Using PI control to eliminate steady state errors

Question

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?

Answer 1

1. Do not ever cancel poles. You will affect observability and/or controllability. Unstable poles are even worse. Bibo stability of a zero depends on its order.

2. I dont see any pole cancellation in your example.

3. In practice you always use PI, never I on its own.