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FDC help: Additional Outputs
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<h2>
Subsystem <i>Additional Outputs</i>
</h2>
<p>The subsystem <i>Additional Outputs</i> of the <i><a href="beaver.htm">Beaver</a></i> model computes a number output signals that were not needed for
solving the equations of motion, and which could not logically be placed in
one of the other subsystems (i.e. <i><a href="adgrp.htm">Airdata
Group</a></i>, <i><a href="aerogrp.htm">Aerodynamics Group</a></i>, <i><a
href="enggrp.htm">Engine Group</a></i>, or <i><a href=
"eqmotion.htm">Aircraft Equations of Motion</a></i>). Deleting
<i>Additional Outputs</i> from the system <i>Beaver</i> will not affect the
solution of the equations of motion. It is easy to add more output
equations to the list that is currently contained in this subsystem.</p>
<p>Since the outputs from this subsystem are not involved in the actual
solution of the state equations, the outputs may depend not only upon the
state-vector <i>x</i> and the inputvectors <i>uaero</i>, <i>uprop</i>, and
<i>uwind</i>, but also upon the time-derivative of the state vector,
<i>xdot</i>. If the outputs from the subsystem <i>Additional Outputs</i>
would have been needed for solving the state equations, this would not be
possible (or at least undesirable), because it would yield an algebraic
loop and it wouldn't have been possible anymore to delete the subsystem <i>Additional Outputs</i> without affecting the solution of the
state equations.</p>
<p>By default, <i>Additional Outputs</i> contains masked subsystem blocks
<i><a href="accel.htm">Accel</a></i>, <i><a href=
"flpath.htm">Flpath</a></i>, and <i><a href="uvwdot.htm">uvwdot</a></i>,
which determine accelerations and specific forces, flightpath variables,
and time-derivatives of the velocity components <i>u</i>, <i>v</i>, and
<i>w</i>, respectively (note: <i>u</i>, <i>v</i>, and <i>w</i> are
<u>not</u> state variables!). More output equations may be included in this
subsystem if desired.</p>
<h3>
Inputs: <i>x</i>, <i>xdot</i>, <i>yhlp</i>, <i>Ftot</i>, <i>Fgrav</i>
</h3>
<pre>
x = [V alpha beta p q r psi theta phi xe ye H]' (states)
xdot = dx/dt = [Vdot alphadot betadot pdot qdot rdot ...
... psidot thetadot phidot xedot yedot Hdot]'
(time-derivative of state-vector)
yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) tan(beta) ...
... sin(psi) cos(psi) sin(theta) cos(theta) ...
... sin(phi) cos(phi) ]'
(sines & cosines, computed in the block <a href=
"hlpfcn.htm">Hlpfcn</a>)
Ftot = [Fx Fy Fz]' (total forces along body-axes,
computed in the block <a href=
"fmsort.htm">FMsort</a>)
Fgrav= [Xgr Ygr Zgr]' (gravity forces along body-axes,
computed in the block <a href=
"gravity.htm">Gravity</a>)
V : airspeed [m/s]
{alpha : angle of attack [rad] or [deg] }
beta : sideslip angle [rad] or [deg]
{p : roll-rate [rad/s] or [deg/s] }
{q : pitch-rate [rad/s] or [deg/s] }
{r : yaw-rate [rad/s] or [deg/s] }
psi : yaw-angle [rad] or [deg]
theta : pitch-angle [rad] or [deg]
phi : roll-angle [rad] or [deg]
{xe : X-coordinate in Earth-axes [m] }
{ye : Y-coordinate in Earth-axes [m] }
{H : altitude [m] }
Vdot : time-derivative of airspeed [m/s^2]
alphadot : time-derivative of alpha [rad/s] or [deg/s]
betadot : time-derivative of beta [rad/s] or [deg/s]
{pdot : time-derivative of p [rad/s^2] or [deg/s^2] }
{qdot : time-derivative of q [rad/s^2] or [deg/s^2] }
{rdot : time-derivative of r [rad/s^2] or [deg/s^2] }
{psidot : time-derivative of psi [rad/s] or [deg/s] }
{thetadot : time-derivative of theta [rad/s] or [deg/s] }
{phidot : time-derivative of phi [rad/s] or [deg/s] }
{xedot : time-derivative of xe [m/s] }
{yedot : time-derivative of ye [m/s] }
Hdot : time-derivative of H [m/s]
Fx : total external force along XB-axis [N]
Fy : total external force along YB-axis [N]
Fz : total external force along ZB-axis [N]
Xgr : gravity force along XB-axis [N]
Ygr : gravity force along YB-axis [N]
Zgr : gravity force along ZB-axis [N]
</pre>
<p>The variables which are not actually used by any of the masked subsystems
within the subsystem <i>Additional Outputs</i> have been bracketed between
curly braces. Of the vector <i>yhlp</i>, only <i>sin(alpha)</i>,
<i>cos(alpha)</i>, <i>sin(beta)</i>, and <i>cos(beta)</i> are used within
<i>Additional Outputs</i>.</p>
<h3>
Outputs
</h3>
<pre>
yfp = [gamma fpa chi Phi]' (flightpath parameters)
yuvw = [udot vdot wdot]' (time-derivatives (!) of u, v, and w)
yacc = [Ax Ay Az axk ayk azk]' (specific forces and accele-
rations)
gamma : flightpath angle [rad] or [deg]
fpa : flightpath acceleration [m/s^2]
chi : azimuth angle [rad] or [deg]
Phi : bank angle [rad] or [deg]
udot : time-derivative of u [m/s^2]
vdot : time-derivative of v [m/s^2]
wdot : time-derivative of w [m/s^2]
Ax : specific force along XB-axis [g]
Ay : specific force along YB-axis [g]
Az : specific force along ZB-axis [g]
axk : kinematic acceleration along XB-axis [g]
ayk : kinematic acceleration along YB-axis [g]
azk : kinematic acceleration along ZB-axis [g]
</pre>
<p><b>Note:</b> the time-derivatives of the body-axes velocity components,
<i>udot</i>, <i>vdot</i>, and <i>wdot</i>, are not needed for solving the
equations of motion, because the true airspeed <i>V</i>, angle of attack
<i>alpha</i>, and sideslip angle <i>beta</i> have been used as state
variables instead of <i>u</i>, <i>v</i>, and <i>w</i>. </p>
<h3>
Parameters to be defined in the Matlab workspace
</h3>
<ul>
<li>
<i>GM1</i>: Vector which contains some basic geometrical properties of
the aircraft, as well as its mass (which is considered to be constant
during the motions of interest). Here, the value of the mass is needed
by the masked subsystem block <i><a href="accel.htm">Accel</a></i>.
<i>GM1</i> can be loaded to workspace from file by means of the routine
<i><a href="datload.htm">DATLOAD</a></i>. Use <i><a href=
"modbuild.htm">MODBUILD</a></i> first if the datafile does not yet
exist.
</li>
</ul>
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