- Q1 Attempt All Parts Of This Question A Control Systems Engineering And Technology Have Hugely Influenced Our Everyd 1 (90.94 KiB) Viewed 45 times
B = 7
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: K Gc(S) = (s + 3)2 (s +5) , Gp(s) = (s + 1)(s + 4) and H(S) = 1. R(S) r(t) + :O E(S) e(t) Gas) Gp(s) C(s) 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 wo 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 (t) = 1.Au(t) is applied to the system, where the function () 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) Page 3 of 7 (1) For the block diagram of a control system shown in Figure Q1b, derive the closed-loop transfer function, C(s)/R(S). [6 marks] D(S) G(s) R(S) E(s) Gr(s) G(s) C(s) H (S) Figure Q1b