Is it possible to use the formula for overshoot and settling to determine where where ones pole should. by using the overshoot and settling time formula i mean, using it to define what $\zeta$ and $\omega_n$ should be, and using them to determine the pole location since a pole is defined as $\zeta \omega_n \pm \sqrt{1- \zeta^2}$ ..
So if we said that i wanted overshoot to be 0 % => $\zeta = 1$ and a settling time to be less than 2, $2>\omega_n$…
This just seems incorrect, because be doing so i am letting $\omega_n$ become negativ, which lead the the pole to located at the RHS, which would make the system unstable, which make me question if this method is correct??
I have this close loop transfer function
http://snag.gy/Vh1SM.jpg
Which overshoots, but why does it overshoot?? The poles are placed such that that the damping = 1… so why do get overshoot??
Best Answer
Sure you can determine where the poles should be, in fact there are many design methods exists using this. The pole locations you provided are wrong, it should be $p_{1,2} = - \zeta \omega_n \mp i \omega_n \sqrt{1 - \zeta^2}$.
The settling time formula for %2 band is $t_s = \frac{4}{\zeta \omega_n}$ which should result in $\omega_n = 2$.
The system you provided overshoots because of the zero of the system. System zeros increase overshoot especially when they are close to the imaginary axis. The overshoot formula is calculated for the system with no zeros.