1. Given a Bode diagram of a dynamic system (a) Find the transfer function of the system G(s). (b) At what frequency the gain of the system |G (jw)| = 1 ? What is the phase of the system at this frequency? (c) At what frequencies is the phase of G (jw) equals –180°? What is gain at these frequencies? (d) Assuming that this system is in a unity feedback configuration, i.e. H(s) = 1 i. What is the steady state error of the closed-loop system to unit step input ? ii. What is the steady state error of the closed-loop system to unit ramp input ? iii. What is the steady state error of the closed-loop system to constant acceleration input r(t) = }t2? (e) What is the steady state response of the open-loop system G(s) to the input r(t) = 2 · sint+ 5 · sin10t

1. Given a Bode diagram of a dynamic system (a) Find the transfer function of the system G(s). (b) At what frequency the gain of the system |G (jw)| = 1 ? What is the phase of the system at this frequency? (c) At what frequencies is the phase of G (jw) equals –180°? What is gain at these frequencies? (d) Assuming that this system is in a unity feedback configuration, i.e. H(s) = 1 i. What is the steady state error of the closed-loop system to unit step input ? ii. What is the steady state error of the closed-loop system to unit ramp input ? iii. What is the steady state error of the closed-loop system to constant acceleration input r(t) = }t2? (e) What is the steady state response of the open-loop system G(s) to the input r(t) = 2 · sint+ 5 · sin10t

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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Question

1. Given a Bode diagram of a dynamic system
(a) Find the transfer function of the system G(s).
(b) At what frequency the gain of the system |G (jw)| = 1 ? What is the phase of the system at this
frequency?
(c) At what frequencies is the phase of G (jw) equals – 180°? What is gain at these frequencies?
(d) Assuming that this system is in a unity feedback configuration, i.e. H(s) = 1
i. What is the steady state error of the closed-loop system to unit step input ?
ii. What is the steady state error of the closed-loop system to unit ramp input ?
iii. What is the steady state error of the closed-loop system to constant acceleration input r(t) = t2?
(e) What is the steady state response of the open-loop system G(s) to the input
r(t) = 2· sint + 5· sin10t

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102
10
10
10'
10
10
w (rad/sec)
-20
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102
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10'
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w [rad/sec]
[6ap]b

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