Given a Bode diagram of a dynamic system, shown in Fig. 4: (a) Find the transfer function of the system G(s) (asymptotes are drawn for you and their slopes are indicated) T (b) Derive the open-loop system response to a harmonic input 2 cos 10t+- (c) Assuming a negative unity feedback configuration: Determine the gain and phase margins of the system Is the system closed-loop stable? Verify your answer using Nyquist plot (use software to generate Nyquist plot and explain how it confirms your conclusion of closed-loop stability/instability) (d) Assuming a proportional controller with gain Kp and negative unity feedback configuration: Can the system be destabilized by a finite gain proportional controller? If yes, find the gain K, that destabilizes the system. If not, explain why not. (e) Find Kp for the system to have a phase margin 20⁰ (f) What is the system phase margin when Kp = 10? At this value of Kp: What is the steady-state error of the closed-loop system to a step input of magnitude A? ● ● ● What is the steady-state error of the closed-loop system to a ramp input of magnitude A? NOTE: parts (b), (c), (e), (f) need to be solved graphically

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...
icon
Related questions
Question
100%
Given a Bode diagram of a dynamic system, shown in Fig. 4:
(a) Find the transfer function of the system G(s)
(asymptotes are drawn for you and their slopes are indicated)
(b) Derive the open-loop system response to a harmonic input 2 cos 10t+ 44
(c) Assuming a negative unity feedback configuration:
Determine the gain and phase margins of the system
Is the system closed-loop stable? Verify your answer using Nyquist plot (use software
to generate Nyquist plot and explain how it confirms your conclusion of closed-loop
stability/instability)
(d) Assuming a proportional controller with gain K₂ and negative unity feedback
configuration:
Can the system be destabilized by a finite gain proportional controller? If yes, find the
gain Kp that destabilizes the system. If not, explain why not.
(e) Find Kp for the system to have a phase margin 20⁰
(f) What is the system phase margin when K₂ = 10? At this value of Kp:
What is the steady-state error of the closed-loop system to a step input of magnitude
A?
|G(jw)|, dB
●
ø, degrees
●
NOTE:
parts (b), (c), (e), (f) need to be solved graphically
What is the steady-state error of the closed-loop system to a ramp input of magnitude
A?
0
-20
-40
-60
-80
0.01
50
0
-50
-100
-150
0.01
20 dB dec
0.1
0.1
1
1
0 dB/dec
w, rad/sec
w, rad/sec
Figure 4
10
10
↑hump
40 dB/dec
100
100
1000
1000
Transcribed Image Text:Given a Bode diagram of a dynamic system, shown in Fig. 4: (a) Find the transfer function of the system G(s) (asymptotes are drawn for you and their slopes are indicated) (b) Derive the open-loop system response to a harmonic input 2 cos 10t+ 44 (c) Assuming a negative unity feedback configuration: Determine the gain and phase margins of the system Is the system closed-loop stable? Verify your answer using Nyquist plot (use software to generate Nyquist plot and explain how it confirms your conclusion of closed-loop stability/instability) (d) Assuming a proportional controller with gain K₂ and negative unity feedback configuration: Can the system be destabilized by a finite gain proportional controller? If yes, find the gain Kp that destabilizes the system. If not, explain why not. (e) Find Kp for the system to have a phase margin 20⁰ (f) What is the system phase margin when K₂ = 10? At this value of Kp: What is the steady-state error of the closed-loop system to a step input of magnitude A? |G(jw)|, dB ● ø, degrees ● NOTE: parts (b), (c), (e), (f) need to be solved graphically What is the steady-state error of the closed-loop system to a ramp input of magnitude A? 0 -20 -40 -60 -80 0.01 50 0 -50 -100 -150 0.01 20 dB dec 0.1 0.1 1 1 0 dB/dec w, rad/sec w, rad/sec Figure 4 10 10 ↑hump 40 dB/dec 100 100 1000 1000
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 9 steps with 3 images

Blurred answer
Knowledge Booster
Nyquist Plot
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,