Kamman – Introductory Control Systems – Exercises #15 – Bode Magnitude Diagrams Answers – page: 1/4

Introductory Control Systems

Exercises #15 – Bode Magnitude Diagrams Answers

Note: All frequency ranges given below are approximate based on the Bode diagram sketch. The range can be

found more accurately and verified using MATLAB®, for example. The estimated range is reasonably

accurate in most cases.

1. ( )( )2

270 ( 10)( )

3 + 40s + 900

s sG s

s s

+=

+

System amplifies the input ( )0 dBM :

1 250 (rad/s)

System attenuates the input ( )0 dBM :

1 (rad/s) and 250 (rad/s)

2. ( )2

10 ( 2)( 50)( )

+15s +100

s sG s

s s

+ +=

System amplifies the input ( )0 dBM :

20 (rad/sec)

System attenuates the input ( )0 dBM :

20 (rad/s)

Kamman – Introductory Control Systems – Exercises #15 – Bode Magnitude Diagrams Answers – page: 2/4

3. ( )2

25 ( 5)( 20)( )

+ 70s + 2500

s sG s

s s

+ +=

System amplifies the input ( )0 dBM :

1 (rad/s)

System attenuates the input ( )0 dBM :

1 (rad/s)

4. ( )( )2

6310 ( 3)( )

60 +15s +100

sG s

s s

+=

+

System amplifies the input ( )0 dBM :

80 (rad/s)

System attenuates the input ( )0 dBM :

80 (rad/s)

Kamman – Introductory Control Systems – Exercises #15 – Bode Magnitude Diagrams Answers – page: 3/4

5. 2

1820( 10)( )

( 2)( +50s+900)

sG s

s s

+=

+

System amplifies the input ( )0 dBM :

40 (rad/s)

System attenuates the input ( )0 dBM :

40 (rad/s)

6. 2

1250( 20)( )

( 100)( +5s+25)

sG s

s s

+=

+

System amplifies the input ( )0 dBM :

16 (rad/s)

System attenuates the input ( )0 dBM :

16 (rad/s)

Kamman – Introductory Control Systems – Exercises #15 – Bode Magnitude Diagrams Answers – page: 4/4

7. 2

1186( 2)( )

( 30)( +4s+25)

sG s

s s

+=

+

System amplifies the input ( )0 dBM :

32 (rad/sec)

System attenuates the input ( )0 dBM :

32 (rad/sec)

8. ( )( )2

7906( )

10 + 70s + 2500

sG s

s s=

+

System amplifies the input ( )0 dBM :

3 85 (r/s)

System attenuates the input ( )0 dBM :

3 (rad/s) and 85 (rad/s)