Find the range of K for stability

[jdoe10]

Homework Statement

Find the range of K for the closed loop system to be stable.
$G_{OL}(s) = \frac{10}{s-5}$

Homework Equations

The Attempt at a Solution

$G_{CL}(s) = \frac{KGol}{1+Gol}$
$G_{CL}(s) = \frac{10K}{s-5+10K}$
$-5+10K>0$
$K>\frac{1}{2}$
is this correct?

 

[LvW]

No - the quation for Gcl is not correct (assuming Gol is the open-loop gain and K is the negative feedback factor).
We have Gcl=Gol/(1-LG)
with Loop Gain LG= - Gol*K.

 

[donpacino]

In this context I am guessing that K is the amplifier block before the open loop gain that can be adjusted, also known as the DC gain of the controller. I am guessing Gol is really the open loop gain of the plant.

 

[donpacino]

Jdoe10, can you provide us with a block diagram or more information?

 

[LvW]

jdoe10 - please, please, be so kind and give us the chance (necessary information) to answer your question.