Consider the negative feedback control system shown in Figure 10.41.

a. Design a \(\mathrm{P}\) controller such that the maximum overshoot in the response to a unit-step reference input is less than \(15 \%\), the \(2 \%\) settling time is less than \(1 \mathrm{~s}\), and the rise time is less than \(0.2 \mathrm{~s}\).

b. Use MATLAB to plot the unit-step response of the closed-loop system. Find the overshoot, \(2 \%\) settling time, and rise time. If the time-domain specifications exceed the requirements, fine-tune and reduce them to be approximately the specified values or less.

FIGURE 10.41 Problem 2. R(s) kp 5 Y(s) $2+12s+5