Robust Control Systems II
Take-home, Spring, 2005
Due: Tuesday, May 24, 2005, Professor Kwatny
A satellite has an astronomical survey mission
that requires accurate pointing of an instrument
package as the satellite moves through space.
The package is isolated from the main satellite
service body to isolate it from vibration and
electrical noise. The goal is to point the package
at the star. For this purpose an optical star sensor
is mounted on the instrument package. However,
control is achieved by rotating the main body
using torque generators on the main body. A
second star sensor can also be mounted on the
main body but because of vibration and noise it
will not be sufficiently accurate on its own.
Consider the design of controllers using one
measurement and two measurements. The
dynamical goals are a settling time of no more
than 20 sec and an overshoot of no more that
15%. The plant dynamics include some parameters that can vary within specified ranges.
The equations of motion are:
1
θ
2
θ
Main instrument
package
22
2222
22
11
11
1
11 11
0100 0
0
0
0001 1
kbkb
JJJJ
du
dt
kb kb J
JJ JJ
θθ
ωω
θθ
ωω
⎡⎤
⎡
⎤
⎢⎥
⎡⎤ ⎡⎤
⎢
⎥
⎢⎥
−−
⎢⎥ ⎢⎥
⎢
⎥
⎢⎥
⎢⎥ ⎢⎥
=+
⎢⎥
⎢⎥ ⎢⎥
⎢⎥
⎢
⎥
⎢⎥
⎢⎥ ⎢⎥
⎢
⎥
⎢⎥
⎢⎥ ⎢⎥
⎣⎦ ⎣⎦
⎢
⎥
−−
⎢⎥
⎣
⎦
⎢⎥
⎣⎦
with parameters
12
0.09 0.4, 0.091
0.083 0.2 , 0.0036
10 10
1, 0.1
nom
nom
kk
kk
bb
JJ
≤
≤=
≤≤ =
==
Try
γ
-iteration and robust stabilization. Discuss the relative performance of these two
designs.