A closed-loop negative feedback system to be used for controlling the position of a load has a differential amplifier with transfer function K, operating a motor with transfer function 1/(sL+ R). The output of the motor operates a gear system with gear ratio N and this, in turn, operates a screw with transfer function 1/s to give the resulting displacement. The position sensor is a potentiometer and this gives a feedback voltage related to the position of the load by the transfer function K₂. Derive the transfer function for the system as a whole, relating the input voltage to the system to the displacement output.
A closed-loop negative feedback system to be used for controlling the position of a load has a differential amplifier with transfer function K, operating a motor with transfer function 1/(sL+ R). The output of the motor operates a gear system with gear ratio N and this, in turn, operates a screw with transfer function 1/s to give the resulting displacement. The position sensor is a potentiometer and this gives a feedback voltage related to the position of the load by the transfer function K₂. Derive the transfer function for the system as a whole, relating the input voltage to the system to the displacement output.
Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
10th Edition
ISBN:9781337399128
Author:Russell E. Smith
Publisher:Russell E. Smith
Chapter9: Components For Electric Motors
Section: Chapter Questions
Problem 14RQ
Related questions
Question
Number 11
![me WGS S 12-
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Page view A Read aloud
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A. 2s + 1/(s + 1)
B. 2s/(s + 1)
C. 2s(s+1)
D. (s+1)/2s
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3. A closed-loop control system has a forward loop with a transfer function of 3/(s+2) and a negative feedback
loop with a transfer function of 5. The overall transfer function of the system is:
A. 5+3/(s+2)
B. 5(s+2)/3
C. 3/(s +17)
D. 15/(s+2)
4. An open-loop control system consists of a d.c. motor with a transfer function of 2/(0.5s + 2) and a process, its
shaft and load, with a transfer function of 1/(0.1s + 0.5). The overall transfer function of the system is:
A. 2/[(0.5s +20)(0.1s +0.5)]
B. [2/(0.5s +2)] + [1/(0.1s +0.5)]
C. 2(0.1s +0.5)/0.5s + 2)
D. (0.5s + 2)(0.1s +0.5)/2
C
5. An open-loop system consists of three elements in series, the elements having transfer functions of 5, 1/s and
1/(s+1). What is the overall transfer function of the system?
6. What is the overall gain of a closed-loop negative feedback system having a forward path gain of 2 and a
feedback path gain of 0.1?
7. What is the overall transfer function of a closed-loop negative feedback system having a forward path
transfer function of 2/(s + 1) and a feedback path transfer function of 0.1?
8. Figure 9.30 shows an electrical circuit and its block diagram representation. What is the overall transfer
function of
of the system?
9. Use block simplification to arrive at the overall transfer function of the systems shown in Figure 9.31.
10. What is the overall transfer function for the systems shown in Figure 9.32?
b
Highlight
11. A A closed-loop negative feedback system to be used for controlling the position of a load has a differential
amplifier with transfer function K₁ operating a motor with transfer function 1/(sL+ R). The output of the
motor operates a gear system with gear ratio N and this, in turn, operates a screw with transfer function 1/s
to give the resulting displacement. The position sensor is a potentiometer and this gives a feedback voltage
related to the position of the load by the transfer function K₂. Derive the transfer function for the system as a
whole, relating the input voltage to the system to the displacement output.
12. A closed-loop negative feedback system for the control of the height of liquid in a tank by pumping liquid
from a reservoir tank can be considered to be a system with a differential amplifier having a transfer function
of 5, its output operating a pump with a transfer function 5/(s+1). The coupled system of tanks has a
transfer function, relating height in the tank to the output from the pump, of 3/(s + 1)(s+2). The feedback
sensor of the height level in the tank has a transfer function of 0.1. Determine the overall transfer function of
the system, relating the input voltage signal to the system to the height of liquid in the tank.
13. For the control system shown in Figure 9.33, determine the output Y(s) in terms of the inputs X₁(s) and X₂(s).
14. For the control system shown in Figure 9.34, determine the output Y(s) in terms of the inputs X₁ (s) and X₂(s).
E
Era](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F585e4a80-646c-4418-ada9-cb992a2ce44b%2Fb62f7042-d6a2-4d67-8d8e-02209711798d%2Fnk2fflt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:me WGS S 12-
/Downloads/instrumentation-and-control-systems-3nbsped-0128234717-9780128234716_compress.pdf
Page view A Read aloud
+
3
A. 2s + 1/(s + 1)
B. 2s/(s + 1)
C. 2s(s+1)
D. (s+1)/2s
TAdd text
R
Draw
V
ix
Search
3. A closed-loop control system has a forward loop with a transfer function of 3/(s+2) and a negative feedback
loop with a transfer function of 5. The overall transfer function of the system is:
A. 5+3/(s+2)
B. 5(s+2)/3
C. 3/(s +17)
D. 15/(s+2)
4. An open-loop control system consists of a d.c. motor with a transfer function of 2/(0.5s + 2) and a process, its
shaft and load, with a transfer function of 1/(0.1s + 0.5). The overall transfer function of the system is:
A. 2/[(0.5s +20)(0.1s +0.5)]
B. [2/(0.5s +2)] + [1/(0.1s +0.5)]
C. 2(0.1s +0.5)/0.5s + 2)
D. (0.5s + 2)(0.1s +0.5)/2
C
5. An open-loop system consists of three elements in series, the elements having transfer functions of 5, 1/s and
1/(s+1). What is the overall transfer function of the system?
6. What is the overall gain of a closed-loop negative feedback system having a forward path gain of 2 and a
feedback path gain of 0.1?
7. What is the overall transfer function of a closed-loop negative feedback system having a forward path
transfer function of 2/(s + 1) and a feedback path transfer function of 0.1?
8. Figure 9.30 shows an electrical circuit and its block diagram representation. What is the overall transfer
function of
of the system?
9. Use block simplification to arrive at the overall transfer function of the systems shown in Figure 9.31.
10. What is the overall transfer function for the systems shown in Figure 9.32?
b
Highlight
11. A A closed-loop negative feedback system to be used for controlling the position of a load has a differential
amplifier with transfer function K₁ operating a motor with transfer function 1/(sL+ R). The output of the
motor operates a gear system with gear ratio N and this, in turn, operates a screw with transfer function 1/s
to give the resulting displacement. The position sensor is a potentiometer and this gives a feedback voltage
related to the position of the load by the transfer function K₂. Derive the transfer function for the system as a
whole, relating the input voltage to the system to the displacement output.
12. A closed-loop negative feedback system for the control of the height of liquid in a tank by pumping liquid
from a reservoir tank can be considered to be a system with a differential amplifier having a transfer function
of 5, its output operating a pump with a transfer function 5/(s+1). The coupled system of tanks has a
transfer function, relating height in the tank to the output from the pump, of 3/(s + 1)(s+2). The feedback
sensor of the height level in the tank has a transfer function of 0.1. Determine the overall transfer function of
the system, relating the input voltage signal to the system to the height of liquid in the tank.
13. For the control system shown in Figure 9.33, determine the output Y(s) in terms of the inputs X₁(s) and X₂(s).
14. For the control system shown in Figure 9.34, determine the output Y(s) in terms of the inputs X₁ (s) and X₂(s).
E
Era
Expert Solution
Step 1
Given A closed loop negative feedback system
Differential amplifier transfer function=k1
Motor with transfer function=
Gear ratio=N
Screw transfer function=1/s
Position sensor transfer function=k2
To determine the transfer function of the system as a whole, relating the input voltage to the system to the displacement output
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