Frequency Response

1
??? ?... ?????? ??????
???????? ????? ??? ????? 1389
???? ???? ?????- ???? ??? ???? ???? ??? ????
2
Frequency Response

3
DIRECT POLAR PLOTS
We can plot transfer function in polar plan
4
DIRECT POLAR PLOTS
1. Proportional element
Transfer function
Polar plot
5
DIRECT POLAR PLOTS

• 2. Integrating element

Transfer function
Polar plot
6
DIRECT POLAR PLOTS

• 3. Inertial element

Transfer function
Polar plot
7
DIRECT POLAR PLOTS

• 4. Oscillating element

Transfer function
Make
8
DIRECT POLAR PLOTS
Polar plot
9
DIRECT POLAR PLOTS

• 5. Differentiating element

Transfer function
1
1
differential
1th-order differential
2th-order differential
Polar plot
10
DIRECT POLAR PLOTS

• 6. Delay element

Transfer function
R1
Polar plot
11
DIRECT POLAR PLOTS
To obtain the direct polar plot of a systems
forward transfer function, the following criteria
are used to determine the key parts of the curve.
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
Example

• Construction of Nyquist loci
• Loop transfer function
• By hand
• Calculate features
• Asymptotes behavior as
• Location of axes crossings

17

• System loop

• Construct Nyquist

18
(No Transcript)
19

• Quantitative analysis
• Limits

20
Im L
Re L
0.3
21

• Asymptotes for large w
• Keep dominant terms

• For w positive imaginary axis
• For w negative - imaginary axis

22
Im L
Re L
0.3
23

• Imaginary axis crossing(s)
• Real part 0

24
Im L
0.8
Re L
0.3
-0.8
25

• Real axis crossing(s)
• Imaginary part 0

26
Im L
Re L
-0.64
0.3
-0.8
27

• Matlab Nyquist

0.8
-0.64
-0.8