(a) Calculate the magnitude and phase of 1

G(s)= s+1'

for w = 0.1, 0.2, 0.5, 1, 2, 5, and 10rad/sec.

(b) Sketch the asymptotes for G ( s), and compare these with the cmnpv.ted results from part (a).

Problem 6. 7 Draw the Bode plots for each of the following systems. Compare the sketches with the plots obtained using MATLAB.

1 G ( s) - ..,.-------,--:::-:-::------:- - (s+1) 2 (s2 +s+4) (a)

(b) G(S)- s - (s + 1)(s + 10)(s2 + 5s + 2500)

(c) G(s) _ 4s(s + 10)

- (s + 50)(4s2 + 5s + 4)

(d) G s _ lO(s + 4)
( )- s(s+1)(s2 +2s+5)

(e) G s _ lOOO(s + 1)
( )- s(s+2)(s2 +8s+64)

(f) G s _ (s + 5)(s + 3)
( )- s(s+1)(s2 +s+4)
(g) Gs _ 4000 ()- s(s+40)
(h) G(s) _ 100 - s(1 + 0.1s)(1 + 0.5s)
(i) 1 G(s)-- s(1+s)(1+0.02s)
Problem