Question

1. What are the poles and zeros of G(s) ? Is the system stable? Explain.

Answer 1

G(S) = S^2 - 4/S(S + 1)^2 poles roots of S(S + 1)^2 = 0 = > S = 0 S = -1,1 zero roots of s^2 - 4 = 0 s = 2, - 2 two poles at left half of s - plain Hence system is unstable A = [-3 2 0 1] B = [2 1] Vertical-bar s I - A Vertical-bar = 0 The roots are of c E - plans (s + 3)(s + 2) + 0 = 0 (s + 3)(s + 2) = 0 s = -3,- 2 poles at - 2,- 3 G(s) = 1/s + 3 y(s) = G(s) x(s) = 1/s + 3 X(t) = sin 3 t x(s) = L^-1{x(t)} = L^-1{sin 3 t} = 3/s^2 + 9 Y(s) = G(s) = 1/s + 3 3/s^2 + 9 = 3/(s + 3) (s^2 + 9) = 1/6/s + 3 + - s/6 + 1/2 /s^2 + 9 Y_s s(t) = L^-1{Y(s)}