Consider the feedback control system shown in Figure 10.44a.

a. If the desired closed-loop poles are located within the shaded regions shown in Figure 10.44b, determine the corresponding ranges of ${\omega }_n$ and $\zeta$ of the closedloop system.

b. Design a PI controller such that the closed-loop poles are at $p_{1,2}=-9\pm 12j$.

c. Compute the steady-state errors of the plant and the closed-loop system to a unit-step reference input.

d. Verify the results in Part (c) using MATLAB by plotting the unit-step responses of the plant and the closed-loop system.

Transcribed Image Text:

FIGURE 10.44 Problem 5. Im 16 -9+12j 10 R(s) kp k 2 Y(s) 60 + S S+5 30 Re (a) (b)