closed-loop poles as the gain is varied that we call a root locus. For most of our work,
the discussion will be limited to positive gain, or K 0.
The root locus shows the changes in the transient response as the gain, K, varies.
First of all, the poles are real for gains less than 25. Thus, the system is overdamped. At
a gain of 25, the poles are real and multiple and hence critically damped. For gains
above 25, the system is underdamped. Even though these preceding conclusions were
available through the analytical techniques covered in Chapter 4, the following
conclusions are graphically demonstrated by the root locus.
Directing our attention to the underdamped portion of the root locus, we see that
regardless of the value of gain, the real parts of the complex poles are always the same