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differential equations, and a large range of output equations.
Description
The full name of this second level in the aircraft model is ‘DeHavilland DHC-2 Beaver dynamics
and output equations’, which signifies that this is in fact the core module of the
toolbox (the first level of the aircraft model handles the workspace output functions and
provides an interface between the aircraft model and MATLAB). For sake of brevity, we
will refer to this subsystem as Beaver level 2 below. This subsystem organises the individual
elements from the nonlinear aircraft model in a block-diagram structure that
resembles figure 3.2 from chapter 3. See figure 8.1 for a picture of Beaver Level 2 itself.
Subsystems and/or blocks
The subsystem Beaver level 2 contains five non-masked subsystems:
• Additional outputs computes several useful output variables which are not required to
solve the equations of motion themselves (and hence, ‘additional’),
• Aerodynamics Group (Beaver) computes the aerodynamic forces and moments for the
Beaver,
• Aircraft equations of motion (Beaver) contains the general differential equations for the
rigid-body dynamics and an aircraft-dependent block that corrects the time-derivatives
of the state variables for the implicitness of the state equations,
• Airdata Group computes airdata (-related) variables,
• Engine Group (Beaver) computes the propulsive forces and moments for the Beaver.
In addition, Beaver level 2 contains four masked blocks:
• FMsort adds all individual contributions to the external forces and moments, and splits
this in a force-vector and a moment-vector,
• Fwind computes the contributions to the external forces and moments due to nonsteady
atmosphere (wind and turbulence),
• Gravity computes the gravitational forces along the aircraft’s body-axes,
• Hlpfcn computes several sines and cosines, which are used multiple times by other
blocks from the aircraft model.
Inputs
uaero = [ de da dr df ]T aerodynamic control inputs, uaero
uprop = [ n pz ]T external propulsion inputs, uprop
uwind = [ uw vw ww u˙w v˙w w˙ w ]T wind velocity components along body-axes
and their time-derivatives, uwind
Outputs
x = [ V a b p q r y q j xe ye H ]T state vector, x
˙x = [ ˙V
˙a
˙b˙ p
˙ q
˙ r
˙y
˙q
˙j
˙ xe ˙ ye ˙H ]T time-derivative of state vector, xdot
ybvel = [ u v w ]T body-axes velocity components, ybvel
yuvw = [ u˙ v˙ w˙ ]T time-derivatives of body-axes velocities, yuvw
ydl = [ pb
2V
qc
V
rb
2V ]T dimensionless angular velocities, ydl
yfp = [ g fpa c F ]T flight-path variables, yfp
ypow = [ dpt P ]T engine power related variables, ypow
8.2. The aircraft model block libraries 141
yacc = [ Ax Ay Az ax,k ay,k az,k ]T specific forces and accelerations, yacc
Caero = [ CXa CYa CZa Cla Cma Cna ]T aerodynamic force and moment coefficients, Caero
Cprop = [ CXp CYp Czp Clp Cmp Cnp ]T propulsive force and moment coefficients, Cprop
FMaero = [ Xa Ya Za La Ma Na ]T dimensional aerodynamic forces and moments, FMaero
FMprop = [ Xp Yp Zp Lp Mp Np ]T dimensional propulsive forces and moments, FMprop
Fgrav = [ Xgr Ygr Zgr ]T gravity force components along body-axes, Fgrav
Fwind = [ Xw Yw Zw ]T corrections to body-axes forces in nonsteady atmosphere, Fwind
yatm = [ r ps T μ g ]T basic atmospheric properties, yatm
yad1 = [ a M qdyn ]T basic airdata variables, yad1
yad2 = [ qc Ve Vc ]T additional airdata (-related) variables, yad2
yad3 = [ Tt Re Rc ]T additional airdata (-related) variables, yad3
Parameters
Several blocks and subsystems from Beaver level 2 require the variables AM, EM, GM1,
GM2, and xinco to be defined in the MATLAB workspace. The following list provides an
overview of the parameter requirements:
AM Aerodynamics Group (Beaver), Aircraft Equations of Motion (Beaver)
EM Engine Group (Beaver)
GM1 Additional Outputs, Aerodynamics Group (Beaver), Aircraft Equations of Motion
(Beaver), Airdata Group, Engine Group (Beaver), Fwind, Gravity
GM2 Aircraft Equations of Motion (Beaver)
xfix Aircraft Equations of Motion (Beaver)
xinco Aircraft Equations of Motion (Beaver)
The definitions for AM, EM, 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).
The vector xinco contains the initial value of the state vector. A steady-state initial
value can be computed using the aircraft trim routine ACTRIM (see section 11.1), or it can
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(70)
