Consider the closed-loop system of Fig. P6.2-1.

(a) Calculate and plot the unit-step response at the sampling instants, for the case that D(z) = 1 .

(b) Calculate the system unit-step response of the analog system, that is, with the sampler, digital controller, and data hold removed. Plot the response on the same graph with the results of part (a).

(c) For the system of Fig. P6.2-1, let D(z) = 1 and T = 0.4 s . Calculate the unit-step response and plot these results on the same graph used for parts (a) and (b).

(d) Use the system dc gains to calculate the steady-state responses for each of the systems of parts (a), (b), and (c). Why are these gains equal?

Transcribed Image Text:

R(s) T= 2s D(z) 1-e-Tr 3 0.5 $+0.5 Figure P6.2-1 System for Problem 6.2-1. C(s)