Using the step responses of (1) an integrating ele-ment and (2) a first-order process to an input change of magnitude M.(a)Show that the step response for an input change of a first-order process G1(s)=K1/(?s+1) can be approximately modeled by the step response of anintegrator.G0(s)= K0/s for low values of t—i.e.,t≪τ (b)What is the relation between K1 if the two responses match fo rt≪τ?(c)This relationship motivates the use of an integratormodel to approximate a first-order process by means of asingle-parameter model. Explain how you would analyze a single step test to find K0 and a time delay (if one exists).
Using the step responses of (1) an integrating ele-ment and (2) a first-order process to an input change of magnitude M.(a)Show that the step response for an input change of a first-order process G1(s)=K1/(?s+1) can be approximately modeled by the step response of anintegrator.G0(s)= K0/s for low values of t—i.e.,t≪τ (b)What is the relation between K1 if the two responses match fo rt≪τ?(c)This relationship motivates the use of an integratormodel to approximate a first-order process by means of asingle-parameter model. Explain how you would analyze a single step test to find K0 and a time delay (if one exists).
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Using the step responses of (1) an integrating ele-ment and (2) a first-order process to an input change of magnitude M.(a)Show that the step response for an input change of a first-order process G1(s)=K1/(?s+1) can be approximately modeled by the step response of anintegrator.G0(s)= K0/s for low values of t—i.e.,t≪τ (b)What is the relation between K1 if the two responses match fo rt≪τ?(c)This relationship motivates the use of an integratormodel to approximate a first-order process by means of asingle-parameter model. Explain how you would analyze a single step test to find K0 and a time delay (if one exists).
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