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systems. See the description of Beaver Level 1 for more information.
8.2. The aircraft model block libraries 121
Figure 8.3: Main FDC library with highlighted aircraft model sublibraries
The remainder of this chapter (pages 122 to 164) provides a detailed description
of all blocks and subsystems from the nonlinear aircraft model, i.e. the system
Beaver or one of its subsystem equivalents. The blocks have been sorted in alphabetical
order; their locations have been referenced with respect to the system
Beaver and the main FDC library FDCLIB.
122 Chapter 8. Aircraft model block reference
12 ODEs Beaver level 1 / Beaver level 2 / Aircraft Equations of Motion / 12 ODEs
Main FDC library / Equations of motion
Type
Aircraft-independent subsystem, essential for solving the equations of motion. The subsystem
is not masked.
Description
The subsystem 12 ODEs contains the twelve non-linear Ordinary Differential Equations
that describe the aircraft dynamics. The equations are valid for all rigid bodies, assuming
a flat, non-rotating Earth; see chapter 2 for a detailed theoretical discussion. The
time-derivatives of the twelve state variables are nonlinear functions of the state variables
themselves and of the external forces and moments. The latter depend upon the
state variables, external control inputs, and external disturbances affecting the airplane.
Subsystems and/or blocks
The subsystem 12 ODEs contains four blocks:
Vabdot computes time-derivatives of true airspeed, angle of attack, and sideslip angle,
pqrdot computes time-derivatives of the angular velocities along the body-axes of the
aircraft,
Eulerdot computes time-derivatives of the Euler angles,
xyHdot computes time-derivatives of the coordinates and the altitude above sea-level.
Inputs
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
ybvel
 = [ u + uw v + vw w + ww ]T body-axes velocity components plus wind, ybvel
Outputs
˙x = [ ˙V
˙a
˙b
˙ p ˙ q ˙ r ˙y
˙q
˙j
˙ xe ˙ ye ˙H ]T time-derivative of state vector, xdot
Note: the vector ˙x that leaves the subsystem 12 ODEs must be corrected for the direct
contribution of ˙b to the aerodynamic side force Ya. This correction is taken into account
by the block xdotcorr (Beaver), which has been described later.
Parameters
The block Vabdot reads the parameter vector GM1 from theMATLAB workspace; the block
pqrdot requires the matrix GM2. The definitions of GM1 and GM2 can be found in appendix
C. These variables can be loaded from the file AIRCRAFT.DAT, using the utility
DATLOAD (see section 12.4.2). If this datafile has somehow inadvertently been deleted, it
can be re-created by running the program MODBUILD (see section 12.6.1).
Connections
in: x comes from the block Integrator; Ftot and Mtot come from FMsort; yhlp comes from
Hlpfcn; ybvel
 is the sum of the output from uvw and the wind velocity components
from the external input vector uwind.
out: ˙x (not corrected for the implicit nature of the ˙b-equation) is connected to the block
xdotcorr (Beaver).
Type browse 12odes at the command-line for on-line help.
8.2. The aircraft model block libraries 123
Accel Beaver level 1 / Beaver level 2 / Additional Outputs / Accel
Main FDC library / Other (output-) equations
Type
Aircraft-independent masked subsystem block, not essential for solving the equations of
motion.
Description
The block Accel computes some accelerations and specific forces (outputs of accelerometers)
in the aircraft’s center of gravity. These output variables are useful for several FCS
design tasks, e.g. turn-coordination by means of feedback of the specific force along the
YB-axis, or manoeuvre load limiting. However, these variables are not required to actually
solve the equations of motion themselves! Computing accelerations outside the center of
gravity will require additional terms, which are not taken into account in this block; refer
to ref.[14] for more details.
Equations
The equations used by the block Accel have been discussed in some more detail in section
3.6.
• Kinematic accelerations ax,k, ay,k, and az,k along the body-axes, measured in the vehicle’s
c.g.:
ax,k = 1
g0
(u˙ + qw − rv) = Fx
W
ay,k = 1
g0
(v˙ + ru − pw) =
Fy
W
az,k = 1
g0
(w˙ + pv − qu) = Fz
W
　
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