[From Bill Powers (930317.1200)]
Allan Randall (930317.1030 EST) --
Looks like we are getting to the nub of the definitional problem
here.
So, is everybody agreed on the following definition?:
disturbance: the total sum environmental influence on the CEV.
No, and the reason we don't agree, once understood, should clear
everything up. The word "influence" is ambiguous for the very
same reason that "disturbance" is ambiguous.
Suppose we have two objects connected by a spring. Initially, the
spring is just slack.
A --- /////////// --- B
By moving A to the left, we can stretch the spring, which in turn
will apply a force to B.
Let's define the CEV of a control system as the _position_ of B
along the x axis. Let's also define the _disturbing variable_ as
the _position_ of A along the x-axis. We can now add an object C,
which is the output of the control system, also connected to B
(the CEV) by a spring:
A --- /////////// --- B --- \\\\\\\\\\ --- C
The output action consists of moving the object C along the x
axis, so we say that the output is measured by the _position_ of
C.
Now let's get the language straight. What are "the two influences
on B?" They are A and C, the positions of the two objects. So
here we are defining an "influence" as "something capable of
affecting something else." If we know the spring constant, we can
say that a movement of A of 1 cm will initially result in k units
of force applied to B, and similarly for C.
Influence, however, has another sense. We can ask, "How much
influence do the positions of A and C have on B?" Now the problem
becomes clearer. If A moves 1 cm to the left while C
simultaneously moves one cm to the right, and the springs are
identical, the answer is NONE. Neither A nor C has, in fact, any
influence on B _in terms of an effect on B_. The total force
acting on B will remain zero, and B will not move.
A and C are classed as being among the objects whose position is
capable of influencing or disturbing B. In normal parlance, we
would class them as influences or disturbances. But that does not
tell us whether, in fact, changing the position of either A or C
will produce any actual change in B. So we can't say _a priori_
whether an influence will have an influence, or whether a
disturbance will cause a disturbance!
When we draw a disturbing variable in a control-system diagram,
we are drawing something analogous to A. The output is analogous
to C.
Disturbing
Variable ----////////--- CEV ---- \\\\\\\\ --- Output
Without knowing anything about the state of the CEV, we can
specify the state of the disturbing variable. If the units
involved are distances, we can specify the location of the
disturbing variable. If we observe the system for a while with
the disturbing variable in the position that has no effect on the
CEV, then suddenly move the disturbing variable to a new position
and keep it there, we may well observe something like this:
···
--------------------------------------------------------------
**************************
Disturbing variable
*********************
-------------------------------------------------------------
*
*
CEV *
*
*********************** * ************
* *
-------------------------------------------------------------
* *
* *************
*
(Opposing) Output *
*
*
**********************
--------------------------------------------------------------
It's clear that the behavior of the CEV is not like the behavior
of the disturbing variable. Neither is it like the behavior of
the control system's output. We would certainly say that the
disturbing variable influences or disturbs the CEV, but we can't
say that the disturbance or influence that actually occurs
reflects the behavior of the disturbing variable.
This is where we have been sliding past each other. It makes no
sense to say that the control system's perceptual signal contains
no information about the CEV. That is why it has seemed so self-
evidently true to you that a disturbance (meaning an actual
change in the CEV) conveys information to the control system --
and so stupid of us to claim that it does not.
But now interpret "disturbance" to mean "state of the disturbing
variable." The diagrams above show (roughly) the behavior of the
system with an integrating control system. Before the change in
the disturbing variable, the CEV had a value of zero. Some time
after the change, the CEV is again approaching a value of zero.
But the states of the disturbing variable and the output are
quite different between these two times. This is why we have
claimed that the control system gets no information about the
disturbing variable: the CEV itself doesn't reflect the state of
the disturbing variable. Knowing that the CEV has a value of zero
tells you nothing about the value of the disturbing variable.
Remember that in an ECS, the perceptual function does not receive
information about the output of the system. It senses ONLY the
CEV. Thus a given state of the CEV is always caused to an
unknowable degree by the state of the output, the rest being due
to the state of the disturbing variable. Not knowing the state of
the output, the perceptual function has no way to know the state
of the disturbing variable, either. For any value of the CEV
within its possible range, the disturbing variable might have any
value within its possible range. There is total uncertainty about
the state of the disturbing variable.
This may have been overkill, but if it leads to mutual
understanding it was worth the effort.
Best,
Bill P.