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

Click For Summary
SUMMARY

The discussion focuses on calculating the sampling time (Ts) for a discrete-time system represented by a Bode plot, comparing a continuous-time plant and its discrete counterpart with a Zero Order Hold (ZOH). The key relationship established is that Ts equals 1 divided by twice the Nyquist frequency (fs/2), leading to the conclusion that Ts = 0.2 seconds when the highest frequency component is approximately 17 rad/sec. Participants confirmed that the conversion from rad/sec to Hz is necessary for accurate sampling rate calculations, emphasizing the importance of using samples/sec in these contexts.

PREREQUISITES
  • Understanding of Bode plots and their significance in control systems
  • Familiarity with Nyquist frequency and its implications for sampling
  • Basic knowledge of Zero Order Hold (ZOH) in discrete-time systems
  • Ability to convert between rad/sec and Hz for frequency calculations
NEXT STEPS
  • Study the Nyquist-Shannon sampling theorem for deeper insights into sampling rates
  • Learn about the implications of Zero Order Hold (ZOH) on system stability and performance
  • Explore advanced Bode plot analysis techniques for discrete-time systems
  • Investigate the effects of sampling time on control system response and stability
USEFUL FOR

Control engineers, systems analysts, and students studying digital signal processing who need to understand the relationship between continuous and discrete-time systems, particularly in the context of Bode plots and sampling theory.

jami8337
Messages
26
Reaction score
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!
 
Physics news on Phys.org
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.
 

Similar threads

Replies
2
Views
1K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
894
  • · Replies 1 ·
Replies
1
Views
3K
Replies
1
Views
6K
  • · Replies 12 ·
Replies
12
Views
8K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K