Consider a DC motor that changes the angular position of some load (t) as a function of an applied voltage Va(t). Friction in the motor causes interference with the electromotive force applied to the load through the armature system. The inner workings of this system are well beyond the scope of IBEHS 4A03 and are left to the electrical engineers in the group. For our purposes, the applications of Kirchhoff's and Faraday's Laws result in the following open loop block diagram for this system: V 4170 Field Amate Disturbance Ta(s) Armature Кт T(S) T₁(s) 1 Va(s) R₁ + Las Js + b Kb Back electromotive force Speed w(s) Roto: windings, Brusa St Laertia J Friction-b Ineti Load Angle 6 91 Position 0(s) Stator winding Brush Com Bearings Where Km is a motor constant, Ra is the armature resistance, La is the armature inductance, I is the inertia of the load, b is the friction of the load on the motor, and K is the gain of the interfering back electromotive force caused by friction in the motor. V (s) is the INPUT for this process, and e(s) is the OUTPUT. You do not need to know anything about electrical systems to answer these questions. 1. Using the block diagram as it presented above, show clearly that the open loop transfer 8(s) function G(s) = is described via the following third-order transfer function. You are Va(s) to assume that the disturbance signal Ta(s) = 0. e(s) G(s) = = Km 2. Va(s) s[(Ra + Las)(b + Js) + K₂Km] After substituting typical process parameters representing a disk drive reading system, the above transfer function takes the following form: 5000 e(s) G(S) = Va(s) s(s+20) (s + 1000) Based on your understanding of process dynamics and time constants, argue that this transfer function can be safely approximated as a second-order transfer function:
Consider a DC motor that changes the angular position of some load (t) as a function of an applied voltage Va(t). Friction in the motor causes interference with the electromotive force applied to the load through the armature system. The inner workings of this system are well beyond the scope of IBEHS 4A03 and are left to the electrical engineers in the group. For our purposes, the applications of Kirchhoff's and Faraday's Laws result in the following open loop block diagram for this system: V 4170 Field Amate Disturbance Ta(s) Armature Кт T(S) T₁(s) 1 Va(s) R₁ + Las Js + b Kb Back electromotive force Speed w(s) Roto: windings, Brusa St Laertia J Friction-b Ineti Load Angle 6 91 Position 0(s) Stator winding Brush Com Bearings Where Km is a motor constant, Ra is the armature resistance, La is the armature inductance, I is the inertia of the load, b is the friction of the load on the motor, and K is the gain of the interfering back electromotive force caused by friction in the motor. V (s) is the INPUT for this process, and e(s) is the OUTPUT. You do not need to know anything about electrical systems to answer these questions. 1. Using the block diagram as it presented above, show clearly that the open loop transfer 8(s) function G(s) = is described via the following third-order transfer function. You are Va(s) to assume that the disturbance signal Ta(s) = 0. e(s) G(s) = = Km 2. Va(s) s[(Ra + Las)(b + Js) + K₂Km] After substituting typical process parameters representing a disk drive reading system, the above transfer function takes the following form: 5000 e(s) G(S) = Va(s) s(s+20) (s + 1000) Based on your understanding of process dynamics and time constants, argue that this transfer function can be safely approximated as a second-order transfer function:
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...
Related questions
Question
Please explain each step clearly, show your work.I am most confused on how to move the disturbance T_d(s)
Thank you, I will give positive feedback
![Consider a DC motor that changes the angular
position of some load (t) as a function of an
applied voltage Va(t). Friction in the motor causes
interference with the electromotive force applied to
the load through the armature system. The inner
workings of this system are well beyond the scope
of IBEHS 4A03 and are left to the electrical engineers
in the group. For our purposes, the applications of
Kirchhoff's and Faraday's Laws result in the following
open loop block diagram for this system:
V
4170
Field
Amate
Disturbance
Ta(s)
Armature
Кт
T(S)
T₁(s)
1
Va(s)
R₁ + Las
Js + b
Kb
Back electromotive force
Speed
w(s)
Roto: windings,
Brusa
St
Laertia J
Friction-b
Ineti
Load
Angle
6
91
Position
0(s)
Stator
winding
Brush
Com
Bearings
Where Km is a motor constant, Ra is the armature resistance, La is the armature inductance, I is
the inertia of the load, b is the friction of the load on the motor, and K is the gain of the interfering
back electromotive force caused by friction in the motor. V (s) is the INPUT for this process, and
e(s) is the OUTPUT. You do not need to know anything about electrical systems to answer
these questions.
1.
Using the block diagram as it presented above, show clearly that the open loop transfer
8(s)
function G(s) = is described via the following third-order transfer function. You are
Va(s)
to assume that the disturbance signal Ta(s) = 0.
e(s)
G(s)
=
=
Km
2.
Va(s) s[(Ra + Las)(b + Js) + K₂Km]
After substituting typical process parameters representing a disk drive reading system, the
above transfer function takes the following form:
5000
e(s)
G(S)
=
Va(s) s(s+20) (s + 1000)
Based on your understanding of process dynamics and time constants, argue that this
transfer function can be safely approximated as a second-order transfer function:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca6b5de9-d666-4be4-bec5-372f49facd74%2Fc0a254f6-ca22-482f-88b3-3b39f12d00e0%2F3iur53b_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a DC motor that changes the angular
position of some load (t) as a function of an
applied voltage Va(t). Friction in the motor causes
interference with the electromotive force applied to
the load through the armature system. The inner
workings of this system are well beyond the scope
of IBEHS 4A03 and are left to the electrical engineers
in the group. For our purposes, the applications of
Kirchhoff's and Faraday's Laws result in the following
open loop block diagram for this system:
V
4170
Field
Amate
Disturbance
Ta(s)
Armature
Кт
T(S)
T₁(s)
1
Va(s)
R₁ + Las
Js + b
Kb
Back electromotive force
Speed
w(s)
Roto: windings,
Brusa
St
Laertia J
Friction-b
Ineti
Load
Angle
6
91
Position
0(s)
Stator
winding
Brush
Com
Bearings
Where Km is a motor constant, Ra is the armature resistance, La is the armature inductance, I is
the inertia of the load, b is the friction of the load on the motor, and K is the gain of the interfering
back electromotive force caused by friction in the motor. V (s) is the INPUT for this process, and
e(s) is the OUTPUT. You do not need to know anything about electrical systems to answer
these questions.
1.
Using the block diagram as it presented above, show clearly that the open loop transfer
8(s)
function G(s) = is described via the following third-order transfer function. You are
Va(s)
to assume that the disturbance signal Ta(s) = 0.
e(s)
G(s)
=
=
Km
2.
Va(s) s[(Ra + Las)(b + Js) + K₂Km]
After substituting typical process parameters representing a disk drive reading system, the
above transfer function takes the following form:
5000
e(s)
G(S)
=
Va(s) s(s+20) (s + 1000)
Based on your understanding of process dynamics and time constants, argue that this
transfer function can be safely approximated as a second-order transfer function:
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 8 images
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,