R(s)
C(s)
D(s)
G(s)
H(s)
Figure 1: Closed-loop system block diagram
Perform the following for problems 1-4:
• Determine the transfer function for the closed-loop system as $\frac{C(s)}{R(s)}$.
• Calculate the values of $\zeta$ and $\omega_n$.
• Based on the poles of each closed-loop system transfer function, predict whether the
response of the system to a step input will be overdamped, critically damped, or
underdamped. Also, determine whether the system is stable or unstable.
• For the systems that are stable and underdamped: calculate the rise time ($T_R$), peak
time ($T_P$), settling time ($T_S$), and % overshoot (% OSH).
• Create a MATLAB script to plot the responses of the closed-loop system transfer
functions to a step input. Submit screenshots of both MATLAB code and plots.
1-1: D(s) = 4
$G(s) = \frac{20}{s^2+10s+60}$
H(s) = 3s