I am kinda confused on how Adding a D(which adds a zero to the complete system) decreases the speed of the system. But when we normally add a zero to the system, it normally causes the system overshoot.
The same goes for the I part of the PID. Normally when we add an pole to the system, we the system would usually become less overshoot, but the I part increases the overshoot??...
What i mean the addition of an Integration and the derivative can be described when we look at at PI or a PD controller. the integrater is $K_i/s$ which adds a pole to the complete transfer function. And the D part is $K_dS$ adds a zero to the complete transfer function.
How does the inverse relation make sense??
This how i understand it:
Adding a pole lead to less overshoot, since adding a pole, adds a decaying part for the transfer function in time domain. $e^{-(1/a)t}$
Adding a zero, depending on the placement of zero either leads high overshoot or less overshoot. If the Zero is placed before the complex conjugated poles, it will lead to overshoot, and if is placed after it leads to less overshoot.