Assignment for HW/CE#7
Revised answer to Problem #2, 4/29/10
No turnin required.
Some recommended problems for final exam preparation not covered in
earlier quizzes:
(Note: The final will be comprehensive!)
1.
Consider the following nonlinear system:
)
2
(
)
2
(
2
2
1
1
2
1
2
1
+
+

=
u
x
x
u
x
x
x
dt
d
a) Find the two equilibrium points for this system if:
)
(
16
)
(
)
(
)
(
32
)
(
)
(
2
2
o
2
2
1
1
o
1
1
t
u
t
u
u
t
u
t
u
t
u
u
t
u
∆
+
=
∆
+
=
∆
+
=
∆
+
=
Answer:
+


+
=
2
4
Or
2
4
20
10
x
x
b) For each of the equilibrium points write a set of linear equations governing small
displacements of the state variables from that equilibrium point assuming we have small
displacements of the inputs from
u
1o
and
u
2o
.
Answer:
1
0
0
1
8
4
0
16
Or
1
0
0
1
8
4
0
16
2
1
2
1
2
1
2
1
2
1
2
1
∆
∆
+
∆
∆

+
+
=
∆
∆
∆
∆
+
∆
∆


=
∆
∆
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 Spring '10
 Brown
 Equilibrium point, Stability theory, Steady state step, state step error

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