In Control Systems, for a second order LTI system, on reducing the gain, the oscillations in the response reduces, increasing the stability. Now as gain is reduced, and since gain-bandwidth product remains same, BW increases. And as rise time is inversely proportional to BW, it decreases.
Now the problem arises when I increase the stability by increasing the damping ratio keeping gain and natural frequency constant, and by the formula of rise time that is a function of the damping ratio and natural frequency it increases, conversely BW reduces.
So is it that increasing the stability by reducing gain increases the bandwidth and by increasing the damping reduces it?
Moreover I was checking out in a simulator, wherein I observed on increasing gain alonw, rise time was decreasing, whereas it should have been opposite.
Can somebody please clarify the relation between stability, BW and rise time, along with the factors thats effect them.