Answer Happy

Please complete all parts of question 1, please show all steps
clearly. will thumbs up if correct. thank you.
Q1. Attempt all parts of this question. (a) Control systems engineering and technology have hugely influenced our everyday lives. Write a concise narrative on the future trends and scopes of control systems engineering and technology including potential challenges. [6 marks] The transfer functions of the control system shown in Figure Q1a are as follows: G(s) K (s + 3)2 (s +5) Gp(s) = (s + 1)(s +4) and H(s) = 1. R(s) O E(S) e(t) Ge(s) r(t) Gd(s) C(s) c(t) H(S) Figure Q1a (b) Sketch the root-locus diagram, including any asymptotes. Indicate the point of instability and the positions of small positive values of K. Comment on the nature of system damping for 0 < KS. [8 marks] (c) Derive an expression for the open-loop frequency response of the system with respect to K for w+ 0 and w+ and hence, show a simple Nyquist sketch of the open-loop response of the system. [6 marks)