EE 141 – Final
Fall 2008
12/09/08
Duration: 3 hours
The final is closed book and closed lecture notes. No calculators.
You can use a single page of handwritten notes.
Please carefully justify all your answers.
G(s)
H(s)
+

Figure 1: Feedback interconnection for Problem 1.
Problem 1:
Consider the following linear differential equation:
d
dt
x
1
=

x
1
+ 2
x
2
(1)
d
dt
x
2
=
x
2
+
u
(2)
1. Assuming that
x
1
(0) = 0 and
x
2
(0) = 0, what is the evolution of
x
1
, in the time domain,
when a step is applied as input at
t
= 0?
2. Assume that we place a controller with transfer function
H
(
s
) =
K
D
s
+
K
P
in a feedback
loop with the system defined by the differential equations (1) and (2), as depicted in
Figure 1.
Design
K
D
and
K
P
so that the rise time of the closedloop system is 0
.
9
seconds and the damping ratio is 1.
3. For your design, compute the overshoot and the settling time.
1
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4. Sketch the step response.
5. Would the closedloop system be able to track a ramp?
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 Spring '09
 Tabuada

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