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which makes it somewhat easier to find a numerical solution for this system, especially
if f2 is a linear function. The practical consequences of this will be outlined for
the dynamic model of the Beaver aircraft in section 3.4.
The resulting state-space model can be used for any rigid body, and in particular
any rigid vehicle. Based on this model, we can develop dynamic simulation models
of aircraft, missiles, spacecraft, road-vehicles, or ships, by identifying the relevant
control inputs and disturbances, and by further developing the equations (2.67) for
the forces and moments. In the next chapter, a dynamic model of the DeHavilland
Beaver airplane will be built on this foundation.
Chapter 3
The aircraft model
Having determined the basic equations of motion, we can now develop a simulation
model of the complete aircraft. This chapter will first outline the general structure of
the overall simulation model, then focus on building the aircraft dynamics model by
identifying the individual contributions to the forces and moments and by building
the necessary airdata equations. Also, several additional observation variables will
be included, in order to make the model suitable for a wide range of applications in
flight simulation, flight dynamics analysis, and flight control system design.
3.1 General structure of the flight simulation model
Figure 3.1 shows the general closed-loop model of an automatically controlled aircraft
that is affected by external disturbances. Most elements in this model are hardware
related: the airframe and powerplant determine the aircraft dynamics, the flight
control computer setup determines the discretization effects and computational delays,
the actuator and sensor hardware determine which signals can be observed and
what control inputs are physically possible, and the pilot interface limits the ways in
which the pilot can interact with the control of the airplane and the autopilot. The
mode-controller logic and the control laws of the flight control system are typically
defined in software.
This chapter will focus on building the aircraft dynamics model, which obviously
forms the core of figure 3.1. The next chapter deals with external atmospheric disturbances,
chapter 5 will include some relevant sensor and actuator models (focusing
on the simulation of radio-navigation signals in particular), and chapter 14 will provide
a detailed example of an automatic flight control system and its mode-controller
for the Beaver aircraft.
3.2 The nonlinear aircraft dynamics
Figure 3.2 gives a graphical overview of the nonlinear rigid body dynamics of an
aircraft. Together, all elements from this figure represent the nonlinear state-space
system from equation (2.66). The state variables are obtained by integrating their
time-derivatives with respect to time, taking into account the initial value of the state
28 Chapter 3. The aircraft model
Actuator
dynamics
Aircraft
dynamics
Sensor
dynamics
AFCS
control
laws
Discretization
effects, computational
delay
Mode
controller h
h
Reference signals
External disturbances
Pinitloert-face
Figure 3.1: Block-diagram of an automatically controlled aircraft
vector, x0. In order to obtain the time-derivatives of the state variables the state variables
are coupled back into the force and moment equations and the equations of
motion themselves. All forces and moments must be expressed in components along
the body-axes of the vehicle (denoted by the superscript B). Forces and moments
which are expressed with respect to other reference frames must be transformed to
body-axes components by pre-multiplying the force and moment vectors with the
appropriate transformation matrix. In the figure, this is illustrated for the aerodynamic
forces and moments, which are transferred from flight-path axes (superscript
W) to body-axes, and for the gravitational forces, which are transferred from Earth
axes (superscript E) to body-axes. Figure 3.2 forms the basis for the development of
the modular structure of the rigid body equations for the FDC toolbox.
3.3 External forces and moments
The next step in the development of the dynamic model is to identify the different
contributions to the external forces and moments acting upon the rigid body. Obviously
these contributions are dependent of the type of vehicle under consideration.
For the Beaver model we will consider forces and moments due to gravitational,
propulsive, and aerodynamic effects, plus the influence of nonsteady atmosphere.
This comprises an in-flight model of a conventional aircraft. Other contributions can
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(18)
