A simple feedback control loop:

input -->

The feedback is simply multiplied by 2.

to

(X2 means multiplied by 2)

--------------------------------------------------------------------

Here's my question:

1. Is this system stable?

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

( H(s) = 1/(s-1), G(s) = 2, transfer func = H/(1+G*H) = 1/(s+1) )

The only pole is at -1, LHP,===> Stable

2. On the otherhand, if the input is a constant dc then 1/(s-1) becomes just "-1" (s=jw, w=0) and the feedback is -X2 (negative feedback) Therefore, the total feedback is (-1)*(-2) = 2 That is the system always multiplies the input by 2 and then feed it back to the system. A positive feedback! ===> Not stable.

Where did I make the mistake?

input -->

***(+-)***---> 1/(s-1) ---*--> outputThe feedback is simply multiplied by 2.

to

***(-)***<---- X2 ------ from *(X2 means multiplied by 2)

--------------------------------------------------------------------

Here's my question:

1. Is this system stable?

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

( H(s) = 1/(s-1), G(s) = 2, transfer func = H/(1+G*H) = 1/(s+1) )

The only pole is at -1, LHP,===> Stable

2. On the otherhand, if the input is a constant dc then 1/(s-1) becomes just "-1" (s=jw, w=0) and the feedback is -X2 (negative feedback) Therefore, the total feedback is (-1)*(-2) = 2 That is the system always multiplies the input by 2 and then feed it back to the system. A positive feedback! ===> Not stable.

Where did I make the mistake?