- The Transfer Functions Of The Control System Shown In Figure Q1a Are As Follows K S 5 Ge S S 3 2 Gr S S 1 1 (40.43 KiB) Viewed 9 times
B= 2
The transfer functions of the control system shown in Figure Q1a are as follows: K (s +5) Ge(s) = (s + 3)2 Gr(s) (s + 1)(8 + 4) and H(S) = 1. s R(s). RS. r(t) + E(s) e(t) Gd(s) Go(s) C(s) c(t) H(s) Figure Q1a (6) 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 <KS. (8 marks) (c) Derive an expression for the open-loop frequency response of the system with respect to K for w+ and w+ c 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. (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, eu < 0.13. Determine the minimum value of that would satisfy the design requirement. 16 marks)