# Using PI control to eliminate steady state errors

In a negative feedback loop i understand the mistake of canceling unstable poles. But take for example a plant

$$G(s)=\frac{1}{s+1}$$

and an I-control

$$F(s)= \frac{1}{s}$$

Then the system has the transfer function

$$T(s)= \frac{FG}{1+FG}=\frac{\frac{1}{s}}{(s+1)+\frac{1}{s}}$$

My question is: Is it valid to cancel s=0 poles? so that system becomes

$$T(s)= \frac{1}{s^2 +s +1}$$

Or does it go against cancelling unstable poles?

• I see only I-Controller. – CroCo Nov 11 '18 at 5:28