All 11 Chapters Covered
r r r
SOLUTION MANUAL
r
,Contents
Preface V
Chapterr2 TherLaplacerTransform 1
Chapterr 3 Mechanicalr Systems 12
Chapterr4 Transfer-Functionr Approachr torModelingrDynamicr Systems 24
Chapterr 5 State-SpacerApproachrtorModelingrDynamicrSystems 43
Chapterr 6 Electricalr Systemsr andr Electromechanicalr Systems 89
Chapterr 7 Fluidr Systemsrandr Thermalr Systems 111
Chapterr 8 Time-Domainr Analysisr ofrDynamicr Systems 125
Chapterr9 Frequency-Domainr Analysisr ofrDynamicr Systems 152
Chapterr 10 Time-DomaimrAnalysisr andr Designr ofrControlr Systems 176
Chapterr 11 Frequency-Domainr Analysisr andr Designr ofrControlr Systems 198
iii
,Preface
ThisrSolutionsr ManualrpresentsrsolutionsrtorallrunsolvedrB-problems.
Forrsomerp
roblems,rsolutionsrincludermorermaterialsrthanrarerrequiredrinrproblemrstatementsrtora
idrtheruserroftherbook.
Thertextrmayrberusedrinrarfewrdifferentrwaysrdependingronrthercourserobjectiverandrt
hertimerallocatedrtorthercourse.
Samplercoursercoveragesrarerlistedrbelow.
Ifrthisrbookrisrusedrasrartextrforrarquarter-
lengthrcourser(withrapproximatelyr30rlecturerhoursrandr 18rrecitationrhours),rChapte
rsr 1r throughr7rmayrbercovered.
Iftherbookrisrusedrasrartextrforrarsemester-
lengthrcourser(withrapproximatelyr40rlecturerhoursrandr26rrecitationrhours),rthenrth
erfirstrninerchaptersrmayrbercoveredror,ralternatively,rtherfirstrsevenrchaptersrplusrCh
aptersr lr0randr11r mayrbercovered.
Ifther courser devotesr 50rtor 60r hoursrtor lectures,r thenrther entirer bookr mayr bercovere
drinrarsemester.
Therinstructorrwillralwaysrhaveranroptionrtoromitrcertainrsubjectsrdependingronrthercou
rserobjective.
KatsuhikorOgata
V
, Solutions to B Problems r r r
CHAPTER 2 r
.r B-2-1. f(t)r =r 0 t<0
=rtre2t t2>0
Noter that
tel= , r r
s?
Referringr torEquationr (2-2),r wer obtain
Fs)r =r d (Ge))=G tee-?') =
r r r 1
(sr +r 2?
B-2-2.
(a) . tr <O
=r 3r sin(5tr +r 45°) tr20
Noterthat
3r sinr (5tr +r 45°)r =r 3r sinr 5tr cosr 45"r +r 3r cosr5tr sinr 45"
=r2sinr5tr +r2r cos5t
r
V
Sor werhave
@-4 ,«»-5' /2 s' +5 °
s?r +s?
= ____ s+5
2.2+2z5
(b) f,(t)r =r 0 t<0
=r0.03(1r -rcosr 2t) t20
F>Gs)r = Ir(t)]r=r0.03rl-r
0.03 s _ 0.12
· s s?r +2? s(s?r +r 4)
1
r r r
SOLUTION MANUAL
r
,Contents
Preface V
Chapterr2 TherLaplacerTransform 1
Chapterr 3 Mechanicalr Systems 12
Chapterr4 Transfer-Functionr Approachr torModelingrDynamicr Systems 24
Chapterr 5 State-SpacerApproachrtorModelingrDynamicrSystems 43
Chapterr 6 Electricalr Systemsr andr Electromechanicalr Systems 89
Chapterr 7 Fluidr Systemsrandr Thermalr Systems 111
Chapterr 8 Time-Domainr Analysisr ofrDynamicr Systems 125
Chapterr9 Frequency-Domainr Analysisr ofrDynamicr Systems 152
Chapterr 10 Time-DomaimrAnalysisr andr Designr ofrControlr Systems 176
Chapterr 11 Frequency-Domainr Analysisr andr Designr ofrControlr Systems 198
iii
,Preface
ThisrSolutionsr ManualrpresentsrsolutionsrtorallrunsolvedrB-problems.
Forrsomerp
roblems,rsolutionsrincludermorermaterialsrthanrarerrequiredrinrproblemrstatementsrtora
idrtheruserroftherbook.
Thertextrmayrberusedrinrarfewrdifferentrwaysrdependingronrthercourserobjectiverandrt
hertimerallocatedrtorthercourse.
Samplercoursercoveragesrarerlistedrbelow.
Ifrthisrbookrisrusedrasrartextrforrarquarter-
lengthrcourser(withrapproximatelyr30rlecturerhoursrandr 18rrecitationrhours),rChapte
rsr 1r throughr7rmayrbercovered.
Iftherbookrisrusedrasrartextrforrarsemester-
lengthrcourser(withrapproximatelyr40rlecturerhoursrandr26rrecitationrhours),rthenrth
erfirstrninerchaptersrmayrbercoveredror,ralternatively,rtherfirstrsevenrchaptersrplusrCh
aptersr lr0randr11r mayrbercovered.
Ifther courser devotesr 50rtor 60r hoursrtor lectures,r thenrther entirer bookr mayr bercovere
drinrarsemester.
Therinstructorrwillralwaysrhaveranroptionrtoromitrcertainrsubjectsrdependingronrthercou
rserobjective.
KatsuhikorOgata
V
, Solutions to B Problems r r r
CHAPTER 2 r
.r B-2-1. f(t)r =r 0 t<0
=rtre2t t2>0
Noter that
tel= , r r
s?
Referringr torEquationr (2-2),r wer obtain
Fs)r =r d (Ge))=G tee-?') =
r r r 1
(sr +r 2?
B-2-2.
(a) . tr <O
=r 3r sin(5tr +r 45°) tr20
Noterthat
3r sinr (5tr +r 45°)r =r 3r sinr 5tr cosr 45"r +r 3r cosr5tr sinr 45"
=r2sinr5tr +r2r cos5t
r
V
Sor werhave
@-4 ,«»-5' /2 s' +5 °
s?r +s?
= ____ s+5
2.2+2z5
(b) f,(t)r =r 0 t<0
=r0.03(1r -rcosr 2t) t20
F>Gs)r = Ir(t)]r=r0.03rl-r
0.03 s _ 0.12
· s s?r +2? s(s?r +r 4)
1
