Q3 (a) For the digital control system given in Figure 3, by adding phantom samplers to show that the z transfer function of the closed-loop system is given by C(z) R(z) G(z) 1+ G(z) H₁H₂(z) + R(s) G(s) C(s) H₂(s) H₁(s) Figure 3 (b) The analogue compensator 5s + 1 D(s) = 0.4s +1 is implemented digitally with sampling period 0.2 seconds to control the depth of a submarine system. Use the pole-zero mapping method to find a digital approximation to the analogue compensator.

Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
10th Edition
ISBN:9781337399128
Author:Russell E. Smith
Publisher:Russell E. Smith
Chapter11: Thermostats, Pressure Switches, And Other Electric Control Devices
Section: Chapter Questions
Problem 23RQ
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Q3
(a)
For the digital control system given in Figure 3, by adding phantom samplers to
show that the z transfer function of the closed-loop system is given by
C(z)
R(z)
G(z)
1+ G(z) H₁H₂(z)
+
R(s)
G(s)
C(s)
H₂(s)
H₁(s)
Figure 3
(b)
The analogue compensator
5s + 1
D(s) =
0.4s +1
is implemented digitally with sampling period 0.2 seconds to control the depth of
a submarine system. Use the pole-zero mapping method to find a digital
approximation to the analogue compensator.
Transcribed Image Text:Q3 (a) For the digital control system given in Figure 3, by adding phantom samplers to show that the z transfer function of the closed-loop system is given by C(z) R(z) G(z) 1+ G(z) H₁H₂(z) + R(s) G(s) C(s) H₂(s) H₁(s) Figure 3 (b) The analogue compensator 5s + 1 D(s) = 0.4s +1 is implemented digitally with sampling period 0.2 seconds to control the depth of a submarine system. Use the pole-zero mapping method to find a digital approximation to the analogue compensator.
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