The forward path transfer function L(s) of the control system shown in Figure (a) has the asymptotic Bode plot shown

Q. The forward path transfer function L(s) of the control system shown in Figure (a) has the asymptotic Bode plot shown in Figure (b). If the disturbance d (t) is given by d(t) = 0.1sin(wt) where w = 5 rad s , the steady-state amplitude of the output y(t) is

Sol:

as r = 0

y = – y L(s) + d

From bode magnitude plot

At ω = 5 rad/sec, magnitude of L(s) = 40 dB

⇒ magnitude of L(s) = 100

From Bode phase plot

∠L(s) = 120° at ω = 5 rad/sec L(s) at 5 rad/sec = 100 ∠-120°