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16.060 Principles of Automatic Control
Fall 2002
Final Exam
Part A: Put your working and answers in the booklet provided.
Question A.1
20 points
Consider the plant
2
1.25
1.25
()
(0
.
5)
.
1.25
Gs
sj
ss
==
+
−+
+
++
a)
The desired closedloop performance specifications are:
8
n
ζω
= 0.707,
=
. Where
should the closedloop poles be located?
b) Using rootlocus techniques, design a PD controller that satisfies the above performance
requirements.
c)
What will be the steadystate error of your compensated system to a unity step input?
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View Full DocumentQuestion A.2
20 points
Consider the system represented by the following pole/zero diagram, where the pole at the origin
represents a step input. The system has unity gain (i.e. the steadystate input/output gain is 1).
X
X
X
j1
j1
step input
10
X
s
not to scale
1
a)
Calculate the magnitude of all residues.
b) What is the time constant associated to each mode?
c)
Write down an exact expression for the step response.
d) Is there a dominant transient mode? If so, which mode is dominant? Justify your answer.
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 Fall '03
 willcox
 Aeronautics

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