></FONT></I>, and <FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><I><A HREF="eulerdot.htm">Eulerdot</A></I></FONT>, which are all contained in <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">12 ODEs</FONT></I>.
<H3>Inputvector: <I>uxyh</I>
</H3>
<PRE> uxyh = [x' Ftot' Mtot' yhlp'], and [u+uw v+vw w+ww]'.
x = [V alpha beta p q r psi theta phi xe ye H]' (states)
Ftot = [Fx Fy Fz]' (total forces along the body-axes,
computed in the block <A HREF="fmsort.htm">FMsort</A>)
Mtot = [L M N]' (total moments along the body-axes,
computed in the block <A HREF="fmsort.htm">FMsort</A>)
yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) ...
... tan(beta) sin(psi) cos(psi) sin(theta) ...
... cos(theta) sin(phi) cos(phi)]'
(frequently used sines & cosines, computed in <A HREF="hlpfcn.htm">Hlpfcn</A>)
[u+uw v+vw w+ww]' = [u v w]' + [uw vw ww]' = ybvel + uwind(1:3);
</PRE>
<I>ybvel</I> is computed in the masked subsystem block <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif"><A HREF="uvw.htm">uvw</A></FONT></I>, <I>uwind</I> is an external inputvector with atmospheric disturbances.
<PRE> {V : airspeed [m/s] }
{alpha: angle of attack [rad] }
{beta : sideslip angle [rad] }
{p : roll rate [rad/s] }
{q : pitch rate [rad/s] }
{r : yaw rate [rad/s] }
psi : yaw angle [rad]
theta: pitch angle [rad]
phi : roll angle [rad]
{xe : x-coordinate in Earth-fixed reference frame [m] }
{ye : y-coordinate '' '' '' '' [m] }
{H : altitude above sea-level [m] }
{Fx, Fy, Fz: total forces along the aircraft's body-axes [N] }
{L, M, N : total moments along the aircraft's body-axes [Nm] }
u : component of the airspeed V along the XB-axis [m/s]
v : component of the airspeed V along the YB-axis [m/s]
w : component of the airspeed V along the ZB-axis [m/s]
uw : component of wind + turbulence along XB-axis [m/s]
vw : component of wind + turbulence along YB-axis [m/s]
ww : component of wind + turbulence along ZB-axis [m/s]
</PRE>
The inputvariables which are not actually used by <I><FONT SIZE=2 FACE="Arial","Helvetica","Sans Serif">xyHdot</FONT></I> have been displayed between accolades.
<H3>Outputvector: <I>yxyh</I>
</H3>
<PRE> yxyh = [xdot ydot Hdot]'
xdot = d(xe)/dt [m/s]
ydot = d(ye)/dt [m/s]
Hdot = dH/dt [m/s]
</PRE>
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