Question

if it has HS C(S) R(s) E(s) Gs) B(S) Fig.I 3) Test the systems stability using Routh's array for a control system shown in Fig.1 if it has H(s)-1/(S+5), G(s)-k/[S(s+3)1, k-20? Find the critical gain K?

Control Engineering

Answer 1

H(s) = 1/s + 5: G(s) = k/s (s + 8) T(s) = G(s)/1 + G(s) H(s) = k/s(s + 3)/1 + -k/s(s + 3) 1/(s + 8) Therefore characteristic Equation: s(s + 3) (s + 5) + k = 0 s(s^2 + 8s + 15) + k = 0 s(s^2 + 8s + 15) + k = 0 s^3 + 8 s^2 + 15s + k = 0 Routh Array: for k = 20, all elements in first row are positive Hence, there are no sign changes and system is stable. Critical gain happens when 120 - k/8 = 0 k = 120