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today.
It would go far beyond the current scope of this report to analyze these other navigation
systems in detail. If modern navigation systems and practices are to be evaluated
in simulations, additional mathematical models will most likely be required.
However, the general approach taken in the previous two sections could serve as a
model for the determination of the governing equations: start by defining the navigation
geometry, and include systematic and random system errors thereafter. It
should be noted that in flight simulations, we can always compute the exact position
of the airplane; constructing a realistic model of a navigation system is therefore
mainly a matter of obtaining a realistic error model.
5.4 Sensors, Actuators, Flight Control Computer
The mathematical model from chapter 3 allows us to compute the motions of the
aircraft, resulting from applied control inputs and external disturbances. Although
the model includes many observation variables that make it suitable for many applications
in aircraft dynamics research and flight control system design, we need
to take into account the difference between the actual values of these variables and
the values which are sensed and displayed on the cockpit instruments, or used for
computations by the flight control computers of the airplane.
In addition, we must remember that this model is based on the actual deflections
of control surfaces, which do not necessarily correspond to the intended control inputs
generated either directly by the pilot (using the flight controls in the cockpit),
or indirectly via an automatic flight control system (using electric signals to define
deflections of actuators, which in turn move the control surfaces).
Both on the input and on the output side of the aircraft model, we may need
to augment the equations by including additional system dynamics, deterministic
errors, stochastic errors, and data-processing influences. Whether or not such refinements
are really necessary obviously depends on the required accuracy for specific
tasks. For instance, while it may very well be possible to build a decent set of flight
control laws using the idealized equations from chapter 3, it is quite possible that
other effects such as sensor noise, actuator dynamics, and time-delays and quantization
effects caused by computer limitations may degrade system performance to
such an extent that additional measures have to be taken.
A striking example of the potential detrimental effects of signal processing in a
digital computer was encountered during the design of the Altitude Hold control law
for the Beaver autopilot (see chapters 14 and 15): the altitude signal was represented
with a Least Significant Bit of approximately 4 feet, which would lay well within the
72 Chapter 5. Radio-navigation, sensors, actuators
required accuracy, but which inadvertently caused the reference input to consist of
a series of 4 feet step-inputs. This resulted in unacceptable control characteristics;
additional filtering of the altitude signal was required to solve the problem [28].
Since the Flight Dynamics and Control toolbox currently does not include a comprehensive
library of sensor and actuator models, despite their potential importance
for flight control system design tasks and flight simulation, this report will not further
elaborate on this subject. However, the toolbox does take into account some
specific ad-hoc representations of time-delays, quantization effects, and actuator dynamics
to represent the Beaver autopilot; see the corresponding block-reference for
details.
Chapter 6
Analytical tools
When developing the aircraft differential equations in chapter 2, much emphasis was
placed on the state-space formulation for the aircraft differential equations. This formulation
will prove to be especially suited for the implementation of the aircraft
model in the SIMULINK environment, and the development and application of analytical
MATLAB and SIMULINK software tools.
Figure 6.1 shows the nonlinear state-space model of the aircraft and the associated
analytical tools. The tools provide the capability to trim the aircraft model
for steady-state flight, perform digital simulations, and derive linear state-space descriptions
of the aircraft dynamics. Linear control system design techniques can be
applied to these linearized aircraft models, and the resulting control laws can be validated
with nonlinear simulations. Notice how this figure corresponds to the upper
part of figure 1.3 from chapter 1, which depicted the flight control system design
cycle in the FDC toolbox.
These analytical functions are mostly generic in nature, and SIMULINK and MATLAB
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