Answer Happy

Question 3 (6 marks) - ULO4 Consider a unity feedback system as shown below. Where Gc(5) is the controller and G(s) is the plant. R(s) G(S) K[s+3) (s+20) G(s) 1 s(S-2) Y(s) a) (3 Marks) Using the Routh-Hurwitz Criterion, determine the range of K for which the system is stable. b) (3 Marks) The root locus of the above system is generated using Matlab as shown below. Using the root locus method, determine the range of K that will produce a stable response.

8 Root Locus 0.8 0.935 0.88 0.66 0.48 0.25 6 0.975 4 0.994 N 2 20 17.5 15 12.5 10 7.5 5 Imaginary Axis (seconds) 35 -2 0.994 0.975 -6 0.935 0.88 0.8 0.66 0.48 0.25 L -8 -20 -15 -10 -5 0 Real Axis (seconds)