Apago PDF Enhancer
, 1-17 Solutions to Problems
Founded in 1807, John Wiley & Sons, Inc. has been a valued source of knowledge and understanding
for more than 200 years, helping people around the world meet their needs and fulfill their
aspirations. Our company is built on a foundation of principles that include responsibility to the
communities we serve and where we live and work. In 2008, we launched a Corporate Citizenship
Initiative, a global effort to address the environmental, social, economic, and ethical challenges we
face in our business. Among the issues we are addressing are carbon impact, paper specifications and
procurement, ethical conduct within our business and among our vendors, and community and
charitable support. For more information, please visit our website: www.wiley.com/go/citizenship.
Copyright © 2011 by John Wiley & Sons, Inc.
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form
or by any means, electronic, mechanical, photocopying recording, scanning or otherwise, except as
permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the
prior written permission of the Publisher or authorization through payment of the appropriate per-
copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-
8400, fax (978) 646-8600. Requests to the Publisher for permission should be addressed to the
Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)
748-6011, fax (201) 748-6008 or online at http://www.wiley.com/go/permissions.
Evaluation copies are provided to qualified academics and professionals for review purposes only, for
use in their courses during the next academic year. These copies are licensed and may not be sold or
transferred to a third party. Upon completion of the review period, please return the evaluation copy
to Wiley. Return instructions and a free of charge return shipping label are available at
www.wiley.com/go/returnlabel. Outside of the United States, please contact your local
representative
ISBN 13 978-0470-54756-4
Copyright © 2011 by John Wiley & Sons, Inc.
, O N E
Introduction
ANSWERS TO REVIEW QUESTIONS
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna
2. Yes - power gain, remote control, parameter conversion; No - Expense, complexity
3. Motor, low pass filter, inertia supported between two bearings
4. Closed-loop systems compensate for disturbances by measuring the response, comparing it to
the input response (the desired output), and then correcting the output response.
5. Under the condition that the feedback element is other than unity
6. Actuating signal
7. Multiple subsystems can time share the controller. Any adjustments to the controller can be
implemented with simply software changes.
8. Stability, transient response, and steady-state error
9. Steady-state, transient
10. It follows a growing transient response until the steady-state response is no longer visible. The
system will either destroy itself, reach an equilibrium state because of saturation in driving
amplifiers, or hit limit stops.
11. Natural response
12. Determine the transient response performance of the system.
13. Determine system parameters to meet the transient response specifications for the system.
14. True
15. Transfer function, state-space, differential equations
16. Transfer function - the Laplace transform of the differential equation
State-space - representation of an nth order differential equation as n simultaneous first-order
differential equations
Differential equation - Modeling a system with its differential equation
SOLUTIONS TO PROBLEMS
50 volts
1. Five turns yields 50 v. Therefore K = = 1.59
5 x 2π rad
Copyright © 2011 by John Wiley & Sons, Inc.
, 1-2 Chapter 1: Introduction
2.
Desired Temperature Voltage Actual
Fuel
temperature difference difference temperature
flow
+ Amplifier and
Thermostat Heater
valves
-
3.
Desired Input Error Aileron Roll Roll
roll voltage voltage position rate angle
angle
+ Aileron Aircraft
Pilot Integrate
position dynamics
controls
control
-
Gyro
Gyro voltage
4.
Input
Speed
Desired voltage Actual
Error Motor
speed speed
+ voltage and
transducer Amplifier drive
system
-
Dancer
Dancer
position
Voltage dynamics
sensor
proportional
to actual speed
Copyright © 2011 by John Wiley & Sons, Inc.
, 1-17 Solutions to Problems
Founded in 1807, John Wiley & Sons, Inc. has been a valued source of knowledge and understanding
for more than 200 years, helping people around the world meet their needs and fulfill their
aspirations. Our company is built on a foundation of principles that include responsibility to the
communities we serve and where we live and work. In 2008, we launched a Corporate Citizenship
Initiative, a global effort to address the environmental, social, economic, and ethical challenges we
face in our business. Among the issues we are addressing are carbon impact, paper specifications and
procurement, ethical conduct within our business and among our vendors, and community and
charitable support. For more information, please visit our website: www.wiley.com/go/citizenship.
Copyright © 2011 by John Wiley & Sons, Inc.
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form
or by any means, electronic, mechanical, photocopying recording, scanning or otherwise, except as
permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the
prior written permission of the Publisher or authorization through payment of the appropriate per-
copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-
8400, fax (978) 646-8600. Requests to the Publisher for permission should be addressed to the
Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)
748-6011, fax (201) 748-6008 or online at http://www.wiley.com/go/permissions.
Evaluation copies are provided to qualified academics and professionals for review purposes only, for
use in their courses during the next academic year. These copies are licensed and may not be sold or
transferred to a third party. Upon completion of the review period, please return the evaluation copy
to Wiley. Return instructions and a free of charge return shipping label are available at
www.wiley.com/go/returnlabel. Outside of the United States, please contact your local
representative
ISBN 13 978-0470-54756-4
Copyright © 2011 by John Wiley & Sons, Inc.
, O N E
Introduction
ANSWERS TO REVIEW QUESTIONS
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna
2. Yes - power gain, remote control, parameter conversion; No - Expense, complexity
3. Motor, low pass filter, inertia supported between two bearings
4. Closed-loop systems compensate for disturbances by measuring the response, comparing it to
the input response (the desired output), and then correcting the output response.
5. Under the condition that the feedback element is other than unity
6. Actuating signal
7. Multiple subsystems can time share the controller. Any adjustments to the controller can be
implemented with simply software changes.
8. Stability, transient response, and steady-state error
9. Steady-state, transient
10. It follows a growing transient response until the steady-state response is no longer visible. The
system will either destroy itself, reach an equilibrium state because of saturation in driving
amplifiers, or hit limit stops.
11. Natural response
12. Determine the transient response performance of the system.
13. Determine system parameters to meet the transient response specifications for the system.
14. True
15. Transfer function, state-space, differential equations
16. Transfer function - the Laplace transform of the differential equation
State-space - representation of an nth order differential equation as n simultaneous first-order
differential equations
Differential equation - Modeling a system with its differential equation
SOLUTIONS TO PROBLEMS
50 volts
1. Five turns yields 50 v. Therefore K = = 1.59
5 x 2π rad
Copyright © 2011 by John Wiley & Sons, Inc.
, 1-2 Chapter 1: Introduction
2.
Desired Temperature Voltage Actual
Fuel
temperature difference difference temperature
flow
+ Amplifier and
Thermostat Heater
valves
-
3.
Desired Input Error Aileron Roll Roll
roll voltage voltage position rate angle
angle
+ Aileron Aircraft
Pilot Integrate
position dynamics
controls
control
-
Gyro
Gyro voltage
4.
Input
Speed
Desired voltage Actual
Error Motor
speed speed
+ voltage and
transducer Amplifier drive
system
-
Dancer
Dancer
position
Voltage dynamics
sensor
proportional
to actual speed
Copyright © 2011 by John Wiley & Sons, Inc.
