A very simple feedback control loop:
input --> *(+-)* ---> 2/(s-1) ---*--> output
There is a feedback connection from -*- to *(+-)*
--------------------------------------------------------------------
Here's my question:
- 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
- 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?