Consider the feedback control system shown in Figure 10.45.

a. Find the values for \(k_{\mathrm{p}}\) and \(T_{\mathrm{I}}\) such that the maximum overshoot in the response to a unit-step reference input is less than \(15 \%\) and the peak time is less than \(0.4 \mathrm{~s}\).

b. \(A\) Verify the results in Part (a) using MATLAB by plotting the unit-step response of the closed-loop system. If the maximum overshoot and the peak time exceed the requirements, fine-tune and reduce them to be approximately the specified values or less.

FIGURE 10.45 Problem 6. R(s) 1 Y(s) 1 Ts 5+2