Bad math, what's it all about?

[From Rick Marken (960116.0800)]

Bruce Abbott (960115.1215 EST) --

Me:

o := o + (k.2i-o)

Rick:

o := o + (k.2i-o)

Bruce:

But doesn't this reduce to just

o := k.2i ?

Rick:

Mathematically, yes. But with the replacement operation I think we just end
up adding an increment, k.2i-o, to o.

Bill Powers (960116.0500 MST) --

No matter how you think about it, o + k.2i - o is just k2.i.

You've left out the slowing factor,

Oops. So my simulation is a proportional rather than an integral control
system. As I said in the part of the post that you didn't scan because of
your compiler policy, I think in way over my head (obviously, since I
didn't notice that o + k.2i - o = k2.i).

I think the relevant points in this discussion are:

1. X(n) = g (Xn-k) does not describe a closed loop system and

2. When loop gain in a positive feedback system is >= 1.0 the system becomes
unstable.

Do these statements make it through the first pass?

Best

Rick