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Problem 7.45PP
The dynamic equations of motion for a station-keeping satellite (such as a weather sateiiite) are 
x — 2ajy — 3af^x = 0t y + 2ew: = tt, 
where
X = radiai perturbation, 
y = longitudinal position perturbation, 
u = engine thrust in the y-direction,
as depicted in Fig. If the orbit is synchronous with the earth’s rotation, then w = 2tt/(3600 * 24)
rad/sec.
(a) Is the state x = [ x x y y ]T observable?
(a) Is the state x = [ x x y y ]T observable?
(b) Choose x = [x x y y ]7 a s the state vector and y as the measurement, and design a full-order 
observer with poles placed at s = -2 cj-3 cj, and -3oj ± 3ojj.
Figure Diagram of a station-keeping satellite in orbit
Step-by-step solution
step 1 of 2
A) There is not enough information to answer this question.
Step 2 of 2
B)
0 1 0 0 
3ar‘ 0 0 2ib
0 0 0 1
0 -2 o 0 0
z = [o 0 1 o]Jsr
1^=-44.5W, 1^=-51.5W-
4 = l l o . ; ,= 5 3 o ’
k 0
+
0
3̂ 0
1̂ 4 1