Sampling Time Calculation for Bode Plots: Plant Comparison & ZOH Preceding

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Discussion Overview

The discussion revolves around calculating the sampling time for Bode plots of a continuous-time plant and its discrete-time counterpart with a Zero Order Hold (ZOH). Participants explore the relationship between sampling frequency, Nyquist frequency, and the conversion of frequency units in the context of Bode plots.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant suggests that the sampling frequency is related to the formula f = 1/T.
  • Another participant notes that the vertical line on the Bode plot indicates the highest frequency component representable in a discrete-time system, which is linked to the sampling frequency.
  • There is a question about whether the highest frequency is represented by fs/2, which is confirmed by another participant as the Nyquist frequency.
  • Participants discuss the relationship between the Nyquist frequency and sampling time, with one stating that Ts = 1/(2*Nyquist frequency).
  • There is a query regarding the conversion of frequency from rad/sec to Hz for use in the equations, which is affirmed by another participant who emphasizes the importance of using Hz for sampling rate calculations.
  • One participant calculates a frequency of approximately 2.55 Hz from a given highest frequency of 16 rad/sec and derives a sampling time of 0.2 seconds.

Areas of Agreement / Disagreement

Participants generally agree on the relationships between Nyquist frequency, sampling frequency, and sampling time, but there are ongoing discussions about unit conversions and specific calculations, indicating some uncertainty in the details.

Contextual Notes

Participants express some uncertainty regarding the conversion of frequency units and the implications for sampling time calculations. There are also unresolved aspects related to the specific values used in the calculations.

jami8337
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Homework Statement


In the figure, the Bode plots of a continuous-time plant (thin line) and of its discrete-time counterpart, representing the discrete-time operation of the plant preceded by a Zero Order Hold (ZOH) (bold line), are displayed. What is the Sampling time used?
Capture.PNG


Homework Equations



I figure it has something to do with f= 1/T, but other than that I am really not sure how to use it with the bode plot, any pointers would be great!
 
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That vertical line tells you something about the highest frequency component you can represent in a discrete-time system, which is very intimately related to the sampling frequency of the system.

Does that help?
 
Ok, is the highest frequency then represented by fs/2 ?
 
jami8337 said:
Ok, is the highest frequency then represented by fs/2 ?
Yes, the Nyquist frequency of the sampling system.
 
So if the Nyquist frequency is fs/2 and fs= 1/Ts,

Ts = 1/2*Nyquist frequency ?
 
jami8337 said:
So if the Nyquist frequency is fs/2 and fs= 1/Ts,

Ts = 1/2*Nyquist frequency ?
Well, to be more precise, Ts = 1/(2*nyquist freq.).
 
Ah yeah that's what I meant. So the highest frequency here would be about 17 rad/sec? Do i need to convert this into Hz in order to use it in the equation?
 
jami8337 said:
Ah yeah that's what I meant. So the highest frequency here would be about 17 rad/sec? Do i need to convert this into Hz in order to use it in the equation?
Yes. That's because sampling rate is always given in samples/sec. and so the sampling time is 1/sampling rate and fs = 1/2 sampling rate. Avoid rad/sec. in sampling questions, in general.
 
Ah ok, so (1/2Π)*16rad/sec = 2.55 Hz

Then Ts= 1/(2*fs) = 0.2

Thats great, thanks for all your help!
 
  • #10
jami8337 said:
Ah ok, so (1/2Π)*16rad/sec = 2.55 Hz

Then Ts= 1/(2*fs) = 0.2

Thats great, thanks for all your help!
Right. 0.2s.
 

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