In class we examined adding a lead controller using both tra

In class we examined adding a lead controller using both transient response (root locus) and frequency response (bode plot) methods. Assuming the above lead controller with Ginc and theta_max as identified above, what omega would you design the controller at to improve the open-loop system below:

Solution

At 2.43 rad/s both Pm & Gm are negative hence unstable system

On using lead controller per rad/s in log scale gain increases =2dB and phase increase = 20 deg

Therefore at 24.3 rad/s Pm = -8.64+20 = 11.36 deg and Gm = -1.51+2 =0.49 dB, hence both are positive so stable system. So frequency would be 24.3 rad/s.