Question

A closed loop control system is described by the following block diagram given in Figure 2 (a). If the transfer function is $G(s) = \frac{9}{s(s+3)}$ and the input is a unit step function, (i) Determine the closed loop transfer function of the system. [2 marks] (ii) Based on the transfer function in (a)(i), evaluate the transient performance of the system by calculating natural frequency, $\omega_n$, damping factor, $\xi$, time delay, $t_d$, rise time, $t_r$, settling time to 5%, $t_s$, maximum overshoot, and time when the maximum overshoot occurs, $t_{max}$. [4 marks] (iii) Determine the output of the system response. [6 marks]

          A closed loop control system is described by the following block diagram given in
Figure 2 (a). If the transfer function is $G(s) = \frac{9}{s(s+3)}$ and the input is a unit step
function,
(i) Determine the closed loop transfer function of the system.
[2 marks]
(ii) Based on the transfer function in (a)(i), evaluate the transient performance
of the system by calculating natural frequency, $\omega_n$, damping factor, $\xi$, time
delay, $t_d$, rise time, $t_r$, settling time to 5%, $t_s$, maximum overshoot, and time
when the maximum overshoot occurs, $t_{max}$.
[4 marks]
(iii) Determine the output of the system response.
[6 marks]

A closed loop control system is described by the following block diagram given in
Figure 2 (a). If the transfer function is G(s) = (9)/(s(s+3)) and the input is a unit step
function,
(i) Determine the closed loop transfer function of the system.
[2 marks]
(ii) Based on the transfer function in (a)(i), evaluate the transient performance
of the system by calculating natural frequency, , damping factor, ξ, time
delay, td, rise time, tr, settling time to 5%, $ts$, maximum overshoot, and time
when the maximum overshoot occurs, tmax.
[4 marks]
(iii) Determine the output of the system response.
[6 marks]

Added by Brittany P.

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