I was asked a question in a control system test which is as follows:
*Introduction of integral action in the forward path of a unity feedback system results in a
- a) marginal stability
- b) system with no steady state error
- c) system with increase stability margin
- d) system with better speed of response*
Since we were told that only one of the option is correct I immediately hit (b) because an integrator is known to make steady state error 0. However, I wondered why the other options would have been incorrect. Now I could rule out marginal stability because a closed loop will stabilize the open loop pole at 0. I also took a random function (s+2)/(s+1) and investigated its phase margin which was higher than that of (s+2)/(s(s+1)). This is enough to rule out option (c) but I am unable to get a physical sense of why an integrator should reduce stability of a system. Also, what defines speed of response of a system, or which parameter I should be looking for to quantify how fast my system is?