Question

Apply Routh-Hurwitz criterion to determine whether the given control system is stable or unstable? b) Tell how many poles of the closed loop transfer function lie in the right half-plane. left half-plane, and on the jo-axis? Justify your answer. a Cis) R(s) +4s-3 .4p832+ 20 15

please do all step clean and neat

Answer 1

Given CE s^4 + 4^3 + 8 s^2 + 20 s + 15 = 0 32 - 20/4 = 12/4 = 3 3 Times 20 - 60 /3 = (o with E) Replace e rightarrow 0 No.of sign changes is zero Therefore Given system is stable Given characteristic Equation CE = s^4 + 4 s^3 + 8 s^2 + 20 s + 15 = 0 This can be written as (s + 1) (s + 3) (s - i squareroot 5) (s + i squareroot 5) = 0 i.e: poles are s = -1, -3, i squareroot 5, i squareroot 5 \r\n No . of poles on Right half plane = 0 No . of poles on Left half plane = 4 There all two poles on jw axis