Consider the system of Fig. P7.2-5, and 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 as a function of the sample period T.

(b) Determine the ranges of K 7 0 for stability for the sample periods T = 1 s, T = 0.1 s, and T = 0.01 s.

(c) Consider the system with all sampling removed and with Gp(s) = K>(s + 1). Find the range of K 7 0 for which the analog system is stable.

(d) Comparing the ranges of K from parts (b) and (c), give the effects on stability of reducing the sample period T.

Transcribed Image Text:

R(s) E(S) T= 1s D(z) 1-8-Ts S M(s) 1 s+1 C(s)