For the robot arm joint control system of Problem 7.5-4 and Fig. P7.5-4:

(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 7.5-4

Consider the robot arm joint control system of Fig. P7.5-4. This system is described in Problem 1.5-4. For this problem, T = 0.1 s and D(z) = 1. It was shown in Problem 6-7 that

(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).

Transcribed Image Text:

200 S -Ts 4 s(s+ 2) 0.01873z + 0.01752 0.8187) (z 1)(z -