The block diagram for a system used to control the orientation of a space satellite is shown in Fig. 2. R(s) E(s) Ge(s)= K (s+20) 10 (s+3)(s+7) G(s)=- C(s) Fig. 2 (a) Write an expression for the steady-state error signal, Ess, and calculate the value of K needed to ensure a steady-state error of less than 15% for a step input. [6 marks] (b) Given that one of the closed-loop system poles is at s= -25.6, determine the location of the dominant closed-loop poles, and estimate (i) the percentage overshoot and (ii) the settling time to within 2% for a unit step input. [9 marks] (s+10) (c) In order to improve the stability of the system, the gain is to be reduced and a component of derivative action, (s + 10), is introduced in the controller, so that G(s) = K' What is the (s+20) minimum value of gain, K', needed to maintain the steady-state error specification of 15% for a step input in this case? [5 marks]