Q. Discuss the closed-loop behavior?

Consider an elementary feedback control system, as shown in Figure, with H = 1. The output variable c and the input e to the direct transmission path are related by

(a) Assuming the system to be initially at rest, for e = u(t), find the complete solution for c(t) when the system is operated in open-loop fashion without any feedback.

(b) With the feedback loop connected and with a forcing function of a unit step, i.e., R(s) = 1/s, describe the nature of the dynamic response of the controlled variable by working with the differential equation for the closed-loop system, without obtaining a formal solution for c(t).

(c) By working solely in terms of transfer functions, discuss the closed-loop behavior.