Name EE106 Feb.26, 08 Quiz 4

flounderconvoyElectronics - Devices

Nov 15, 2013 (3 years and 8 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