Consider the feedback control system shown in Figure 10.43.

a. Find the values for \(k_{\mathrm{p}}\) and \(T_{\mathrm{D}}\) such that the maximum overshoot in the response to a unit-step reference input is less than \(5 \%\) and the \(2 \%\) settling time is less than \(0.5 \mathrm{~s}\).

b. Compute the steady-state error of the closed-loop system to a unit-step reference input.

c. 1 Verify the results of Parts (a) and (b) using MATLAB by plotting the unitstep response of the closed-loop system. If the maximum overshoot and the settling time exceed the requirements, fine-tune and reduce them to be approximately the specified values or less.

FIGURE 10.43 Problem 4. R(s)- S 0.1s 1 +0.8s +1 Y(s)