# Jitter

**URL:** <http://discourse.iapct.org/t/jitter/5942>\
**Category:** CSG1995\
**Created:** [June 22, 1995, 4:21pm UTC](http://discourse.iapct.org/t/jitter/5942 "1995-06-22T16:21:22Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![\_Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/_/a9adbd/32.png) [@\_Martin\_Taylor](http://discourse.iapct.org/u/_Martin_Taylor)\
**Post date:** [June 22, 1995, 4:21pm UTC](http://discourse.iapct.org/t/jitter/5942/1 "1995-06-22T16:21:22Z")

</div>

[Martin Taylor 950622 12:00]

> Bill Powers (950621.1415 MDT) to Hans Blom (950621a)

> &nbsp;&nbsp;&nbsp;&nbsp;When there would be no noise in the system, all errors would be  
> &nbsp;&nbsp;&nbsp;&nbsp;zero if there are no conflicts.
> 
> This isn't true in a negative feedback control system. If there are  
> systematic disturbances, there must be error to drive the output that  
> systematically opposes the disturbances. The error signal itself can be  
> small in comparison with the reference signal, but it must be amplified  
> so the result is sufficient output to handle the range of disturbances.

This straightforward fact highlighted an issue that has been on the edge  
of my consciousness for quite a long time: it concerns jitter.

Many control systems, including human ones, show jitter, which is a  
non-systematic high-frequency deviation about the mean value of whatever  
signal one examines. Various uses for jitter have been proposed, some  
of which I heard as an undergraduate, some on CSG-L. But I have not heard  
the following, and I am wondering whether those with practical experience  
with either human or artifical control systems may know whether it is true.

First, what I hope are facts, then the speculation:

Without jitter, and in the absence of friction or dead zones, the perceptual  
signal settles at a level that differs from the reference by an amount  
D/(1+G). That is the "small" error signal to which Bill P. refers. With  
jitter, the error signal deviates around this mean value and the deviation  
is, as Bill has elsewhere noted, essentially uncorrelated with the disturbance  
(as it must be if the jitter and the disturbance occur in different  
frequency bands).

Is it possible that the control system might in some way use the jitter  
to affect its output so that the jittered error averages zero regardless  
of the DC value of the disturbance?

Commentary:

If the speculation is correct, it would imply that the jitter occurs outside  
the control bandwidth of the the control loop, and does not affect the output  
moment-by-moment. The error signal would have to be filtered at the output  
stage into, say, "controllable" and "uncontrollable" frequency bands. The  
"controllable" band is what is normally considered when dealing with the  
operations of the control loop.

Suppose now that the "uncontrollable" jitter-based signal is low-pass  
filtered or in some way averaged. Any deviation of it from zero is  
independent of the disturbance, and could affect the output additively  
until that jitter deviation approaches zero. The result would be that  
the mean value of the perceptual signal would come to have zero error,  
or much close to zero than without the jitter.

I can see that even the jitter deviation average would still need to have  
some small remanent error, but it seems to me that the incremental output  
based on it could potentially increase the apparent system gain very greatly.  
Is this idea something quite stupid, quite well known, or untried?

Martin

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**Author:** ![William\_T\_Powers4](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/w/977dab/32.png) [@William\_T\_Powers4](http://discourse.iapct.org/u/William_T_Powers4)\
**Post date:** [June 22, 1995, 5:36pm UTC](http://discourse.iapct.org/t/jitter/5942/2 "1995-06-22T17:36:02Z")

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[From Bill Powers (950622.1130 MDT)]

Martin Taylor (950622.1200) --

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If the speculation is correct, it would imply that the jitter  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;occurs outside the control bandwidth of the the control loop, and  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;does not affect the output moment-by-moment. The error signal  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;would have to be filtered at the output stage into, say,  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"controllable" and "uncontrollable" frequency bands. The  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"controllable" band is what is normally considered when dealing  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;with the operations of the control loop.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Suppose now that the "uncontrollable" jitter-based signal is low-  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;pass filtered or in some way averaged. Any deviation of it from  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;zero is independent of the disturbance, and could affect the output  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;additively until that jitter deviation approaches zero. The result  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;would be that the mean value of the perceptual signal would come to  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;have zero error, or much closer to zero than without the jitter.

There seems to be a contradiction here. If the error signal is divided  
into a controllable and uncontrollable frequency band, the controllable  
band would be the one between zero frequency and the maximum frequency  
of good control. The uncontrollable band would be from that maximum  
frequency upward. The jitter would be in that upper band.

If you then low-pass filter the upper band, you will be applying a high-  
pass filter (to isolate the upper band) and then a low-pass filter,  
which will leave -- nothing.

Jitter is helpful only when there is slip-stick friction in the  
controlled variable. If the jitter is just large enough to cause the  
static friction to break free, the effect is to add noise to the system  
but to permit the average value of the controlled variable to change  
smoothly. The net result can be an improvement in control (I'm sure you  
knew all about this).

> **···**
>
> -----------------------------------------------------------------------  
> Best,
> 
> Bill P.

---

<div class="post-metadata">

**Author:** ![\_Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/_/a9adbd/32.png) [@\_Martin\_Taylor](http://discourse.iapct.org/u/_Martin_Taylor)\
**Post date:** [June 22, 1995, 6:02pm UTC](http://discourse.iapct.org/t/jitter/5942/3 "1995-06-22T18:02:06Z")

</div>

[Martin Taylor 950622 13:50]

> Bill Powers (950622.1130 MDT)

> There seems to be a contradiction here. If the error signal is divided  
> into a controllable and uncontrollable frequency band, the controllable  
> band would be the one between zero frequency and the maximum frequency  
> of good control. The uncontrollable band would be from that maximum  
> frequency upward. The jitter would be in that upper band.
> 
> If you then low-pass filter the upper band, you will be applying a high-  
> pass filter (to isolate the upper band) and then a low-pass filter,  
> which will leave -- nothing.

Yes, you are right. I guess it was a silly idea. The error signal of  
interest would be entirely within the bandwidth of the disturbance, and  
after high-pass filtering, it wouldn't be seen.

We are left with the uses of jitter that have already been adduced, of  
which getting around slip-stick is one. Avoiding dead-zones and linearizing  
responses around the zero-point is another, that might be even more valuable  
in human systems. But apparently not to get an apparent increase in  
system gain.

Martin

---

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**Author:** ![Peter\_J\_Burke](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/p/a5b964/32.png) [@Peter\_J\_Burke](http://discourse.iapct.org/u/Peter_J_Burke)\
**Post date:** [June 22, 1995, 10:33pm UTC](http://discourse.iapct.org/t/jitter/5942/4 "1995-06-22T22:33:00Z")

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[Peter Burke 950622 15:30 PDT]

> [Martin Taylor 950622 12:00]  
> \>Bill Powers (950621.1415 MDT) to Hans Blom (950621a)
> 
> Many control systems, including human ones, show jitter, which is a  
> non-systematic high-frequency deviation about the mean value of whatever  
> signal one examines. Various uses for jitter have been proposed, some  
> of which I heard as an undergraduate, some on CSG-L. But I have not heard  
> the following, and I am wondering whether those with practical experience  
> with either human or artifical control systems may know whether it is true.

I have always wondered if it would not be possible to use such "jitter"  
in the output of a system to "test" then environment for the proper sign  
to put on the output by tracking the effects of these small changes  
(jitters) on the movement of the perceptual signal closer to or further  
from the reference signal. I have always wondered how a system learns the  
proper sign to apply in the first instance, and how to change it when  
necessary because things in the environment have changed.

> **···**
>
> On Thu, 22 Jun 1995 mmt@BEN.DCIEM.DND.CA wrote:
> 
> ------------------------------------------------------------------  
> Peter J. Burke Phone: 509/332-0824  
> Sociology Fax: 509/335-6419  
> Washington State University  
> Pullman, WA 99164-4020 E-mail: burkep@unicorn.it.wsu.edu  
> -------------------------------------------------------------------

---

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**Author:** ![\_Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/_/a9adbd/32.png) [@\_Martin\_Taylor](http://discourse.iapct.org/u/_Martin_Taylor)\
**Post date:** [June 22, 1995, 10:47pm UTC](http://discourse.iapct.org/t/jitter/5942/5 "1995-06-22T22:47:20Z")

</div>

[Martin Taylor 950622 18:40]

> Peter Burke 950622 15:30

> I have always wondered if it would not be possible to use such "jitter"  
> in the output of a system to "test" then environment for the proper sign  
> to put on the output by tracking the effects of these small changes  
> (jitters) on the movement of the perceptual signal closer to or further  
> from the reference signal.

You are referring to the high-frequency jitter I discussed earlier today  
in connection with a silly notion Bill Powers shot down very quickly.

It isn't possible to use the jitter for the purpose you suggest, either.

Control works because the output moves the perception in a direction to  
reduce the error. But this takes a finite time. You will have seen  
talk of exponential decay in the error signal, and the like. If the  
output had sufficient gain at high frequencies--the frequencies of the  
jitter--there would be some frequencies at which the signal would be  
amplified around the loop, the opposite of control.

You can only test the sign of the output within the frequency range for  
which control is possible.

> I have always wondered how a system learns the  
> proper sign to apply in the first instance, and how to change it when  
> necessary because things in the environment have changed.

The magic word is "reorganization." If the sign is wrong, the error signal  
in the loop rapidly builds higher and higher. As generally conceived, one  
of the "intrinsic variables" controlled in the reorganization process is  
error. One of the ways reorganization may do its controlling is to change  
the signs of some links in the hierarchy. When the sign of the output  
switches to a correct value, the error will decline. If the enviroment  
changes so as to invert the effective sign, reorganization will come into  
play again.

All of which is much oversimplified. There isn't any magic, that's the  
main point.

Martin

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**Author:** ![Bruce\_Abbott](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/ba8739/32.png) [@Bruce\_Abbott](http://discourse.iapct.org/u/Bruce_Abbott)\
**Post date:** [June 22, 1995, 11:14pm UTC](http://discourse.iapct.org/t/jitter/5942/6 "1995-06-22T23:14:09Z")

</div>

[From Bruce Abbott (950622.1810 EST)]

> Peter Burke 950622 15:30 PDT --

> Many control systems, including human ones, show jitter, which is a  
> non-systematic high-frequency deviation about the mean value of whatever  
> signal one examines. Various uses for jitter have been proposed, some  
> of which I heard as an undergraduate, some on CSG-L. But I have not heard  
> the following, and I am wondering whether those with practical experience  
> with either human or artifical control systems may know whether it is true.

Peter, I believe I read somewhere that at least some adaptive controllers  
use a method like this, introducing a small, known change in output in order  
to determine its effect on the controlled variable (and thus on the error)  
and then using this information to adjust the parameters of the control  
loop. It was noted that these outputs act as disturbances to the controlled  
variable and thus tend to degrade the performance of a system with  
already-established good control, but that the benefits in terms of improved  
control when control is initially poor or absent outweigh the slight loss  
such a system entails.

Regards,

Bruce

---

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**Author:** ![Bill\_Leach1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/848f3c/32.png) [@Bill\_Leach1](http://discourse.iapct.org/u/Bill_Leach1)\
**Post date:** [June 23, 1995, 4:39am UTC](http://discourse.iapct.org/t/jitter/5942/7 "1995-06-23T04:39:24Z")

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\<[Bill Leach 950623.00:07 U.S. Eastern Time Zone]

> [Martin Taylor 950622 12:00]

It is called "dither", and yes it is common and yes your general  
suppositions about it such as how it works and why are correct.

Dither is commonly used on hydralic systems requiring precise control and  
rapid response. If the requirement is only for rapid response or only  
average position is important then dither frequency may be in the  
controller bandpass and indeed will be an AC signal applied in the  
controller itself.

If precision is also an important consideration then usually, the dither  
is applied to a second (small) spool valve connected around the main  
control valve. By design, the dither frequency is chosen to be close to  
the maximum physical response speed of the system.

In practice the dither amplitude and frequency are adjusted to obtain  
acceptable (or optimal) system response. For example, a dither value set  
is made and then the system is tested under "no load" conditions for  
response speed and for sensitivity to very small reference changes. A  
family of curves is then plotted for various loading conditions and an a  
value is selected based upon the most important conditions for the  
particular application.

-bill

---

<div class="post-metadata">

**Author:** ![Bill\_Leach1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/848f3c/32.png) [@Bill\_Leach1](http://discourse.iapct.org/u/Bill_Leach1)\
**Post date:** [June 25, 1995, 4:00pm UTC](http://discourse.iapct.org/t/jitter/5942/8 "1995-06-25T16:00:59Z")

</div>

\<[Bill Leach 950625.10:17 U.S. Eastern Time Zone]

> [Peter Burke 950622 15:30 PDT]

Peter; there are a number of control situations where the application of  
a disturbance to the output of the system has been used to characterize  
certain system dynamics. Such is generally used in a very limited set of  
control applications. Also, sometimes such applied disturbances would be  
called about anything but "jitter" (ie: applied disturbance output  
exceeds six times the normal perceptual variance).

However, the most common use of jitter (that I am aware of anyway) is to  
prevent what is called in jargon "taking a set". Most mechanical  
positioning devices will exhibit a "stickyness" (sheer friction vs.  
rolling friction) that may interfere with "good" control.

Thus, systems that are expected to frequently remain motionless for  
extended periods of time but still need to be "sensitive" to small  
changes in reference or perception will often apply a dither.

There are probably as many techniques as there are systems using dither.  
One interesting method is used with systems employing actuators of  
comparitively high power, final element of comparitively high mass and a  
torsion link between the actuator and the final element. In such a  
system, the dither is applied to the output signal such that the dither  
frequency is at the resonant frequency of the assembly. The actuator  
then will swing back and forth past the "ideal" control point but the  
attached final element will remain stationary. Of course the "image" for  
the above description is a bit misleading in that the signal amplitude is  
usually small enough that the actuator "motion" is almost imperceptable  
to the observer. The real purpose is to keep all of the bearing surfaces  
in as close to continous motion as possible.

-bill