Briefly discuss the importance of A/D and D/A converters for the case of digital control. Also, draw a detailed block diagram to show where a digital computer can be placed in the control loop. Q4 (a)
Briefly discuss the importance of A/D and D/A converters for the case of digital control. Also, draw a detailed block diagram to show where a digital computer can be placed in the control loop. Q4 (a)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question
![Q4
Briefly discuss the importance of A/D and D/A converters for the case of digital
control. Also, draw a detailed block diagram to show where a digital computer
can be placed in the control loop.
(a)
(b)
Consider the open-loop system as shown in Figure Q4.
T
Y(s)
ZOH
G,(s)
R(s)
U(s)
Figure Q4
The plant is described as:
* = (, )x + (;)u
y = [1 0]x
(i)
Find the transfer function of the plant, Gp(s). Note, that the transfer
function Y(s) can be defined as,
Y(s) = C(sl – A)-'B + D
where A, B, C, D and I are state, input, output, feedforward and
identity matrix respectively.
Find the sampled-data transfer function G(z). Assume a sample
period of T, and the transfer function of the ZOH as (1-eT/s.
(ii)
rane
(iii)
Find the sampled-data transfer function, G(z), for T= 0.5 s.
(iv)
Explain why it is not practical to make sample time too low to
reduce the effective delay of sample and hold. Note, that the
effective delay of sample and hold is typically half of the sample
time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd84942ab-67a3-4593-8510-487f55a9ad56%2Fa9219daa-8e5d-4e38-81f0-3009ce1723db%2Fx3oq0z8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q4
Briefly discuss the importance of A/D and D/A converters for the case of digital
control. Also, draw a detailed block diagram to show where a digital computer
can be placed in the control loop.
(a)
(b)
Consider the open-loop system as shown in Figure Q4.
T
Y(s)
ZOH
G,(s)
R(s)
U(s)
Figure Q4
The plant is described as:
* = (, )x + (;)u
y = [1 0]x
(i)
Find the transfer function of the plant, Gp(s). Note, that the transfer
function Y(s) can be defined as,
Y(s) = C(sl – A)-'B + D
where A, B, C, D and I are state, input, output, feedforward and
identity matrix respectively.
Find the sampled-data transfer function G(z). Assume a sample
period of T, and the transfer function of the ZOH as (1-eT/s.
(ii)
rane
(iii)
Find the sampled-data transfer function, G(z), for T= 0.5 s.
(iv)
Explain why it is not practical to make sample time too low to
reduce the effective delay of sample and hold. Note, that the
effective delay of sample and hold is typically half of the sample
time.
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