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Consider the closed loop digital control system shown in Fig. 1, where the sampling period is T=In(2). y(t) → ZOH u(k) D(z) → G(s) r(k) e(k) Fig. 1 3 and D(z)=- s+3 z-0.125 G(s): z-1 Y(z) 1) Find the closed loop z-transfer function W(z)=- R(z) 2) Compute the discrete-time output y(kT ) in response to a unit-step reference. 3) Find the steady state errors to a unit-step reference and to a unit-ramp reference.

Consider the closed loop digital control system shown in Fig. 1, where the sampling period is T=In(2). y(t) → ZOH u(k) D(z) → G(s) r(k) e(k) Fig. 1 3 and D(z)=- s+3 z-0.125 G(s): z-1 Y(z) 1) Find the closed loop z-transfer function W(z)=- R(z) 2) Compute the discrete-time output y(kT ) in response to a unit-step reference. 3) Find the steady state errors to a unit-step reference and to a unit-ramp reference.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the closed loop digital control system shown in Fig. 1, where the sampling period is T=In(2). y(t) D(z) ZOH G(s) r(k) e(k) u(k) T Fig. 1 3 and D(z)= s+3 z-0.125 G(s) = z-1 Y(z) 1) Find the closed loop z-transfer function W(z) = R(z) 2) Compute the discrete-time output y(kT) in response to a unit-step reference. 3) Find the steady state errors to a unit-step reference and to a unit-ramp reference.
Transcribed Image Text:Consider the closed loop digital control system shown in Fig. 1, where the sampling period is T=In(2). y(t) D(z) ZOH G(s) r(k) e(k) u(k) T Fig. 1 3 and D(z)= s+3 z-0.125 G(s) = z-1 Y(z) 1) Find the closed loop z-transfer function W(z) = R(z) 2) Compute the discrete-time output y(kT) in response to a unit-step reference. 3) Find the steady state errors to a unit-step reference and to a unit-ramp reference.
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