There are two types of feedback, negative and positive. In this problem we explore their difference.

(a) Consider negative feedback. Suppose you have a system with transfer function H(s) = Y(s)/E(s) where E(s) = C(s) − Y(s), and C(s)and Y(s) are the transforms of the feedback system’s reference c(t) and output y(t). Find the transfer function of the overall system G(s) = Y(s)/C(s).

(b) In positive feedback, the only equation that changes is E(s) = C(s) + Y(s), the other equations remain the same. Find the overall feedback system transfer function G(s) = Y(s)/C(s).

(c) Suppose that C(s) = 1/s, H(s) = 1/(s + 1) determine G(s)for both negative and positive feedback. Find y(t) = L⁻¹[Y(s)] for both types of feedback and comment on the difference in these signals.