> On Mar 20, 1:44 am, Jerry Avins <j...@ieee.org> wrote:
>> minfitl...@yahoo.co.uk wrote:
>>> On Mar 17, 6:08 am, Jerry Avins <j...@ieee.org> wrote:
>>> To the extent that their embodiment
>>>> introduces delay, the proportional signal must also be delayed if the
>>>> derivative is to apply at the same instant. For servos, this rules out
>>>> sophisticated embodiments.
>>> Delay??? You don't get delay from differentiation - noise problems yes
>>> and that's why it needs to be band limited.
>>> The main problem with too much phase-advance is that it causes an
>>> increase in high freq gain. This in turn leads to amplification of
>>> structural resonances (or other related problems). There is also a
>>> problem of crossing unity gain more than once. You need to draw this
>>> to see why but suppose you have
>> You don't get delay from differentiation, but you do get delay from
>> differentiators. In analog circuits, the delay is small. It is due to
>> transistor effects and usually ignored.
>>
>>> k/s^2 .(1+st1)^3/(1+st2)^3
>> That's analog. Try it with digital. The difference equation will include
>> terms like z^-1. Those are delays.
>>
>>> This gives a slope of -12db?octave then +6dB/octave then a -ve roll-
>>> off - 3 crossings (possibly) of 0dB. We then have 3 phase-margins!!
>> Great! Notice that a one-sample delay at Fs/2 represents a 180 degree
>> phase lag.
>>
>
> Of course but that's why you need to sample at least 10-20 times the
> max freq of interest. Digital costs - you don't get anything for
> nothing and besides - you always need to think first if a digital
> design is necessary.
First, note that "great!" was intended as sarcasm. Second, observe that
the delay of a differentiator you can actually use is nearly independent
of the sample rate. Although that applies to floating point also, it's a
little easier to see with fixed point. If you sample fast enough, the
short differentiator's output will usually be zero and sometimes |1|.
> One of the problems today is the 'lets do it digital' blind school of
> engineering. I expect soon most engineers won't know how a transistor
> works.
> Anyway - delays are no problem if you sample high enough, if you
> cannot then you need to re-think but it helps even in digital control
> to think analogue.
Quantizing in time and magnitude forces one to modify analog techniques
to a degree that can make them unrecognizable.
Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●March 20, 20072007-03-20
On Mar 20, 1:44 am, Jerry Avins <j...@ieee.org> wrote:
> minfitl...@yahoo.co.uk wrote:
> > On Mar 17, 6:08 am, Jerry Avins <j...@ieee.org> wrote:
> > To the extent that their embodiment
> >> introduces delay, the proportional signal must also be delayed if the
> >> derivative is to apply at the same instant. For servos, this rules out
> >> sophisticated embodiments.
>
> > Delay??? You don't get delay from differentiation - noise problems yes
> > and that's why it needs to be band limited.
> > The main problem with too much phase-advance is that it causes an
> > increase in high freq gain. This in turn leads to amplification of
> > structural resonances (or other related problems). There is also a
> > problem of crossing unity gain more than once. You need to draw this
> > to see why but suppose you have
>
> You don't get delay from differentiation, but you do get delay from
> differentiators. In analog circuits, the delay is small. It is due to
> transistor effects and usually ignored.
>
> > k/s^2 .(1+st1)^3/(1+st2)^3
>
> That's analog. Try it with digital. The difference equation will include
> terms like z^-1. Those are delays.
>
> > This gives a slope of -12db?octave then +6dB/octave then a -ve roll-
> > off - 3 crossings (possibly) of 0dB. We then have 3 phase-margins!!
>
> Great! Notice that a one-sample delay at Fs/2 represents a 180 degree
> phase lag.
>
Of course but that's why you need to sample at least 10-20 times the
max freq of interest. Digital costs - you don't get anything for
nothing and besides - you always need to think first if a digital
design is necessary.
One of the problems today is the 'lets do it digital' blind school of
engineering. I expect soon most engineers won't know how a transistor
works.
Anyway - delays are no problem if you sample high enough, if you
cannot then you need to re-think but it helps even in digital control
to think analogue.
F.
Reply by Tim Wescott●March 19, 20072007-03-19
minfitlike@yahoo.co.uk wrote:
-- snip --
>
>
> Hasn't anybody heard of phase advance? Simple undergrad stuff - come
> on...don't reinvent the wheel.
>
> F.
>
And how are you going to achieve this phase advance without either
non-causal filtering or differentiators?
Much of that 'simple undergraduate stuff' is simple because it aids
teaching, not because it is unconditionally useful in the real world or
even physically possible. Where it is physically possible, and
sometimes useful, one has to be exquisitely aware of its limitations to
keep oneself from applying it where it will do more harm than good.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Posting from Google? See http://cfaj.freeshell.org/google/
"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by Peter Nachtwey●March 19, 20072007-03-19
Scott L wrote:
> In my math doodlings, I wrote the second derivative as:
>
> (e[n] + e[n-2] - 2*e[n-1]) / dt^2
>
> I.e., the typical finite difference approximation (obviously not
> centered). Are you saying that's too naive in the presence of noise?
Yes, but forget about noise for now. The real enemy is quantizing. I
see application every day where the feed back resolution is only 0.0001m
but even if the feedback resolution is .00001m there is still problems.
Assume the sample time is .001s and the resolution is .00001m then
the best resolution on the acceleration is 10m/s^2 or a little over 1g.
That isn't really usable for motion control. If you try to use the
0.00001m resolution you will be severely limited in how high the double
derivative gain can be increased without the control output going
wild. Low pass output filter will help only a little but not enough.
Fortunately, most system can be modeled as having just one or two poles
so a normal PID will do well enough until you start to push it to point
where higher order un-modeled poles start to affect control. Then you
must start identifying these higher frequency poles too and add higher
order derivative gains the the controller so these poles can be placed
somewhere safe. In the process you will need feedback to that can
measure these gains directly or you need some sort of filter or observer
that can estimate the higher order derivatives better than you can
measure them directly.
When noise is added the problem is even worse.
Peter Nachtwey
Reply by Jerry Avins●March 19, 20072007-03-19
minfitlike@yahoo.co.uk wrote:
...
> Hasn't anybody heard of phase advance? Simple undergrad stuff - come
> on...don't reinvent the wheel.
You can't use analog grease on a digital axle.
Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by Jerry Avins●March 19, 20072007-03-19
minfitlike@yahoo.co.uk wrote:
> On Mar 17, 6:08 am, Jerry Avins <j...@ieee.org> wrote:
> To the extent that their embodiment
>> introduces delay, the proportional signal must also be delayed if the
>> derivative is to apply at the same instant. For servos, this rules out
>> sophisticated embodiments.
>>
> Delay??? You don't get delay from differentiation - noise problems yes
> and that's why it needs to be band limited.
> The main problem with too much phase-advance is that it causes an
> increase in high freq gain. This in turn leads to amplification of
> structural resonances (or other related problems). There is also a
> problem of crossing unity gain more than once. You need to draw this
> to see why but suppose you have
You don't get delay from differentiation, but you do get delay from
differentiators. In analog circuits, the delay is small. It is due to
transistor effects and usually ignored.
> k/s^2 .(1+st1)^3/(1+st2)^3
That's analog. Try it with digital. The difference equation will include
terms like z^-1. Those are delays.
> This gives a slope of -12db?octave then +6dB/octave then a -ve roll-
> off - 3 crossings (possibly) of 0dB. We then have 3 phase-margins!!
Great! Notice that a one-sample delay at Fs/2 represents a 180 degree
phase lag.
Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●March 19, 20072007-03-19
On Mar 17, 6:08 am, Jerry Avins <j...@ieee.org> wrote:
To the extent that their embodiment
> introduces delay, the proportional signal must also be delayed if the
> derivative is to apply at the same instant. For servos, this rules out
> sophisticated embodiments.
>
Delay??? You don't get delay from differentiation - noise problems yes
and that's why it needs to be band limited.
The main problem with too much phase-advance is that it causes an
increase in high freq gain. This in turn leads to amplification of
structural resonances (or other related problems). There is also a
problem of crossing unity gain more than once. You need to draw this
to see why but suppose you have
k/s^2 .(1+st1)^3/(1+st2)^3
This gives a slope of -12db?octave then +6dB/octave then a -ve roll-
off - 3 crossings (possibly) of 0dB.We then have 3 phase-margins!!
F.
Reply by ●March 19, 20072007-03-19
On Mar 17, 6:18 am, Tim Wescott <t...@seemywebsite.com> wrote:
> Scott L wrote:
> > On Mar 16, 7:57 am, "Peter Nachtwey" <p...@deltacompsys.com> wrote:
>
> >>You can't use an
> >>accelerometer or other hardware so you should look into a higher order
> >>Butterworth filter or observer. The observer can be used to estimate
> >>the second derivative without the lag of a Butterworth filter.
>
> > In my math doodlings, I wrote the second derivative as:
>
> > (e[n] + e[n-2] - 2*e[n-1]) / dt^2
>
> > I.e., the typical finite difference approximation (obviously not
> > centered). Are you saying that's too naive in the presence of noise?
>
> Yes. You need to low-pass that to get a good answer. You can combine
> the differentiator and the low-pass, and you can cascade two such
> differentiators (you'll want to get the 1st-differentiator answer
> anyway). I'm feeling too lazy to go into depth here (it's in my book),
> but you're looking for a transfer function in the z domain that looks like:
>
> /(1-d)(z-1)\ 2
> H_d(z) = | ---------- |
> \ z - d /
>
> (note that you could use two different roll-off frequencies and probably
> want to -- just using one and squaring the transfer function is another
> instance of laziness on my part).
>
> If you don't know z transforms, buy my book or look athttp://www.wescottdesign.com/articles/zTransform/z-transforms.html.
>
> --
>
> Tim Wescott
> Wescott Design Serviceshttp://www.wescottdesign.com
>
> Posting from Google? Seehttp://cfaj.freeshell.org/google/
>
> "Applied Control Theory for Embedded Systems" came out in April.
> See details athttp://www.wescottdesign.com/actfes/actfes.html
Hasn't anybody heard of phase advance? Simple undergrad stuff - come
on...don't reinvent the wheel.
F.
Reply by Tim Wescott●March 16, 20072007-03-16
Scott L wrote:
> On Mar 16, 7:57 am, "Peter Nachtwey" <p...@deltacompsys.com> wrote:
>
>>You can't use an
>>accelerometer or other hardware so you should look into a higher order
>>Butterworth filter or observer. The observer can be used to estimate
>>the second derivative without the lag of a Butterworth filter.
>
>
> In my math doodlings, I wrote the second derivative as:
>
> (e[n] + e[n-2] - 2*e[n-1]) / dt^2
>
> I.e., the typical finite difference approximation (obviously not
> centered). Are you saying that's too naive in the presence of noise?
>
Yes. You need to low-pass that to get a good answer. You can combine
the differentiator and the low-pass, and you can cascade two such
differentiators (you'll want to get the 1st-differentiator answer
anyway). I'm feeling too lazy to go into depth here (it's in my book),
but you're looking for a transfer function in the z domain that looks like:
/(1-d)(z-1)\ 2
H_d(z) = | ---------- |
\ z - d /
(note that you could use two different roll-off frequencies and probably
want to -- just using one and squaring the transfer function is another
instance of laziness on my part).
If you don't know z transforms, buy my book or look at
http://www.wescottdesign.com/articles/zTransform/z-transforms.html.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Posting from Google? See http://cfaj.freeshell.org/google/
"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by Jerry Avins●March 16, 20072007-03-16
Scott L wrote:
> On Mar 16, 7:57 am, "Peter Nachtwey" <p...@deltacompsys.com> wrote:
>> You can't use an
>> accelerometer or other hardware so you should look into a higher order
>> Butterworth filter or observer. The observer can be used to estimate
>> the second derivative without the lag of a Butterworth filter.
>
> In my math doodlings, I wrote the second derivative as:
>
> (e[n] + e[n-2] - 2*e[n-1]) / dt^2
>
> I.e., the typical finite difference approximation (obviously not
> centered). Are you saying that's too naive in the presence of noise?
Differentiators have a gain that is proportional to frequency. They
emphasize high-frequency noise to the point that it can dominate the
signal. Digital or analog, their high-frequency responses are always
limited on control applications. To the extent that their embodiment
introduces delay, the proportional signal must also be delayed if the
derivative is to apply at the same instant. For servos, this rules out
sophisticated embodiments.
Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯