So I'm finishing a little write-up for the presentation that I'm giving 
in March, and I realize that I can look at a Bode plot and have a pretty 
good idea of what the system step response is going to look like.  But 
what I can't do is explain why, or justify any conclusions without 
mathematics that go way beyond the scope of my talk.

On the one hand I have the utter precision of taking the inverse Fourier 
transform of the frequency response, which doesn't yield much intuition 
but does give you an impulse response thats as exact as your frequency 
response.  On the other hand I have some hand-waving observations about 
looking for sharp amplitude or phase changes, or that long, low bump in 
the amplitude response you get from a well-damped PID controller that 
results in a long, small tail in your time-domain response, but all 
that'll do is speed up someone else's acquisition of their own intuition.

Is there a middle ground?  Can anybody recommend any good references for 
anything in between?  Something that would take 2 - 4 slides in a 
presentation would be absolutely perfect.

Thanks much.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Tim Wescott wrote:

> So I'm finishing a little write-up for the presentation that I'm giving
> in March, and I realize that I can look at a Bode plot and have a pretty
> good idea of what the system step response is going to look like.  But
> what I can't do is explain why, or justify any conclusions without
> mathematics that go way beyond the scope of my talk.
> 
> On the one hand I have the utter precision of taking the inverse Fourier
> transform of the frequency response, which doesn't yield much intuition
> but does give you an impulse response thats as exact as your frequency
> response.  On the other hand I have some hand-waving observations about
> looking for sharp amplitude or phase changes, or that long, low bump in
> the amplitude response you get from a well-damped PID controller that
> results in a long, small tail in your time-domain response, but all
> that'll do is speed up someone else's acquisition of their own intuition.
> 
> Is there a middle ground?  Can anybody recommend any good references for
> anything in between?  Something that would take 2 - 4 slides in a
> presentation would be absolutely perfect.
> 
> Thanks much.

With a little practice, a Bode plot can yield the locations of poles and
zeros by inspection, provided they aren't too close. At first at least,
laying the asymptotes with a straightedge helps. Parlaying that
information to impulse response (I always found step response easier)
requires the implicit assumption of minimum phase, which is usually
pretty accurate for most circuits.

There's a little-known gotcha. A lead-lag network to improve phase
margin is usually designed so that its pole cancels the servo's second
zero -- the one that tips the rolloff from 6 dB/octave to 12 and
therefore the phase asymptote from 90 degrees to 180. By the time the
networks pole kicks in, the loop gain is below unity and it doesn't
hurt. All well and good, but the cancellation is never complete, so
there's a hitch in the gain and phase curves that designers sometimes go
to great lengths to minimize.

Don't. The time-domain detail caused by the mismatch is also a hitch.
The step response shows a rise that extents most of the way to the
asymptotic value pretty quickly, then rises the rest of the way with a
longer time constant. The better the match, the closer the initial rise
gets to the final value, and the longer it takes to go the rest of the
way. I ran into this first with an op-amp circuit that settled to within
98% in 200 ns, and took nearly a millisecond to settle the rest of the
way to within the noise. After days of thinking and tweaking, I ended up
with 95% in 200 ns and all the way in 250. It turns out that the time
constant of the tail is nearly one over the difference of the two
frequencies one hopes will cancel. There's a price for everything.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Tim Wescott <t...@wescottnospamdesign.com> wrote in message
news:<1...@corp.supernews.com>...
> So I'm finishing a little write-up for the presentation that I'm giving 
> in March, and I realize that I can look at a Bode plot and have a pretty 
> good idea of what the system step response is going to look like.  But 
> what I can't do is explain why, or justify any conclusions without 
> mathematics that go way beyond the scope of my talk.
> 
> On the one hand I have the utter precision of taking the inverse Fourier 
> transform of the frequency response, which doesn't yield much intuition 
> but does give you an impulse response thats as exact as your frequency 
> response.  On the other hand I have some hand-waving observations about 
> looking for sharp amplitude or phase changes, or that long, low bump in 
> the amplitude response you get from a well-damped PID controller that 
> results in a long, small tail in your time-domain response, but all 
> that'll do is speed up someone else's acquisition of their own intuition.
> 
> Is there a middle ground?  Can anybody recommend any good references for 
> anything in between?  Something that would take 2 - 4 slides in a 
> presentation would be absolutely perfect.
> 
> Thanks much.
Tim, a presentation where?   A trade show?  March is trade show
season.

I know what you are trying to do.  It will be interesting to see what
you come up with.  I find it hard to pick out the zeros and poles
accurately from a Bode plot even if I know where the poles and zeros
are.  How do you get a computer a computer to pick out the poles and
zeros from a Bode plot?   This should be interesting.

If you remember I use the least squares system identification method
using data in the time domain.  I then compute the model in the z
domain then the s-domain and then I can make the bode plots.   I do it
backwards.  However, I am still interested in your approach,
especially if you have real applications where your method can be
applied.  One should always be willing to add another arrow to his
quiver.

Peter Nachtwey

Tim Wescott <t...@wescottnospamdesign.com> wrote in message
news:<1...@corp.supernews.com>...
> So I'm finishing a little write-up for the presentation that I'm giving 
> in March, and I realize that I can look at a Bode plot and have a pretty 
> good idea of what the system step response is going to look like.  But 
> what I can't do is explain why, or justify any conclusions without 
> mathematics that go way beyond the scope of my talk.
I took some ideas from my mind, I know that these are elemtary ones,
but the purpose is only to think like a newbie: Damp factor is the
most representative variable from the time response, OK? So, if we
have it, we can pre-visualize, on mind, the time response shape,
alright??? For example:0.7<Damp<1 =>exponential | 0<Damp<0.7 => Means
that overshoot exist (damped sinusoidial)| Damp=0 => Oscilatory
response, looks like a system with non-energy consumption. Damp factor
has a relation with the Phase Margin (PM) (if PM < 60 degree, a linear
relation, remember??)The phase margin can be obtained from open-loop
bode diagram analysis. But how to explain that damp factor values like
that cause what you've said? Speak a little about root locus, show a
root locus diagram of open-loop transfer function (graphs, sometimes,
speak more clear that
math expression, isn't???) and explain the relation between the
"THETA" angle and the damp factor (something like that:
Damp=cos(THETA), while THETA = arctan(Pole(Im)/Pole(Re))), this close
the thought. Well, I know that sounded elementary for you (I read your
resume), but this is a vision of a less-then-one-year junior
electrical engineer (almost nothing, hehehe)
> On the one hand I have the utter precision of taking the inverse Fourier 
> transform of the frequency response, which doesn't yield much intuition 
> but does give you an impulse response thats as exact as your frequency 
> response.  On the other hand I have some hand-waving observations about 
> looking for sharp amplitude or phase changes, or that long, low bump in 
> the amplitude response you get from a well-damped PID controller that 
> results in a long, small tail in your time-domain response, but all 
> that'll do is speed up someone else's acquisition of their own intuition.
Yes, I'm sure that is a hard math work. I like maths, but the
practical way of
the engineering is more atractive and involves "feeling" (this word
sound romantic not technical, hehe). To put Fourier's thought in 4
slides is not enough. I agree with you.
> Is there a middle ground?  Can anybody recommend any good references for 
> anything in between?  Something that would take 2 - 4 slides in a 
> presentation would be absolutely perfect.
> 
> Thanks much.
I hope I've added some new ideas. Good luck and fell free to contact

Roberto Feliciano Dias Filho
Recife-PE/Brazil

Peter Nachtwey wrote:

> Tim Wescott <t...@wescottnospamdesign.com> wrote in message
news:<1...@corp.supernews.com>...
> 
>>So I'm finishing a little write-up for the presentation that I'm giving 
>>in March, and I realize that I can look at a Bode plot and have a pretty 
>>good idea of what the system step response is going to look like.  But 
>>what I can't do is explain why, or justify any conclusions without 
>>mathematics that go way beyond the scope of my talk.
>>
>>On the one hand I have the utter precision of taking the inverse Fourier 
>>transform of the frequency response, which doesn't yield much intuition 
>>but does give you an impulse response thats as exact as your frequency 
>>response.  On the other hand I have some hand-waving observations about 
>>looking for sharp amplitude or phase changes, or that long, low bump in 
>>the amplitude response you get from a well-damped PID controller that 
>>results in a long, small tail in your time-domain response, but all 
>>that'll do is speed up someone else's acquisition of their own intuition.
>>
>>Is there a middle ground?  Can anybody recommend any good references for 
>>anything in between?  Something that would take 2 - 4 slides in a 
>>presentation would be absolutely perfect.
>>
>>Thanks much.
> 
> Tim, a presentation where?   A trade show?  March is trade show
> season.

Yes, see my other post "Shameless Plug".
> 
> I know what you are trying to do.  It will be interesting to see what
> you come up with.  I find it hard to pick out the zeros and poles
> accurately from a Bode plot even if I know where the poles and zeros
> are.  How do you get a computer a computer to pick out the poles and
> zeros from a Bode plot?   This should be interesting.

Well you don't, but if you do an IFFT on a Bode plot (particularly one 
that's taken in sampled-time) you should get an impulse response.
> 
> If you remember I use the least squares system identification method
> using data in the time domain.  I then compute the model in the z
> domain then the s-domain and then I can make the bode plots.   I do it
> backwards.  However, I am still interested in your approach,
> especially if you have real applications where your method can be
> applied.  One should always be willing to add another arrow to his
> quiver.
> 
> Peter Nachtwey

Well, I was looking for arrows for my quiver, actually -- mostly I 
wanted to know if there's a way that you can look at a Bode plot and, by 
inspection, get a good idea of what the step response is going to look 
like.  I can sort of do this intuitively, but that's from 10 years of 
looking at Bode plots and fiddling with time-domain responses and I 
don't always get it right.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com