Answer Happy

for question 1
Where A = B = 9 , so r(t) = 1.9u(t) and ess<0.19
plz solve part c and d in 35 mins i will thumb up
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 + 5) (s + 1)(s + 4) Gp(s) and H(s) = 1. = (s + 3)2 > R(s) r(t) + E(S) e(t) Gc(s) Ge(s) C(s). c(t) H(s) 4 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 <0. [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]