1. Sketch the Nyquist plots of the following loop transfer functions and determine whether the system is stable by applying the Nyquist criterion:
L(s) = Gc(s)G(s) = K/(s(s2 + s + 6)
L(s) = Gc(s)G(s) = K(s + 1) / (s2(s + 6))
If they system is stable, find the maximum value for K by determining the point where the Nyquist plot crosses the u-axis.
2. A closed-loop system with unity feedback has a loop transfer function L(s) = Gc(s)G(s) = K(s +20) / s2
Determine the gain K so that the phase margin is 45 degrees.
For the gain K selected in part (a), determine the gain margin.
Predict the bandwidth of the closed-loop system.