(a) Control systems engineering and technology have hugely influenced our everyday lives. Write a concise narrative on t
Posted: Sat May 21, 2022 8:19 am
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(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: Gc(s) K (s + 3)2 Gp(s) (s + 5) (s + 1)(+4) and H(s) = 1. R(S) C(s) E(S) e(t) G(s) Ge(s) r(t) + c(t) H(S) Figure Q10 (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 SO. (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 08 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. [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]