Question

Consider a second-order system with the transfer function \frac{Y(s)}{R(s)} = \frac{\omega_n^2}{s^2 + 2\zeta \omega_n s + \omega_n^2}, \quad \text{where,} \quad \omega_n^2 = 16 + \alpha + \beta + \delta, \quad \zeta = \frac{1 + \alpha}{3 + \beta + \delta}. a) If the input r(t) is a unit step, obtain the output response y(t). b) Calculate the maximum percent overshoot $M_p$, the rise time $t_r$, and the settling time $t_s$. c) By using matlab, obtain the unit step response y(t) and submit the screen shot (plot) of your plot with your exam. Note: Make sure that your calculated values of $M_p$, $t_r$, and $t_s$ agree with the plot.

          Consider a second-order system with the transfer function
\frac{Y(s)}{R(s)} = \frac{\omega_n^2}{s^2 + 2\zeta \omega_n s + \omega_n^2}, \quad \text{where,} \quad \omega_n^2 = 16 + \alpha + \beta + \delta, \quad \zeta = \frac{1 + \alpha}{3 + \beta + \delta}.
a) If the input r(t) is a unit step, obtain the output response y(t).
b) Calculate the maximum percent overshoot $M_p$, the rise time $t_r$, and the settling time $t_s$.
c) By using matlab, obtain the unit step response y(t) and submit the screen shot (plot) of
your plot with your exam.
Note: Make sure that your calculated values of $M_p$, $t_r$, and $t_s$ agree with the plot.

Consider a second-order system with the transfer function
(Y(s))/(R(s)) = (^2)/(s^2 + 2ζs + ^2), where, ^2 = 16 + α+ β+ δ, ζ= (1 + α)/(3 + β+ δ).
a) If the input r(t) is a unit step, obtain the output response y(t).
b) Calculate the maximum percent overshoot Mp, the rise time tr, and the settling time ts.
c) By using matlab, obtain the unit step response y(t) and submit the screen shot (plot) of
your plot with your exam.
Note: Make sure that your calculated values of Mp, tr, and ts agree with the plot.

Added by Matthew W.

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