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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

          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

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 (C(s))/(R(s)).
• Calculate the values of ζ and .
• 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 (TR), peak
time (TP), settling time (TS), 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) = (20)/(s^2+10s+60)
H(s) = 3s

Added by Joshua M.

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