[From Bruce Abbott (960112.2015)]
Rick Marken (960112.1400) --
So in your post of (960112.1040 EST) you say that Killeen's model is a
positive feedback system that is in equilibrium (which means a loop
gain < 1.0).
To be in equilibrium the loop gain has to be 1.0, which results from the
balance of opposing forces. Loop gain would be > 1.0 as the system
increases its output rate; the increased output rate effectively reduces the
gain, reducing the rate of increase in output, until gain = 1.0. If the
system were to be briefly pushed above its equilibrium rate, gain would be
further reduced, leading to reduced output rate and increased gain. The
system will stabilize at loop gain = 1.0. The relationship of gain to rate
of output is one of negative feedback on the gain; the relationship of rate
of output to rate of output is one of positive feedback on the output. The
negative feedback on the gain is what allows the system to stabilize at some
value other than zero or max; the point at which gain becomes 1.0 is the
If gain were positive and < 1.0, we would have positive feedback that would
stabilize at zero, but note that the gain abruptly becomes 1.0 at zero
(effectively), because then 0 = 0 each time around the loop.
But in your earlier post (960111.1145 EST) you scold me for
ignoring your mathematical proof that Killeen's model is a control system
(suggesting a negative feedback system with high loop gain). Is Killeen's
model both a positive and a negative feedback system all at once? Is
it like god: father, son and holy spirit all rolled into one?
Yes. But don't forget that the model has two loops, an inner and an outer.
The inner loop can be described as I stated above; the outer loop is an
ordinary control system with negative feedback and high loop gain.