Briefly discuss the importance of A/D and D/A converters for the case of digitalcontrol. Also, draw a detailed block diagram to show where a digital computercan be placed in the control loop.Q4(а)(b)Consider the open-loop system as shown in Figure Q4.T.Y(s)ZOHG,(s)R(s)U(s)Figure Q4The plant is described as:* = (, -)x + ()uy = [1 0]x(i)Find the transfer function of the plant, Gp(s). Note, that the transferfunction Y(s) can be defined as,Y(s) = C(sl – A)~'B + Dwhere A, B, C, D and I are state, input, output, feedforward andidentity matrix respectively.(ii)Find the sampled-data transfer function G(z). Assume a sampleperiod of T, and the transfer function of the ZOH as (1-eTs)/s. [Continued overleafPage 4 of 5(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 toreduce the effective delay of sample and hold. Note, that theeffective delay of sample and hold is typically half of the sampltime.

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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

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Digital to Analog Converters

Digital to analog converters are commonly known as DAC, digital analog converter, D2A, or Digital-to-Analog converters. DACs are one of the important devices used in the electronics and electrical domain. DACs are the systems that convert a digital signal into an analog signal, whereas an analog to digital converter or ADC performs the opposite function. Digital signals are those signals that can represent the information or data as a set of discrete values. At a particular instant of time, a digital signal can only take a particular value of data. A digital signal is characterized by two unique values; zeros and ones, or true and false, represented by the Boolean domain. These are also known as binary signals or logic signals. Unlike digital signals, an analog signal is represented by continuous values, where at any time instant, the analog signal is represented by a real number.

Question

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
(а)
(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.
(ii)
Find the sampled-data transfer function G(z). Assume a sample
period of T, and the transfer function of the ZOH as (1-eTs)/s. [
Continued overleaf
Page 4 of 5
(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 sampl
time.

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