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Outputs
˙xnew = [ ˙V ˙a
˙b˙ p
˙ q
˙ r
˙y
˙q
˙j
˙ xe ˙ ye ˙H ]T modified time-derivative of state vector, xdot
Parameters
The block xfix tries to read the multiplication vector xfix from in the MATLAB workspace.
If the variable xfix is not present in the workspace when the aircraft model is accessed by
e.g. a simulation or a linearization process, it will automatically be set to its default value
ones(1,12). If it is desired to artificially fix specific states, xfix should either be entered
8.2. The aircraft model block libraries 163
manually (it must be a vector of length 12, with all elements being either one or zero), or
be defined by running the utility FIXSTATE (see section 12.6.2).
Connections
in: the unmodified vector ˙x comes from the block xdotcorr (Beaver).
out: the modified vector x˙ , whose elements may have been artificially set to zero, is
connected to the block Integrator.
Type browse xfix at the command-line for on-line help. Information about FIXSTATE can
be displayed on screen by typing browse fixstate at the command-line.
164 Chapter 8. Aircraft model block reference
xyHdot Beaver level 1 / Beaver level 2 / Aircraft Equations of Motion / 12 ODEs / xyHdot
Main FDC library / Equations of motion
Type
Aircraft-independent masked subsystem block, contains three (out of twelve) state equations.
Description
The block xyHdot computes the time-derivatives of the aircraft’s X and Y-coordinates xe
and ye, measured with respect to the Earth-fixed reference frame, and of the the altitude
H. These three variables form a subset of the twelve state variables of the nonlinear
aircraft model. For most purposes it is possible to omit xe and ye from the simulation
model, because the motions of the aircraft are not affected by its position relative to the
Earth. The coordinates are useful, however, for navigational purposes. Notice that it is
not possible to omit the altitude H from the simulation model, because of the altitudedependency
of the air temperature, pressure, and density, which affect the aerodynamic
and propulsive forces and moments.
Equations
The equations used by the block xyHdot have been discussed in some more detail in section
2.4.
• Time-derivative of the X-coordinate xe, [ms−1]:
x˙e = {ue cos q + (ve sin j + we cos j) sin q} cos y − (ve cos j − we sin j) sin y
• Time-derivative of the Y-coordinate ye, [ms−1]:
y˙e = {ue cos q + (ve sin j + we cos j) sin q} sin y + (ve cos j − we sin j) cos y
• Rate of climb or descent, [ms−1]:
˙H
= −z˙e = ue sin q − (ve sin j + we cos j) cos q
Inputs
ybvel
= [ u + uw v + vw w + ww ]T body-axes velocity components plus wind, ybvel
uxyH = [ xT Ftot
T Mtot
T yhlp
T ]T input vector to xyHdot, uxyH
where:
x = [ V a b p q r y q j xe ye H ]T state vector, x
Ftot = [ Fx Fy Fz ]T total external forces, Ftot
Mtot = [ L M N ]T total external moments, Mtot
yhlp = [ cos a sin a cos b sin b tan b sin y cos y sin q cos q sin j cos j ]T
frequently used sines and cosines, yhlp
Outputs
yxyH = [ ˙ xe ˙ ye ˙H ]T time-derivatives of the coordinates and altitude, yxyH (part of x˙ )
Parameters
None.
Connections
in: x comes from the block Integrator; Ftot and Mtot come from the block FMsort; yhlp
comes from the block Hlpfcn; ybvel
is the sum of the output from uvw and the wind
velocity components from the external input vector uwind.
out: yxyH is muxed together with the time-derivatives of the other state variables into a
single vector ˙x (not corrected for the implicit nature of the ˙b-equation). This timederivative
of the state vector x is then connected to the block xdotcorr.
Type browse xyhdot at the command-line for on-line help.
Chapter 9
Wind and turbulence block reference
In chapter 4 we discussed the nonsteady nature of the atmosphere, providing some
basic wind and turbulence models that were suitable for implementation in SIMULINK.
This chapter will provide a detailed description of the resulting SIMULINK
blocks. If you want to manipulate these blocks, or gain a better insight in the structure
of these blocks, it is recommended to unmask the blocks and compare the internal
block equations with the descriptions from this chapter. See section 7.8 for more
information about the masked interface of the FDC systems.
9.1 The wind and turbulence blocklibrary
All wind and turbulence blocks have been collected in the SIMULINK blocklibrary
WINDLIB, which is shown in figure 9.1. This library can be accessed from the main
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(80)
