EE221A Linear System Theory
Problem Set 10
Professor C. Tomlin
Department of Electrical Engineering and Computer Sciences, UC Berkeley
Fall 2010
Issued 12/2; Due 12/9
Problem 1: Controllability and Observability.
An approximate linear model of the longitudinal dynamics of a certain aircraft, for a particular set of flight
conditions, has the linearized state and control vectors:
x
=
v
α
θ
q
u
=
bracketleftbigg
δ
μ
bracketrightbigg
(1)
where
v
represents the change in forward velocity,
α
the change in angle of attack,
θ
the change in pitch
angle, and
q
the change in pitch rate. The two inputs are
δ
, the deflection of the elevators, and
μ
, the throttle
position.
The state space equation for this model is ˙
x
=
Ax
+
Bu
where
A
=

0
.
045
0
.
036

32

2

0
.
4

3

0
.
3
250
0
0
0
1
0
.
002

0
.
04
0
.
001

3
.
2
B
=
0
0
.
1

30
0
0
0

10
0
(2)
(a) Suppose a malfunction prevents manipulation of the input
δ
.
Is it possible to completely control the
aircraft using only
μ
? Only
δ
?
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 Fall '10
 ClaireTomlin
 Electrical Engineering, Electromagnet, 1 m, Department of Electrical Engineering and Computer Sciences, DT DT DT, Professor C. Tomlin

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