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 n n and of the closedloop system b Design a PI controller such that the closed loop poles are at p 1 , 2 9 12 j p 1 , 2 9 12 j 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 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)

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Question: 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,

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 $ω_{n}$ and $ζ$ of the closedloop system.

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

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.

FIGURE 10.44 Problem 5. Im 16 -9+12j 10 R(s) kp k 2

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)

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