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

In summary, the conversation discusses the Bode plots of a continuous-time plant and its discrete-time counterpart, as well as the sampling time used in the system. The highest frequency represented in a discrete-time system is related to the Nyquist frequency, which can be calculated using the sampling frequency (fs). The highest frequency in the given system is approximately 17 rad/sec, which needs to be converted into Hz before using it in the equation. The sampling time (Ts) can be calculated as 1/(2*fs), which in this case is 0.2s.
  • #1
jami8337
26
0

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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  • #2
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?
 
  • #3
Ok, is the highest frequency then represented by fs/2 ?
 
  • #4
jami8337 said:
Ok, is the highest frequency then represented by fs/2 ?
Yes, the Nyquist frequency of the sampling system.
 
  • #5
So if the Nyquist frequency is fs/2 and fs= 1/Ts,

Ts = 1/2*Nyquist frequency ?
 
  • #6
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.).
 
  • #7
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?
 
  • #8
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.
 
  • #9
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.
 

1. What is the significance of sampling time in Bode plots?

The sampling time in Bode plots refers to the interval at which data points are collected and plotted on the frequency response graph. It is an important factor in accurately representing the system's behavior and determining its stability.

2. How does the sampling time affect the accuracy of Bode plots?

The sampling time can affect the accuracy of Bode plots in two ways. Firstly, a longer sampling time can result in a lower resolution and less detailed frequency response plot. Secondly, if the sampling time is too short, it can introduce errors and distortions in the plot due to aliasing. Therefore, selecting an appropriate sampling time is crucial for obtaining accurate Bode plots.

3. Can the sampling time be adjusted after collecting data for a Bode plot?

Yes, the sampling time can be adjusted after collecting data for a Bode plot. However, it is recommended to maintain a consistent sampling time throughout the entire data collection process to ensure accuracy and consistency in the results.

4. How do I determine the optimal sampling time for a Bode plot?

The optimal sampling time for a Bode plot depends on the system's dynamics and the desired frequency range. It is generally recommended to use a sampling time that is at least ten times smaller than the system's fastest dynamics. However, if the system's dynamics are not known, it is best to perform a sensitivity analysis by varying the sampling time and observing its effect on the Bode plot.

5. What are the consequences of using an incorrect sampling time in a Bode plot?

Using an incorrect sampling time in a Bode plot can result in inaccurate representation of the system's behavior, leading to incorrect conclusions about its stability and performance. It can also introduce errors and distortions in the plot, making it difficult to interpret the results accurately. Therefore, it is crucial to carefully select an appropriate sampling time for obtaining reliable Bode plots.

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