A very simple feedback control loop:

input -->

There is a feedback connection from -
--------------------------------------------------------------------

Here's my question:

1. Is this system stable?

The output/input transfer function is 2/(s+1)

( H(s) = 2/(s-1), transfer function = H/(1+H) = 2/(s+1) )

The only pole of the transfer function is at -1, LHP,===> Stable

2. On the otherhand, if the input is a constant dc then 2/(s-1) becomes just "-2" (s=jw, w=0, 2/(s-1) = -2) Therefore, the total feedback is (-1)*(-2) = 2 (negative feedback)

The feedback is 2*input.

A positive feedback! ===> Not stable.

The bode plot shows the same thing: open loop transfer function = 2/(s-1) ==> At w=0, phase = -180 deg and gain = positve => Not stable!

Where is the mistake?

input -->

***(+-)***---> 2/(s-1) ---*--> outputThere is a feedback connection from -

***- to ***(+-)*Here's my question:

1. Is this system stable?

The output/input transfer function is 2/(s+1)

( H(s) = 2/(s-1), transfer function = H/(1+H) = 2/(s+1) )

The only pole of the transfer function is at -1, LHP,===> Stable

2. On the otherhand, if the input is a constant dc then 2/(s-1) becomes just "-2" (s=jw, w=0, 2/(s-1) = -2) Therefore, the total feedback is (-1)*(-2) = 2 (negative feedback)

The feedback is 2*input.

A positive feedback! ===> Not stable.

The bode plot shows the same thing: open loop transfer function = 2/(s-1) ==> At w=0, phase = -180 deg and gain = positve => Not stable!

Where is the mistake?