# Can we reshape the root locus by adding a pole instead of a zero (as is done in PD controller) to get required Ts while O.S. being the same?

I was studying about PD controllers, which made use of adding a zero at such location which gave the required settling time(Ts) while keeping the overshoot same as it was in the uncompensated system. My question is can we achieve the same by adding a pole instead of a zero? Because even the pole will reshape the root locus. If not then why ? Is it something to do with the changes that happens to the response of a system when zeroes and poles are added?

• I think adding some response plots and a root locust plot would make this question clearer. Commented Apr 3 at 12:32
• To reduce settling time and overshoot, effectively means the following desired movements of CL poles: faster CL dominant pole, or higher damping ratio of CL dominant pole-pair. So in root locus the CL pole-pair must be moved towards real axis and/or to the left. Adding zeros will attract the poles and can accomplish this. Besides the poles, it's important to realize that zeros also contribute to overshoot and ringing! And any zero placed in the forward path will appear in the CL transfer function (whereas if placed in the feedback path, it won't!)... Commented Apr 3 at 12:56
• ... In some circumstances, e.g. a single dominant pole (often at the origin), and for a particular (limited!) range of gain, adding a pole rather than a zero can also draw the dominant pole to the left, in the pattern where they come together east-west then diverge going north-south. The important thing is that once they start moving north/south, more gain will degrade damping ratio. The room for playing around in this manner, is more limited though Commented Apr 3 at 12:58
• @PeteW: to shift the phase of a resonance peak by 90 degrees, so you can have over-unity gain through the resonance and keep the loop stable. Seriously -- I was handed a loop that did that; it took me two weeks of failing to make it work better without the lag filter before I gave up and did what I was being told. Commented Apr 6 at 19:38
• It was a dynamically-tuned torque balancing gyro. You drove the gyro wheel to stay centered in its case, and inferred the rates from the amount of current to the torquers. It had a honkin' big resonance at the gyro's nutation frequency, 180 degrees phase shift. If you applied the usual rule of staying well below the resonance the loop bandwidth would be worthless, even with notch filters to help things out. Commented Apr 6 at 22:44