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GM1 and GM2, changing only the figures for the lengths, wing-surface, mass, and
moments and products of inertia. Re-using this code not only saves time, but it also
ensures that the data structure of GM1 and GM2 will remain compatible with the
aircraft-independent parts in the SIMULINK model.
12.6.2 FIXSTATE
The utility FIXSTATE assists with the definition of a vector xfix in the MATLAB workspace,
which is used as a multiplication factor by the block xfix in the aircraft model
(see chapter 8). This block is used to constrain state variables to their initial values
for analytical purposes.
Normally the state variables in the aircraft model are simply determined by the
equations of motion, but in some cases it may be useful to artificially force certain
states to remain equal to their initial values. For instance, we may want to neglect
longitudinal-lateral cross-coupling effects when studying the fundamental aircraft
modes, or emulate an ideal ‘Speed Hold’ flight control law by artificially fixing the
value of the airspeed.
To this means, the block xfix performs an element-by-element multiplication of
the time-derivative of the state vector, x˙ , and a gain vector of the same length, xfix.
The elements of xfix are identical to either one or zero, meaning: the actual derivative
is either taken into account or completely disregarded. See chapter 8 for a detailed
description of the block xfix.
FIXSTATE offers four user choices, as shown in figure 12.3:
1. Fix asymmetrical state variables. This causes the variations in asymmetrical
state variables b, p, r, y, and j to be neglected, which effectively constrains the
airplane to symmetrical motions only. In addition, FIXSTATE will ask whether
the lateral Earth-coordinate ye needs to be fixed as well.
220 Chapter 12. Support functions reference
Figure 12.3: Main menu of FIXSTATE
2. Fix symmetrical states. This causes the variations in the symmetrical state variables
V, a, q, and q to be neglected, which effectively constrains the airplane to
asymmetrical motions only. In addition, FIXSTATE will ask whether it should
fix the longitudinal Earth coordinate xe and the altitude H too.
3. Fix arbitrary states. After selecting this option, FIXSTATE will ask the user to
specify a vector with the element numbers of the state variables to be fixed.
With the state vector being x = [ V a b p q r y q j xe ye H ]T, we can for
instance fix q and xe by specifying the vector [8 10], as q and xe are the eighth
and tenth elements of x, respectively.
4. Don’t fix any states. This option resets the default value of xfix, being a unity
vector of length 12, taking into account all state derivatives in order to allow all
aircraft states to vary freely. The same effect can be achieved by deleting xfix
from the workspace altogether.
After specifying the states to be fixed, FIXSTATE will try to re-initialize the aircraft
model. This is only possible if the initial value of the state vector xinco is present in
the workspace. Such initial conditions can be loaded from datafile with TRILOAD
utility, computed in advance using the trim routine ACTRIM, or entered manually. If
xinco cannot be found, a warning message will be displayed.
FIXSTATE needs to be run (or xfix needs to be defined manually) prior to simulations
or other analysis requiring one or more aircraft states to be constrained to
their initial values. For the common situation in which all states are allowed to vary
freely, it will not be necessary to explicitly define xfix, as the block xfix within the
aircraft model will automatically use the default value of ones(1,12) if xfix hasn’t
been defined.
12.6. Model-specific helper functions 221
12.6.3 RESULTS
During simulations of the Beaver model, the time-trajectories of the input and output
signals are collected in the matrices In and Out. The definitions of these variables
can be found in appendix D. The MATLAB macro RESULTS extracts individual
input- and output-trajectories from these matrices, using easy-to-understand variable
names that closely resemble the symbols from appendix A (e.g. ‘alpha’ for the angle
of attack a, or ‘deltar’ for the rudder deflection dr). This simplifies post-simulation
analysis, as a command such as plot(time,deltae) is much easier to remember than
the equivalent plot(time,In(:,1)).
RESULTS will only work correctly if the matrices In and Out correspond to the
default definitions from appendix D. If the input/output definitions in the aircraft
simulation model are changed, e.g. in order to add more observation variables, implement
additional input signals, or rearrange the output matrix, it will be necessary
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(100)
