For the antenna control system of Problem 7.5-5 and Fig. P7.5-5:

(a) Plot the z-plane root locus.

(b) Plot the w-plane root locus.

(c) Determine the range of K for stability using the results of part (a).

(d) Determine the range of K for stability using the results of part (b).

Problem 7.5-5

Problem 1.5-1

Transcribed Image Text:

Consider the antenna control system of Fig. P7.5-5. This system is described in Problem 1.5-1. For this problem, T = 0.05 s and D(z) = 1. It was shown in Problem 5.3-15 that -T's - 8 20 S s(s+ 6)] 0.02268z +0.02052 (z - 1)(z- 0.7408) (a) Write the closed-loop system characteristic equation. (b) Use the Routh-Hurwitz criterion to determine the range of K for stability. (c) Check the results of part (b) using the Jury test. (d) Determine the location of all roots of the characteristic equation in both the w-plane and the z-plane for the value of K > 0 for which the system is marginally stable. (e) Determine both the s-plane frequency and the w-plane frequency at which the system will oscillate when marginally stable, using the results of part (d). (f) Show that the frequencies in part (e) satisfy (7-10).