It is well known that the addition of phase lag to a closed-loop system is destabilizing. A sampler/data-hold device adds phase lag to a system, as described in Section 3.7. A certain analog control system has a bandwidth of 10 Hz. By this statement we mean that the system (approximately) will respond to frequencies less than 10 Hz, and (approximately) will not respond to frequencies greater than 10 Hz. A sampler/zero-order-hold device is to be added to this control system.

(a) It has been determined that the system can tolerate the addition of a maximum of 108 phase lag within the system bandwidth. Determine the approximate minimum sampling rate allowed, along with the sample period T.

(b) Repeat part (a) for a maximum of 5° phase lag. 

(c) Repeat part (a) for a maximum of 20° phase lag.