All11ChaptersCovered
l l l
SOLUTION MANUAL
l
,Contents
Preface V
Chapterl2 ThelLaplacelTransform 1
Chapterl 3 Mechanicall Systems 12
Chapterl4 Transfer-Functionl Approachl tolModelinglDynamicl Systems 24
Chapterl 5 State-SpacelApproachltolModelinglDynamiclSystems 43
Chapterl6 Electricall Systemsl andl Electromechanicall Systems 89
Chapterl 7 Fluidl Systemslandl Thermall Systems 111
Chapterl 8 Time-Domainl Analysisl oflDynamicl Systems 125
Chapterl9 Frequency-Domainl Analysisl oflDynamicl Systems 152
Chapterl 10 Time-DomaimlAnalysisl andl Designl oflControll Systems 176
Chapterl 11 Frequency-Domainl Analysisl andl Designl oflControll Systems 198
iii
,Preface
ThislSolutionslManuallpresentslsolutionsltolalllunsolvedlB-problems.
Forlsomelpr
oblems,lsolutionslincludelmorelmaterialslthanlarelrequiredlinlproblemlstatementsltolaid
lthel userl ofthel book.
Theltextlmaylbelusedlinlalfewldifferentlwaysldependinglonlthelcourselobjectivelandlth
eltimelallocatedltolthelcourse.
Samplelcourselcoverageslarellistedlbelow.
Iflthislbooklislusedlaslaltextlforlalquarter-
lengthlcoursel(withlapproximatelyl30llecturelhourslandl 18lrecitationlhours),lChapter
sl 1l throughl7lmaylbelcovered.
Ifthelbooklislusedlaslaltextlforlalsemester-
lengthlcoursel(withlapproximatelyl40llecturelhourslandl26lrecitationlhours),lthenlthel
firstlninelchapterslmaylbelcoveredlor,lalternatively,lthelfirstlsevenlchapterslpluslChapt
ersl ll0landl11l maylbelcovered.
Ifthel coursel devotesl 50ltol 60l hoursltol lectures,l thenlthel entirel bookl mayl belcovered
inlalsemester.
l
Thelinstructorlwilllalwayslhavelanloptionltolomitlcertainlsubjectsldependinglonlthelcour
selobjective.
KatsuhikolOgata
V
, Solutions to B Problems l l l
CHAPTER 2 l
.l B-2-1. f(t)l =l 0 t<0
=ltle2t t2>0
Notel that
tel= , l l
s?
Referringl tolEquationl (2-2),l wel obtain
Fs)l =l d (Ge))=G tee-?') =
l l l 1
(sl +l 2?
B-2-2.
(a) . tl <O
=l 3l sin(5tl +l 45°) tl20
Notelthat
3l sinl (5tl +l 45°)l =l 3l sinl 5tl cosl 45"l +l 3l cosl5tl sinl 45"
=l2sinl5tl +l2l cos5t l
V
Sol welhave
@-4 ,«»-5' /2 s' +5 °
s?l +s?
= ____ s+5
2.2+2z5
(b) f,(t)l =l 0 t<0
=l0.03(1l -lcosl 2t) t20
F>Gs)l = Ir(t)]l=l0.03ll-l
0.03 s _ 0.12
· s s?l +2? s(s?l+l 4)
1
l l l
SOLUTION MANUAL
l
,Contents
Preface V
Chapterl2 ThelLaplacelTransform 1
Chapterl 3 Mechanicall Systems 12
Chapterl4 Transfer-Functionl Approachl tolModelinglDynamicl Systems 24
Chapterl 5 State-SpacelApproachltolModelinglDynamiclSystems 43
Chapterl6 Electricall Systemsl andl Electromechanicall Systems 89
Chapterl 7 Fluidl Systemslandl Thermall Systems 111
Chapterl 8 Time-Domainl Analysisl oflDynamicl Systems 125
Chapterl9 Frequency-Domainl Analysisl oflDynamicl Systems 152
Chapterl 10 Time-DomaimlAnalysisl andl Designl oflControll Systems 176
Chapterl 11 Frequency-Domainl Analysisl andl Designl oflControll Systems 198
iii
,Preface
ThislSolutionslManuallpresentslsolutionsltolalllunsolvedlB-problems.
Forlsomelpr
oblems,lsolutionslincludelmorelmaterialslthanlarelrequiredlinlproblemlstatementsltolaid
lthel userl ofthel book.
Theltextlmaylbelusedlinlalfewldifferentlwaysldependinglonlthelcourselobjectivelandlth
eltimelallocatedltolthelcourse.
Samplelcourselcoverageslarellistedlbelow.
Iflthislbooklislusedlaslaltextlforlalquarter-
lengthlcoursel(withlapproximatelyl30llecturelhourslandl 18lrecitationlhours),lChapter
sl 1l throughl7lmaylbelcovered.
Ifthelbooklislusedlaslaltextlforlalsemester-
lengthlcoursel(withlapproximatelyl40llecturelhourslandl26lrecitationlhours),lthenlthel
firstlninelchapterslmaylbelcoveredlor,lalternatively,lthelfirstlsevenlchapterslpluslChapt
ersl ll0landl11l maylbelcovered.
Ifthel coursel devotesl 50ltol 60l hoursltol lectures,l thenlthel entirel bookl mayl belcovered
inlalsemester.
l
Thelinstructorlwilllalwayslhavelanloptionltolomitlcertainlsubjectsldependinglonlthelcour
selobjective.
KatsuhikolOgata
V
, Solutions to B Problems l l l
CHAPTER 2 l
.l B-2-1. f(t)l =l 0 t<0
=ltle2t t2>0
Notel that
tel= , l l
s?
Referringl tolEquationl (2-2),l wel obtain
Fs)l =l d (Ge))=G tee-?') =
l l l 1
(sl +l 2?
B-2-2.
(a) . tl <O
=l 3l sin(5tl +l 45°) tl20
Notelthat
3l sinl (5tl +l 45°)l =l 3l sinl 5tl cosl 45"l +l 3l cosl5tl sinl 45"
=l2sinl5tl +l2l cos5t l
V
Sol welhave
@-4 ,«»-5' /2 s' +5 °
s?l +s?
= ____ s+5
2.2+2z5
(b) f,(t)l =l 0 t<0
=l0.03(1l -lcosl 2t) t20
F>Gs)l = Ir(t)]l=l0.03ll-l
0.03 s _ 0.12
· s s?l +2? s(s?l+l 4)
1
