----- Original Message -----
From: "Harry Lin"
Sent: Monday, August 23, 2004 8:40 PM
Subject: Is this very simple system stable?
Okay, I agree with you here.
This doesn't mean it is unstable. If the loop gain was one then you
it is metastable. Actually a non inverting first or second order
system with poles in the left half plain will be unstable for any
negative feedback. Your example seems to show that an inverting
unstable first order system will be unstable for any positive feedback
or equivalently a no inverting unstable first order system will be
unstable for any negative feedback. By inverting I mean a DC gain less
Positive feedback is not necessarily unstable. Notice though that H(s)
is unstable. Maybe this is why the result is less then intuitive.
Bad intuition about loop gains and stability. Interesting tough.
The system is stable. I believe the misstep is in the assumption that
constant input to the system will produce the same constant input to the
1/(s-1) block. After transients have settled, the input to the 1/(s-1)
block will actually be opposite in sign from the system input.
The transfer function from the system input to the input of the 1/(s-1)
block is (s-1)/(s+1).
Here's another question:
The bode plot of the open loop transfer function
2/(s-1) shows that
At w=0, phase = -180 deg and gain = (20*log(2)), a negative margin
Is that an indication of "unstable"?
If not, what are the correction conditions for a stable system
according to its bode plot?
(positive gain margin, positive phase margin, am I right? )