For the system of Problem 7.2-5 and Fig. P7.2-5:

(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 7.2-5

Consider the system of Fig. P7.2-5 with T = 1 s. Let the digital controller be a variable gain K such that
D(z) = K. Hence m(kT) = Ke(kT).
(a) Write the closed-loop system characteristic equation.
(b) Determine the range of K for which the system is stable.
(c) Suppose that K is set to the lower limit of the range in part (b) such that the system is marginally stable.
Find the natural-response term that illustrates the marginal stability.
(d) Repeat part (c) for the upper limit of the range of K.

Transcribed Image Text:

R(s) E(S) T= 1 s D(z) 1-8-7's S M(s) Gp(s) 1 s+1] C(s)