ENGINEERING aS
Fourth Edition oa
_ KATSUHIKO OGATA
,
,SOLUTIONS
MANUAL
MODERN
CONTROL
ENGINEERING
Fourth Edition
KATSUHIKO OGATA
, Publisher: Tom Robbins
Associate Editor: Alice Dworkin
Supplement Editor: Jessica Romeo
Executive Managing Editor: Vince O'Brien
Managing Editor: David A. George
Production Editor: Barbara A. Till
Supplement Cover Management/Design: Paul Gourhan
Manufacturing Buyer: Ilene Kahn
Crontice © 2002, 1997, 1990, 1970 by Prentice Hall
feaii@e Prentice-Hall, Inc.
amma Upper Saddle River, NJ 07458
All rights reserved. No part of this book may be reproduced in any form or
by any means, without permission in writing from the publisher.
The author and publisher of this book have used their best efforts in
preparing this book. These efforts include the development, research, and
testing of the theories and programs to determine their effectiveness. The
author and publisher make no warranty of any kind, expressed or implied,
with regard to these programs or the documentation contained in this
book. The author and publisher shall not be liable in any event for
incidental or consequential damages in connection with, or arising out of,
the furnishing, performance, or use of these programs.
Printed in the United States of America
LO: Ra7aons das aK
ISBN O-13-060908-0
Pearson Education Ltd., London
Pearson Education Australia Pty. Ltd., Sydney
Pearson Education Singapore, Pte. Ltd.
Pearson Education North Asia Ltd., Hong Kong
Pearson Education Canada, Inc., Toronto
Pearson Educacfon de Mexico, S.A. de C.V.
Pearson Education—Japan, Tokyo
Pearson Education Malaysia, Pte. Ltd.
Pearson Education, Upper Saddle River, New Jersey
Fourth Edition oa
_ KATSUHIKO OGATA
,
,SOLUTIONS
MANUAL
MODERN
CONTROL
ENGINEERING
Fourth Edition
KATSUHIKO OGATA
, Publisher: Tom Robbins
Associate Editor: Alice Dworkin
Supplement Editor: Jessica Romeo
Executive Managing Editor: Vince O'Brien
Managing Editor: David A. George
Production Editor: Barbara A. Till
Supplement Cover Management/Design: Paul Gourhan
Manufacturing Buyer: Ilene Kahn
Crontice © 2002, 1997, 1990, 1970 by Prentice Hall
feaii@e Prentice-Hall, Inc.
amma Upper Saddle River, NJ 07458
All rights reserved. No part of this book may be reproduced in any form or
by any means, without permission in writing from the publisher.
The author and publisher of this book have used their best efforts in
preparing this book. These efforts include the development, research, and
testing of the theories and programs to determine their effectiveness. The
author and publisher make no warranty of any kind, expressed or implied,
with regard to these programs or the documentation contained in this
book. The author and publisher shall not be liable in any event for
incidental or consequential damages in connection with, or arising out of,
the furnishing, performance, or use of these programs.
Printed in the United States of America
LO: Ra7aons das aK
ISBN O-13-060908-0
Pearson Education Ltd., London
Pearson Education Australia Pty. Ltd., Sydney
Pearson Education Singapore, Pte. Ltd.
Pearson Education North Asia Ltd., Hong Kong
Pearson Education Canada, Inc., Toronto
Pearson Educacfon de Mexico, S.A. de C.V.
Pearson Education—Japan, Tokyo
Pearson Education Malaysia, Pte. Ltd.
Pearson Education, Upper Saddle River, New Jersey