A Figure 10.61 shows the root locus of a unity negative feedback control system, where \(K\) is the proportional control gain.

a. Determine the transfer function of the plant. Use MATLAB to plot the root locus based on your choice of the plant, compare it with the root locus shown in Figure 10.61, and check the accuracy of your plant transfer function.

b. Give comments on the stability of the closed-loop system when \(K\) varies from 0 to \(\infty\).

c. Give comments on the transient performance of the closed-loop system when \(K=0.5\) and 5 . Use MATLAB to plot the corresponding unit-step responses and verify your comments.

Transcribed Image Text:

3 2 1 K=1.37 K=0.5 K=5 K=5 K=1.37 0. K=0.5 K=26 K=26 L Imaginary axis FIGURE 10.61 Problem 5. -2 10 K=5 K=0.5 K=1.37 -3 -2 -1 0 1 Real axis