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Connections
in: x comes from the block Integrator; uwind is an external input vector containing the
components of the wind (and/or turbulence) velocity, plus their time-derivatives.
out: Fwind is connected to FMsort.
Type browse fwind at the command-line for on-line help.
152 Chapter 8. Aircraft model block reference
Gravity Beaver level 1 / Beaver level 2 / Gravity
Main FDC library / Gravity and wind forces
Type
Aircraft-independent masked subsystem block, essential for solving the equations of motion.
Description
The block Gravity computes the resolution of the aircraft’s weight in body-axes components,
using the pitch and roll angle to determine the attitude of the airplane (the yawangle
does not affect the gravitational force components). The gravitational acceleration
varies with height; its local value is obtained from the block Atmosph.
Equations
The equations used by the block Gravity have been discussed in some more detail in section
3.3.3.
• Contribution of the aircraft’s weight to the body-axes force components, [N]:
Xgr = − Wsin q
Ygr = Wcos q sin j
Zgr = Wcos q cos j
where W = mg is the weight of the aircraft, measured in [N].
Inputs
x = [ V a b p q r y q j xe ye H ]T state vector, x
yatm = [ r ps T μ g ]T basic atmospheric properties, yatm
Outputs
Fgrav = [ Xgr Ygr Zgr ]T gravity force components along body-axes, Fgrav
Parameters
Gravity needs the parameter vector GM1 to be present the MATLAB workspace, in order
to extract the mass m of the aircraft (the mass has been implemented as a parameter, i.e. it
is assumed to be constant during the relative short time intervals considered). The definition
of GM1 can be found in appendix C. GM1 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; yatm comes from Atmosph.
out: Fgrav is connected to FMsort.
Type browse gravity at the command-line for on-line help.
8.2. The aircraft model block libraries 153
Hlpfcn Beaver level 1 / Beaver level 2 / Hlpfcn
Main FDC library / Other (output-) equations
Type
Aircraft-independent masked subsystem block, essential for solving the equations of motion.
Description
The block Hlpfcn is used to compute frequently used sines and cosines of the angle of
attack, the sideslip angle, and the Euler angles, in order to reduce the number of duplicate
sine and cosine evaluations in the simulation model. Since the outputs from this block are
used by several other subsystems, Hlpfcn has been placed in an internal feedback loop of
the aircraft model.
Equations
Hlpfcn simply determines the required sines and cosines, and stores the results in a single
vector.
Inputs
x = [ V a b p q r y q j xe ye H ]T state vector, x
Outputs
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
(Please notice that this vector also includes a term ‘tan b’ and that the selected cosine-sine
sequence is unfortunately not very intuitive.)
Parameters
None.
Connections
in: x comes from the block Integrator.
out: yhlp is connected to uvw, xdotcorr, Eulerdot, pqrdot, Vabdot, xyHdot, and uvwdot (Additional
Outputs).
Type browse hlpfcn at the command-line for on-line help.
154 Chapter 8. Aircraft model block reference
Integrator Beaver level 1 / Beaver level 2 / Aircraft Equations of Motion / Integrator
Main FDC library / Equations of motion
Type
Standard SIMULINK block, essential for solving the equations of motion.
Description
The block Integrator is used to obtain the time-trajectories of the twelve state variables
by integrating the corresponding derivatives, starting with the initial value of the state
vector, that needs to be defined in the MATLAB workspace before starting a simulation.
Equations
The Integrator block determines the new value of the state vector by integrating its timederivative
over the current time-interval, and adding this result to its previous value.
• Update of the state vector for the current time-step:
x(tn+1) = x(tn) +
Z tn+1
tn
˙x(t)dt; n = 0, 1, . . .
where the integral is approximated using a numerical integration method. See section 6.1
for more information.
Inputs
˙x = [ ˙V
˙a
˙b
˙ p ˙ q ˙ r ˙y
˙q
˙j
˙ xe ˙ ye ˙H ]T time-derivative of state vector, xdot
Outputs
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(75)
