7        Here is a closed loop system system with a variable gain.

The transfer function, G(s), has the Bode' plot shown below.

• (10 pts)  Sketch the Nyquist plot for the given Bode' plot.  (Use the graph below.)
• (10 pts)  Determine the gain which produces a phase margin of 50^o.

Here is the Bode plot for the system, with  -130^o marked. That's the phase you need for a 50^o phase margin.  The phase reaches that point at f = 0.62 Hz.  At that frequency, the magnitude is 5 db, so you need to reduce the magnitude by 5 db to get the phase margin.  That brings the DC gain to -10 db, for virtually 100% SSE - a very poor system.  And, BTW. a gain of -10 db is a gain of 0.3 approximately.