Both frequency domain Bode method and the root locus method can be used for designing lead and lag compensators for control systems. Which method would you prefer in each of the following cases?

a. Compensator design for a system with large time delays.

b. Lead compensator design for a stable system with negligible time delay.

c. Lag compensator design for an unstable system with negligible time delay.

(i) Even though a lag compensator has a destabilizing effect in general, it can be used to stabilize some unstable systems. Using sketches of Bode diagrams for a typical situation, explain why this is true. What is a major shortcoming of this method of compensation?

(ii) Specifications on peak time, settling time, and percentage overshoot are commonly used in controller design using the root locus method. Using sketches of design regions on the s-plane, give an example for a situation where all three specifications are necessary and an example where one specification is redundant.