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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). r(t) + E(S) e(t) Gds) Go(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 <K SOO. [8 marks) (c) Derive an expression for the open-loop frequency response of the system with respect to K for w+ 0 and w+ 0 and hence, show a simple Nyquist sketch of the open-loop response of the system. [6 marks) (d) With the aid of the Routh-Hurwitz stability criterion, investigate the range of the gain that would guarantee the stability of the system and hence, find the frequency of oscillation at the marginal stability point. A=2. B=2 (8 marks] (e) An input r(t) = 1.Au(t) is applied to the system, where the function u(t) is the unit step function. It is desired that the steady-state error, ess < 0.18. Determine the minimum value of that would satisfy the design requirement. [6 marks)