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0066_Frame_C30 Page 19 Thursday, January 10, 2002 4:43 PM

KS Frequency Response
35

30

25

20
Mag (dB)

15

10

5

0
−2 −1 0 1 2
10 10 10 10 10
Frequency (rad/sec)
2
FIGURE 30.5 H Design KS frequency response.
Complementary Sensitivity Frequency Response
10
0

−10
−20

−30
Mag (dB) −40

−50

−60

−70
−80

−90
−1 0 1 2
10 10 10 10
Frequency (rad/sec)
2
FIGURE 30.6 H Design complementary sensitivity frequency response.
Example 30.3 (LQG/LTR Design for First Order Unstable Missile Model)
We consider an unstable missile described by a simple first order model with state x (pitch attitude),
control input u (fin elevator deflection), process noise w I = x (angular wind gust), and sensor noise w 2 = θ.
It is assumed that the missile’s center of gravity (c.g.) is aft of its center of pressure (c.p.)—where lift
is concentrated. This assumption results in a missile pitch instability. It is also assumed that the missile’s

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