Shown below is the feedback system for this problem.  The system has an adjustable gain amplifier with a gain, K, and a system with a transfer function, G(s)

        The transfer function for the system being controlled - the plant - is given by:

You need to investigate the behavior of this system.

Plot the locus of poles of the closed loop system as a function of gain.

• Plot the locus of poles of the closed loop system as a function of gain.
• Clearly indicate any points where poles leave the real axis or where they rejoin the real axis.
• Show the value of the gain, K, where those points occur.

        Here is the root locus for this system.  The two black points show:

• The two closed loop poles come together and become complex at about s - 2.2 (at a gain of .34)
• The two closed loop poles come back together and then move along the real axis at about s = -7.8 (at a gain of 11.6 or 11.7).