For the system of Problem P10.20, we wish to achieve the same phase margin and K_v, but in addition, we wish to limit the bandwidth to less than 10 rad/s but greater than 2 rad/s. Use a lead-lag compensation network to compensate the system. The lead lag network could be of the form

where a is to be selected for the lag portion of the compensator, and b is to be selected for the lead portion of the compensator. The ratio a is chosen to be 10 for both the lead and lag portions.

Problem P10.20

An uncompensated control system with unity feedback has a plant transfer function

We want to have a velocity error constant of K_v - 20. We also want to have a phase margin of approximately 45° and a closed-loop bandwidth greater than ω= 4 rad/s. Use two identical cascaded phase-lead networks to compensate the system.