[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