A control loop is used to maintain a variable Y(s) close to a set point Ysp(s), as shown in the block diagram of Figure Q2b (on the next page). All symbols have the usual definitions (see attached data). You may assume that all quantities are deviation variables. (i) Neglecting the effect of U(s), find an expression for y(t) for a step change of d(t)=1 occurring at time t=2. (ii) Find the closed-loop transfer functions relating Y(s) to Ysp(s) and Y(s) to D(s). (iii) For the result of part 2a)(ii), and assuming a P controller with a gain K=4, find and expression for y(t) if a step change of d(t)=1 occurs at t=2 without any change in the set point. Draw a plot of y(t) and discuss its behaviour at long times