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Consider the following system, with reference input r(t) and disturbance input (t). (a) Find the transfer function GR(s) with output Y(s) and input R(s), and the transfer func- tion Gp(s) with output Y(s) and input D(s), such that Y(s) = GR(s)R(s)+Gp(s)D(s). (b) Describe the relationship between the characteristic equation of GR(8) and the charac- teristic equation of Gp(8). (c) Find the steady-state output response due to a unit step disturbance input (while pre- suming the ramp input is 0), as a function of the gains K1, K2. (d) For K2 = }, what values of K1 ensure that the steady-state output response in (c) is less than or equal to 0.05? D(s) R(s) K1 2K2 Y{s) s+3 s+4

Consider the following system, with reference input r(t) and disturbance input (t). (a) Find the transfer function GR(s) with output Y(s) and input R(s), and the transfer func- tion Gp(s) with output Y(s) and input D(s), such that Y(s) = GR(s)R(s)+Gp(s)D(s). (b) Describe the relationship between the characteristic equation of GR(8) and the charac- teristic equation of Gp(8). (c) Find the steady-state output response due to a unit step disturbance input (while pre- suming the ramp input is 0), as a function of the gains K1, K2. (d) For K2 = }, what values of K1 ensure that the steady-state output response in (c) is less than or equal to 0.05? D(s) R(s) K1 2K2 Y{s) s+3 s+4

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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4. Consider the following system, with reference input r(t) and disturbance input d(t). (a) Find the transfer function GR(s) with output Y (s) and input R(s), and the transfer func- tion Gp(s) with output Y(s) and input D(s), such that Y (s) = GR(8)R(s)+GD(s)D(s). (b) Describe the relationship between the characteristic equation of GR(8) and the charac- teristic equation of Gp(s). (c) Find the steady-state output response due to a unit step disturbance input (while pre- suming the ramp input is 0), as a function of the gains K1, K2. (d) For K2 = }, what values of K1 ensure that the steady-state output response in (c) is less than or equal to 0.05? D(s) R(s) + K1 2K2 Y(s) 8+3 8+4
Transcribed Image Text:4. Consider the following system, with reference input r(t) and disturbance input d(t). (a) Find the transfer function GR(s) with output Y (s) and input R(s), and the transfer func- tion Gp(s) with output Y(s) and input D(s), such that Y (s) = GR(8)R(s)+GD(s)D(s). (b) Describe the relationship between the characteristic equation of GR(8) and the charac- teristic equation of Gp(s). (c) Find the steady-state output response due to a unit step disturbance input (while pre- suming the ramp input is 0), as a function of the gains K1, K2. (d) For K2 = }, what values of K1 ensure that the steady-state output response in (c) is less than or equal to 0.05? D(s) R(s) + K1 2K2 Y(s) 8+3 8+4
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