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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)