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uestion No.4 (CLO 1,2) (10 marks) epetitive Control refers to a class of control methods used to compensate for periodic disturbances or eriodic reference inputs. One such system is shown below. \frac{s+K}{2} \frac{1}{s+4} R E Y \frac{1}{s+1} a. Find the input-to-output transfer function $T(s) = \frac{Y(s)}{R(s)}$ b. Find the input-to-error transfer function $T_e(s) = \frac{E(s)}{R(s)}$ c. Assuming the closed-loop system is stable, show that the steady-state error, $e_\infty = \lim_{t \to \infty} e(t)$, is zero, if $R(s) = \frac{as+b}{s^2+2^2}$, i.e., the reference input is a sinusoid with frequency 2.

          uestion No.4 (CLO 1,2) (10 marks)
epetitive Control refers to a class of control methods used to compensate for periodic disturbances or
eriodic reference inputs. One such system is shown below.
\frac{s+K}{2}
\frac{1}{s+4}
R
E
Y
\frac{1}{s+1}
a. Find the input-to-output transfer function $T(s) = \frac{Y(s)}{R(s)}$
b. Find the input-to-error transfer function $T_e(s) = \frac{E(s)}{R(s)}$
c. Assuming the closed-loop system is stable, show that the steady-state error, $e_\infty = \lim_{t \to \infty} e(t)$, is
zero, if $R(s) = \frac{as+b}{s^2+2^2}$, i.e., the reference input is a sinusoid with frequency 2.

uestion No.4 (CLO 1,2) (10 marks)
epetitive Control refers to a class of control methods used to compensate for periodic disturbances or
eriodic reference inputs. One such system is shown below.
(s+K)/(2)
(1)/(s+4)
R
E
Y
(1)/(s+1)
a. Find the input-to-output transfer function T(s) = (Y(s))/(R(s))
b. Find the input-to-error transfer function Te(s) = (E(s))/(R(s))
c. Assuming the closed-loop system is stable, show that the steady-state error, e∞ = limt →∞ e(t), is
zero, if R(s) = (as+b)/(s^2+2^2), i.e., the reference input is a sinusoid with frequency 2.

Added by Noah A.

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