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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 Qla are as follows: K Gc(s) (s + 5) Gp(s) = (s + 1)(s + 4) and H(s) = 1. = 2 (s + 3)2 R(s) 10 E(S) e(t) C(s). Gc(s) Gps) c(0) Hs) Figure Qla (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 → 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 K that would guarantee the stability of the system and hence, find the frequency of oscillation at the marginal stability point. [8 marks] (e) An input r(t) = 1.Au() is applied to the system, where the function u(t) is the unit step function. It is desired that the steady-state error, ess < 0.1B. Determine the minimum value of K that would satisfy the design requirement. [6 marks] =

. Replace the letters A - F (highlighted in Yellow) with the numerical computation generated from the pre-assessment activity. For example, if A = 1 and B = 2 then 3A = 31, AB = 12, and A.B = 1.2. = =