Question 13.10: Sketch the root locus for the system shown in Figure 13.21. ...

Control Systems Engineering

Sketch the root locus for the system shown in Figure 13.21. Also, determine the range of gain, K, for stability from the root locus plot.

13.21

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Treat the system as if z were s, and sketch the root locus. The result is shown in Figure 13.22. Using the root locus program discussed in Appendix H.2 at www.wiley.com/go/Nise/ControlSystemsEngineering8e, search along the unit circle for 180°. Identification of the gain, K, at this point yields the range of gain for stability. Using the program, we find that the intersection of the root locus with the unit circle is 1 ∠ 60°. The gain at this point is 0.5. Hence, the range of gain for stability is 0 < K < 0.5.

Students who are using MATLAB should now run ch13apB7 in Appendix B. You will learn how to use MATLAB to plot a root locus on the z-plane as well as superimpose the unit circle. You will learn how to select interactively the intersection of the root locus and the unit circle to obtain the value of gain for stability. This exercise solves Example 13.10 using MATLAB.

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