Shown below is the Nyquist plot for a system with an open loop transfer function, KG(s).  The proportional controller, K, and G(s) are embedded in a closed loop system as shown below.  G(s) is a stable transfer function.

Answer the following questions

• As shown, the KG(s) plot below is drawn for K = 1.  Is the system stable (i.e. are all of the closed loop poles in the LHP?) for a gain of K = 1?
• If the gain, K, is changed to a value K = 0.3, then:
• Sketch the KG(jw) plot for K = .3.  Your sketch should be drawn on the plot below.
• Label any important points (DC point, etc.) giving values as best possible (not 5 place accuracy!).
• Determine - using your sketch - if the system is stable for K = 0.3.
• Determine - using the ideas in doing your sketch - the range of gains for which the system is stable.
• Determine how many closed loop poles are in the RHP.
• From the sketch, determine as many aspects of G(s) as you can.  (Things like DC gain, # poles, etc.)