The block diagram form of a closed-loop control system is shown in Figure Q1. For parts (a) (c) of Question 1 assume that H(s) = 1. R(s) r(t) + E(S) K + Gp(s) 500 s+ 5 1 20s K H(s)+ Figure Q1 (a) Derive the closed-loop transfer function from input r(t) to output c(t). C(s) c(t) [6 marks] (b) Find the values of K and K, so that the unit-step response of the dominant closed-loop poles produces a 25% overshoot and a settling time of 0.137 seconds. [8 marks]