control systeem berekenen pool/zero

[de zon]

Consider the error feedback system including its transferfunction (s-1)/(s+9)and constant controller gain k:


R ------> K -------> (s - 1)/(s + 9) ------------> Y
......|.................................................|
.......<---------negative feedback loop<--

a: Determine all gains k for which the closed loop is stable.

b: Now take k = 1 . Determine the transferfunction from r to y and determine the poles and zeros of this transferfunction.


My question:
I thought that I knew how to deal with this situations, but I got stuck when finding the poles.

I think the transferfunction will be: (k * (s-1)/(s+9))/(1 + k * (s-1)/(s+9))
You can find the poles by making the denominator equal to zero at some point and 'find' "s" ..

Is there somebody who is able to help me out?

[wnvl]

Pole is

For a stable system, the real part of the pole should be less than -1.





This means k should be between -1 and 4, for a stable system.