a) Refer to the block diagram below. Using block diagram algebra, find the transfer functions between Ysp(s) and Y(s), as well as between the disturbance D(s) and Y(s).

b) Consider the steam-heated CSTR system with cascade control . The block diagram of this system is shown below. Note that both reactor temperature, T, and steam flow, F, are controlled (i.e., they are CVs), but T is more important to control than F, so the control systems are cascaded, as shown. Derive the transfer function for this system relating changes in the disturbance D(s) to the ultimate output, T(s).

D(s) G (8) E(s) C(s) U(S) s) Y(s) G (5) G,() G (3) Y(s) G(s) D(S) Ga(s) Tsp(S) s C1(s) + ELS T(S) Ge(s) Gc(s) G.2(s) Gp2() F() Gpl(s) G2(S) Gl(s)