[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

equilibrium point.

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.

Regards,

Bruce