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Sheet 4

This document contains a sheet from an Automatic Control course. It lists 9 problems involving analyzing control systems using Bode diagrams and determining phase and gain margins. The problems involve plotting Bode diagrams, calculating phase and gain margins, and determining gain values needed for specified phase margins. The sheet provides the transfer functions and block diagrams of various open-loop control systems to analyze.

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45 views2 pages

Sheet 4

This document contains a sheet from an Automatic Control course. It lists 9 problems involving analyzing control systems using Bode diagrams and determining phase and gain margins. The problems involve plotting Bode diagrams, calculating phase and gain margins, and determining gain values needed for specified phase margins. The sheet provides the transfer functions and block diagrams of various open-loop control systems to analyze.

Uploaded by

bipico9217
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Aswan University

Fourth Year
Faculty of Engineering
Automatic Control (II) Course
Electrical Engineering Department
First Semester
Computers and Systems Section
Sheet No. 4

Sheet No. 4

1- Plot a Bode diagram for the following transfer functions:


25
a. 𝐺(𝑠) =
𝑠 2 +4𝑠+25
9(𝑠 2 +0.2𝑠+1)
b. 𝐺(𝑠) =
𝑠(𝑠 2 +1.2𝑠+9)
2- Obtain the phase and gain margin of the system shown in below for the two cases where K=10 and
K=100.

R(s) C(s)
K
+
- s ( s  1)( s  5 )

3- For the figure shown in below, determine the gain K such that the phase margin is 50° . What is the
gain margin in this case?
C(s)
R(s) K (s  2)
+
- s2

4- Consider the unity-feedback control system whose open-loop transfer function is:
𝑎𝑠 + 1
𝐺(𝑠) =
𝑠2
- Determine the value of a so that the phase margin is 45° .

5- Consider the unity-feedback system with the open-loop transfer function:


10
𝐺(𝑠) =
(𝑠 + 1)

- Obtain the steady-state output of the system when it is subjected to each of the following
inputs:
a. 𝑟(𝑡) = sin⁡(𝑡 + 30)
b. 𝑟(𝑡) = 2𝑐𝑜𝑠⁡(2𝑡 − 45)
c. 𝑟(𝑡) = sin(𝑡 + 30) − 2cos⁡(2𝑡 − 45)

6- Given:
𝜔𝑛2
𝐺(𝑠) =
(𝑠 2 + 2𝜁𝜔𝑛 𝑠 + 𝜔𝑛2 )
1
Show that: |𝐺(𝑗𝜔𝑛 )| =
2𝜁

With my best wishes Dr. Mountasser M. Mohamed


Aswan University
Fourth Year
Faculty of Engineering
Automatic Control (II) Course
Electrical Engineering Department
First Semester
Computers and Systems Section
Sheet No. 4

7- Draw a Bode diagram of the open-loop transfer function G(s). Determine the phase margin and
gain margin.
a.

R(s) C(s)
25
+
- s ( s  1 )( s  10 )

G(s)

b.

R(s) C(s)
20( s  1)
+ s ( s  2 s  10)( s  5)
2
-
G(s)

8- Consider a unity-feedback control system with the open-loop transfer function:

𝐾
𝐺(𝑠) =
𝑠(𝑠 2 + 𝑠 + 4)

- Determine the value of the gain K such that the phase margin is 50° . What is the gain
margin with this gain K?

9- Draw a Bode diagram of the open-loop transfer function, and determine the value of the gain K
such that the phase margin is 50° . What is the gain margin with this gain K?

C(s)
R(s) 20 K ( s  0 . 1)
+
- s ( s  1)( s  0 . 5 )

G(s)

With my best wishes Dr. Mountasser M. Mohamed

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