Sample Exam 5: Chapters 6, 8, and 12
1) Convolve graphically continuous-time signals
/
and
K.1p
.
2) Using the sliding tape method find the discrete-time convolution
IELgEL
, where
U3)
Z%
Z%
Z
ZA
x Z%
a/¡¢[£@¤g¥§¦,¢
3) Consider the continuous-time linear system represented in the state space form by
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ª
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P«
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ª
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ª
./«u¬
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q"
¨
ª
L®
ª
@
®
I«
¨
]«
¯
"°E
¨
ª
"
ª
/I«
a) Find the system transfer function.
b) Find the system impulse response.
c) Find the system transition matrix using the Laplace transform.
d) Find the system output response (
¯
"
) due to the system input
q"±³²
®´/µ¶
./
.
4) Consider the discrete-time linear system represented in the state space form by
¨
ª
U
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·
ª
U
¬
·
«
¨
x
«
¨
ª
EL
ª
E3
«
¬
¨
«
-L
¨
ª
E
ª
-
«
¨
«
¯
-LF°w j
¨
ª
UL
ª
ULK«
a) Find the system transfer function.
b) Find the system transition matrix.
c) Find the system output response (
¯
UL
) due to the system input
-L¸@¹Eaº
¶
E3
.
5) The open-loop system transfer function is given by
»
8¼#
¼
¬p½
Assuming the unity feedback system, find the sensitivity function of the closed-loop system with respect
to parameter
½
.
Hints:
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5
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