How Do You Draw a Bode Plot for a Given Transfer Function?

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Discussion Overview

The discussion revolves around the process of drawing a Bode plot for a given transfer function in an open loop control system. Participants explore the mathematical and graphical representation of the transfer function, including the individual components and their contributions to the overall plot.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a transfer function and requests feedback on their initial Bode plot, indicating they have not yet completed the summation graph.
  • Another participant suggests using WolframAlpha to verify the Bode plot and questions the values obtained by the original poster.
  • There is a discussion about the absence of upward-sloping asymptotes in the Bode plot, with a participant explaining that an upward slope requires specific terms in the numerator.
  • Participants discuss the rules for calculating the slopes of the Bode plot lines, including the logarithmic relationships and how to represent them graphically.
  • One participant expresses uncertainty about how to draw the lines accurately, particularly regarding the angles of the slopes.
  • Another participant emphasizes the importance of the original transfer function in determining the gain and corner frequencies for the Bode plot.
  • There are mentions of different interpretations of the results, with one participant noting discrepancies between their manual's answer and the plotted results discussed in the thread.
  • Participants question the understanding of limits as s approaches zero and how that relates to the Bode plot, indicating a gap in their studies.
  • There is a request for clarification on the diagrams shared, with some participants noting differences in axes and scales between their plots and those referenced by others.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the Bode plot construction and the mathematical principles involved. There is no consensus on the correct approach or interpretation of the results, with multiple competing views and some unresolved questions about the methodology.

Contextual Notes

Some participants indicate limitations in their understanding of certain mathematical concepts, such as limits and logarithmic calculations, which may affect their ability to accurately draw the Bode plot. There are also discrepancies in the results obtained from different sources, leading to confusion about the correct representation of the transfer function.

  • #31
I think you'll find that the factored version of the transfer function spells out the poles conveniently in terms of the natural angular frequency (rad/sec).

Then this logic does not match Nascent's graph who posted right before you. The break point seems to be at 0.1

the slope increases by 40 db/decade

Increase or decrease - that depends whether this expression is in the nominator or denominator
 
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  • #32
Femme_physics said:
Then this logic does not match Nascent's graph who posted right before you. The break point seems to be at 0.1
Right. His graph has frequency f in Hz along the x-axis. Natural frequency ω is in rad/sec, where ##ω = 2\pi f##.
Increase or decrease - that depends whether this expression is in the nominator or denominator
Heh. Yes, by "increase" I meant steeper descent for each pole. Zeros in the numerator have the opposite effect, tilting the slope upwards by 20 db/decade for each zero.
 
  • #33
Femme_physics said:
Then this logic does not match Nascent's graph who posted right before you. The break point seems to be at 0.1
That's because gneill helpfully threw in a new transfer function, for clarity.
Increase or decrease - that depends whether this expression is in the nominator or denominator
Certainly.
 
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  • #34
NascentOxygen said:
That's because gneill helpfully invented another transfer function, for clarity.
Ah yes, er, that too :smile:

Actually I went back to the original transfer function for the thread, since I though it might be helpful to compare with the related plots.
 
  • #35
gneill said:
I went back to the original transfer function for the thread, since I though it might be helpful to compare with the related plots.
The original TF had poles at -1 and -4. Though easy to get confused here, I know. :wink:
 
  • #36
NascentOxygen said:
The original TF had poles at -1 and -4. Though easy to get confused here, I know. :wink:

Aurrgh! So much for short term memory. Heck, it was only three pages ago, too!
 
  • #38
The way I described it, is how I learned it some time ago.

However, after gneill's and NascO's comments, I've looked it up on wiki, and I found this section on how to draw Bode plots by hand:
http://en.wikipedia.org/wiki/Bode_plot#Rules_for_handmade_Bode_plot
This is basically what they already said.

In the end I believe it is somewhat arbitrary, since the real transfer function plot does not consist of straight lines.
But I certainly concur that we should follow the standard methods.

Here's the graph I've made with the "actual" transfer function for ##G(s)={400 \over (s+1)(s+4)}##, my version, and NascO/gneill's version.

attachment.php?attachmentid=55077&stc=1&d=1359286223.jpg


As you can see, it doesn't really matter (my version is actually closer), but I do propose to follow NascO/gneill's suggestions.
 

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  • #39
Well, now that ILS has cleared that up... :wink:

there is no stopping yet, because as I pointed out earlier, we are only halfway there!

http://physicsforums.bernhardtmediall.netdna-cdn.com/images/icons/icon2.gif Don't forget that the Bode Plot requires a plot of angle vs. frequency as well as dB vs. frequency.

BTW, I think we have left FemmePhysics some miles back along the way. Should we turn back to look for her?
 
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  • #40
NascentOxygen said:
BTW, I think we have left FemmePhysics some miles back along the way. Should we turn back to look for her?

I'm sure that FP will track us down in due course. Probably just waiting for the dust to settle :smile:
 
  • #41
I'm here! Except, I already had the Control Systems semester test yesterday. The sad part is that everything BUT the Bode Plot I'm sure I got right ;) But at least I didn't have to DRAW a graph, the graphs were given to me, I just had to find the function that describes it. So far I'm able to keep a 90+ average (out of a 100) with the help of physicsforums, or most specific you guys.
I had some solved examples to work with...hopefully I got it right. I might approach this thread before the final test of my degree (May-July), provided you'll still be around :)

I really appreciate your help, especially ILS that always goes above and beyond (amazing). If I didn't get the bode plots right I'll come here to whine, rest be assured!

Now I have machine parts test to take in 5 days so I better get in shape. :-) I appreciate your help, guys.
 

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