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Section 3.8 Design Examples 193

3.8 DESIGN EXAMPLES

In this section we present two illustrative design examples. In the first example, we pre-
sent a detailed look at modeling a large space vehicle (such as a space station) using a
state variable model. The state variable model is then used to take a look at the stability
of the orientation of the spacecraft in a low earth orbit. The design process depicted in
Figure 1.15 is highlighted in this example. The second example is a printer belt drive
modeling exercise. The relationship between the state variable model and the block dia-
gram discussed in Chapter 2 is illustrated and, using block diagram reduction methods,
the transfer function equivalent of the state variable model is obtained.

EXAMPLE 3.7 Modeling the orientation of a space station
The International Space Station, shown in Figure 3.27, is a good example of a multi-
purpose spacecraft that can operate in many different configurations. An important
step in the control system design process is to develop a mathematical model of the
spacecraft motion. In general, this model describes the translation and attitude motion
of the spacecraft under the influence of external forces and torques, and controller and
actuator forces and torques. The resulting spacecraft dynamic model is a set of highly
coupled, nonlinear ordinary differential equations. Our objective is to simplify the
model while retaining important system characteristics. This is not a trivial task, but an
important, and often neglected component of control engineering. In this example, the
rotational motion is considered. The translational motion, while critically important to
orbit maintenance, can be decoupled from the rotational motion.
Many spacecraft (such as the International Space Station) will maintain an
earth-pointing attitude. This means that cameras and other scientific instruments
pointing down will be able to sense the earth, as depicted in Figure 3.27. Conversely,

FIGURE 3.27
The International
Space Station
moments after the
Space Shuttle
undocked from the
Station. (Courtesy
of NASA.)