Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
E(t)=u(t) num(z) 20 den(z) $2+9s+20 Zero-Order Hold Digital Controller Plant Y(t) Fig. 2 A closed-loop sampled-data system with digital controller 2. Consider the closed-loop sampled-data system that is given in Fig. 2. a) Design a unity-dc-gain phase-lag compensator that yields a phase margin of 45 degree. Use ww1 = 10.6 rad/sec. b) Start simulink and construct the model that is given in Fig.2. Additionally, in order to plot the Y(t) by using workspace use a clock and a workspace blocks which are named as t, ytSampled. Set the sampling time -1 for all workspace blocks. Use the result of e for Digital Controller. Select an appropriate time for simulation and run it by clicking on the start button. Plot the Y(t) by using t and ytSampled. c) Plot the Bode diagram of this system and determine the phase and gain margin. d) Repeat a, b and c for ww₁ = 23 rad/sec and ww₁ = 83.6 rad/sec. e) Discuss the effect of the phase-lead compensator for different w₁values (Hint: Consider both the transient and steady-state responses). Does the increment in the ww₁ destabilize this system? Explain your answer by proving the mathematical expressions.

E(t)=u(t) num(z) 20 den(z) $2+9s+20 Zero-Order Hold Digital Controller Plant Y(t) Fig. 2 A closed-loop sampled-data system with digital controller 2. Consider the closed-loop sampled-data system that is given in Fig. 2. a) Design a unity-dc-gain phase-lag compensator that yields a phase margin of 45 degree. Use ww1 = 10.6 rad/sec. b) Start simulink and construct the model that is given in Fig.2. Additionally, in order to plot the Y(t) by using workspace use a clock and a workspace blocks which are named as t, ytSampled. Set the sampling time -1 for all workspace blocks. Use the result of e for Digital Controller. Select an appropriate time for simulation and run it by clicking on the start button. Plot the Y(t) by using t and ytSampled. c) Plot the Bode diagram of this system and determine the phase and gain margin. d) Repeat a, b and c for ww₁ = 23 rad/sec and ww₁ = 83.6 rad/sec. e) Discuss the effect of the phase-lead compensator for different w₁values (Hint: Consider both the transient and steady-state responses). Does the increment in the ww₁ destabilize this system? Explain your answer by proving the mathematical expressions.

Introductory Circuit Analysis (13th Edition)
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...
See similar textbooks
icon
Related questions
Question
E(t)=u(t) num(z) 20 den(z) $2+9s+20 Zero-Order Hold Digital Controller Plant Y(t) Fig. 2 A closed-loop sampled-data system with digital controller 2. Consider the closed-loop sampled-data system that is given in Fig. 2. a) Design a unity-dc-gain phase-lag compensator that yields a phase margin of 45 degree. Use ww1 = 10.6 rad/sec. b) Start simulink and construct the model that is given in Fig.2. Additionally, in order to plot the Y(t) by using workspace use a clock and a workspace blocks which are named as t, ytSampled. Set the sampling time -1 for all workspace blocks. Use the result of e for Digital Controller. Select an appropriate time for simulation and run it by clicking on the start button. Plot the Y(t) by using t and ytSampled. c) Plot the Bode diagram of this system and determine the phase and gain margin. d) Repeat a, b and c for ww₁ = 23 rad/sec and ww₁ = 83.6 rad/sec. e) Discuss the effect of the phase-lead compensator for different w₁values (Hint: Consider both the transient and steady-state responses). Does the increment in the ww₁ destabilize this system? Explain your answer by proving the mathematical expressions.
Transcribed Image Text:E(t)=u(t) num(z) 20 den(z) $2+9s+20 Zero-Order Hold Digital Controller Plant Y(t) Fig. 2 A closed-loop sampled-data system with digital controller 2. Consider the closed-loop sampled-data system that is given in Fig. 2. a) Design a unity-dc-gain phase-lag compensator that yields a phase margin of 45 degree. Use ww1 = 10.6 rad/sec. b) Start simulink and construct the model that is given in Fig.2. Additionally, in order to plot the Y(t) by using workspace use a clock and a workspace blocks which are named as t, ytSampled. Set the sampling time -1 for all workspace blocks. Use the result of e for Digital Controller. Select an appropriate time for simulation and run it by clicking on the start button. Plot the Y(t) by using t and ytSampled. c) Plot the Bode diagram of this system and determine the phase and gain margin. d) Repeat a, b and c for ww₁ = 23 rad/sec and ww₁ = 83.6 rad/sec. e) Discuss the effect of the phase-lead compensator for different w₁values (Hint: Consider both the transient and steady-state responses). Does the increment in the ww₁ destabilize this system? Explain your answer by proving the mathematical expressions.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE 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,
SEE MORE TEXTBOOKS