Question about a PD controller.

[nylonman]

Hi, I'm taking a control engineering course and I've got a little doubt about PD controllers.

Here is my root locus plot: http://imageshack.us/photo/my-images/535/controlw.png/

I have the system defined by the poles in the root locus with some design specifications that are satisfied when the complex poles are in the same position as the green stars. In order to move the branches of the root locus a PD controller is used, so a zero appears in the plot. With a specific gain the specifications are satisfied as shown in the right plot.

My question is: the specifications are computed assuming a normalized second order system, so the transfer function of the final system would have only the two complex conjugate poles. I know that the leftmost pole can be ignored, but what about the remaining zero? Wouldn't it affect the response?

Any help will be appreciated!

 

[viscousflow]

When placing your two right most poles using the gain kd, your left most pole will tend to move toward the zero position at some position specified by kd also. So if you're ignoring the left most pole only, then it has the same effect of ignoring both the left most pole and the zero, since the zero is only there to assure that the pole moves towards it (As shown by the green line)

 

[RobertT]

The zero is just an "end point" of the locus of the left most pole.

In other words, if the gain is large enough, the left most pole coincides at the zero which is still good because it sits on the negative real axis. However, system response is slower due to the pole approaching right-half plane.