# Name EE106 Feb.26, 08 Quiz 4

Electronics - Devices

Nov 15, 2013 (4 years and 6 months ago)

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Name EE106
Feb.26, 08

Quiz 4

The digital control system of Fig.1 has the
plan
t G(s) = 48/[(s+4)(s+8)]

Find the transfer function for the plant

Gzoh(s) = [1
-
exp(
-
sT)]G(s) in the Z domain.

s

The system sample rate is 40 Hz.

You may leave your answer as a sum.

Gzoh(s) = 48 [1
-
exp(
-
sT)] = 12
-

12 [1
-
exp(
-
sT)]

(s+4)(s+8) s (s+4) (s+8) s

Gzoh(z) = 12 1
-

exp(
-
4T)
-

1
-
exp(
-
8T)

z
-

exp(
-
4T) z
-
exp(
-
8T)

Gzoh(z) = Z{L
-
1
(Gzoh(s))*} = 0.095
-

0.1813

z
-
0.905 z
-
0.8187

A certain digital control system i
s to have the unity gain frequency of ωo=60rad/sec.

The system sample rate is 100Hz.

Find zo, the mapping of jωo in the Z plane.

zo = exp(j60/100) = exp(j34.38
O
)

zo =

exp(j34.38
O
)

Find wo, the mapping of jωo in the W plane

wo = j(2/T)tan(ωoT/2) = j200tan(17.19
O
) = j35.26

wo =

j61.87

Note that z = (2/T+w)

(2/T
-
w)

x*(t)
zoh

G(s)

c
*
(t)

FIG 1