How do you find and manipulate the dominant poles on a pzmap (pole-zero map) to achieve the desired results?

Tim Chung, 04 Dec 02

First off, the dominant poles are those poles of the system that are closest to the jw-axis. These poles have greater effects on the system response than those that are further away.

Manipulating the poles (for instance, via pole-placement) can be done to achieve a particular damping ratio, z, and undamped natural frequency, w_n. Examining a dominant complex conjugate pair of poles, we find that the damping ratio is related to the angle of the pole from the jw-axis, and the undamped natural frequency is the distance from the origin to the pole. Another way to see this is to note that the imaginary component of the pole is equal to the damped natural frequency, w_d.

Thus, you can relate the location of the poles of the system to the behavior of the system, and therefore can change those locations to achieve desired behaviors.