Page 221 - Modern Control Systems

Section 3.8 Design Examples 195

Topics emphasized in I his example
Maintain space station attitude
in earth pointing orientation while
Establish the control goals
minimizing control moment gyro
1 momentum.
Space station orientation and
Identify the variables to be controlled
control moment gyro momentum.
I

Write the specifications
i
Establish the system configuration
1 See Eqs. (3.96 - 3.98) for
Obtain a model of the process, the the nonlinear model.
actuator, and the sensor See Eqs. (3.99-3.100) for
1 the linear model.
Describe a controller and select key
parameters to be adjusted
i
FIGURE 3.28 Optimize the parameters and
Elements of the analyze the performance
control system
design process 1
emphasized in the If the performance does not meet the If the performance meets the specifications,
spacecraft control specifications, then iterate the configuration. then finalize the design.
example.

2
= 3AI C X Ic, (3.95)
T g
where n is the orbital angular velocity (n = 0.0011 rad/s for the space station), and c is

-sin 6>2 cos #3
c = sin 01 cos 6 2 + cos 6^ sin 6 2 sin 0 3
|_cos 0\ cos 6 2 - sin 0] sin d 2 sin 0 3 j

The notation 'X' denotes vector cross-product. Matrix I is the spacecraft inertia ma-
trix and is a function of the space station configuration. It also follows from Equa-
tion (3.95) that the gravity gradient torques are a function of the attitude 8 h 0 2, and 0 3.
We want to maintain a prescribed attitude (that is earth-pointing By = 6 2 = 0 3 = 0),
but sometimes we must deviate from that attitude so that we can generate gravity gra-
dient torques to assist in the control moment gyro momentum management. Therein
lies the conflict; as engineers we often are required to develop control systems to
manage conflicting goals.
Now we examine the effect of the aerodynamic torque acting on the space station.
Even at the high altitude of the space station, the aerodynamic torque does affect the