# Quality control

**URL:** <http://discourse.iapct.org/t/quality-control/9338>\
**Category:** CSG1995\
**Created:** [May 19, 1995, 4:11pm UTC](http://discourse.iapct.org/t/quality-control/9338 "1995-05-19T16:11:34Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Richard\_Marken](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/r/9fc348/32.png) [@Richard\_Marken](http://discourse.iapct.org/u/Richard_Marken)\
**Post date:** [May 19, 1995, 4:11pm UTC](http://discourse.iapct.org/t/quality-control/9338/1 "1995-05-19T16:11:34Z")

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[From Rick Marken (950519.0900)]

Hans Blom (950518) --

> how do we measure the quality of control, what yardstick do we apply?

I am willing to assume RMS error: essentially your

> SUM {r (i) - x (i)}^2

But I also think of it in terms of stability, measured as expected over  
observed variance of the controlled variable. In a tracking task, stability  
is:

S = 1- sqrt([V(D)+V(H)]/V(C))

where V(D) is disturbance variance, V(H) is handle variance and V(C) is  
cursor variance. The numerator of the expression on the right is a measure of  
the estimated variance of C under the assumption that H and D have  
independent influences on C. If V(C) is much smaller than V(H)+V(D) it means  
that the influences of H and D on C are not independent; in fact they are  
negatively correlated, resulting in reduced variance of C. In other words,  
when control is good [V(D)+V(H)]\>\>V(C) and S will be \<\< 0. When there is no  
control, [V(D)+V(H)]=V(C) and S = 0.

The virtue of the stability measure is that is doesn't require knowledge of  
the momentary value of the reference state of C (r(i) in your equation).

Me:

> By the way, Hans, I have developed a simple PCT type control model that  
> meets and exceeds your specifications for a controller that has  
> "approximately zero response time" while it "tracks a repeating  
> waveform".

Hans:

> Does it work with all kinds of "arbitrary" disturbances?

Of course.

> I do not accept a teacher's word for it unless it "feels" right.

Suppose it feels wrong because not only the teacher's words but the data  
as well contradict something that you always thought was true? Do you still  
go with your feelings?

> Something like doing science.

Well, scientists do have this penchant for data.

Me:

> Do you agree that all control systems -- living and non-living -- are  
> typically organized around the control of their own perceptions?

Hans:

> This phrasing doesn't "feel" right. I do not control all of my percept-  
> ions, but I do think that I use all of my perceptions in order to con-  
> trol.

While you have been on the net, we have demonstrated over and over, using  
models and data, that the only variable controlled in a control loop is the  
perceptual signal. This does not mean that living systems control "all" their  
perceptions; some perceptions are not under control. It does mean that your  
"feeling" that you "use" perceptions in order to control contradicts the  
facts of how control works. Perceptions are not "used"; they are controlled.

Me:

> ... Hans' own very complicated "model- based" controller ... was  
> unable to maintain control in the face of ANY disturbance at all.

Hans:

> This seems to be one of your famous more extreme statements...The demo  
> demonstrates a very different concept of control from what you are used to.

My statement is not extreme at all. When a disturbance is applied to the  
controlled variable in your demo it is fully effective; there is no  
resistance to it. In terms of stability, the S measure (given my equation  
above) is close to 0, ie. there is no control. I have no idea what the "very  
different concept of control" is that is being demonstrated by your demo, but  
it's sure not the kind of control I want to find in the control systems I  
depend on.

Me:

> The ability of a control system to control depends on how much output it  
> can generate per unit error (gain), the upper limit of this output  
> (strength) and speed (integral and transport lag).

Hans

> Your statement seems to imply that control is better the higher the  
> controller's gain and the faster its speed.

No. I simply meant that those are loop parameters that influence the quality  
of control (measured as RMS or S). I am well aware of the fact that the  
stability of a control loop requires a trade-off between gain and speed;  
high gain systems must be slower than low gain ones.

Best

Rick