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ol Systems Engineering, International Adaptation, 8th Edition by Nise, Exams of Systems Engineering

Rhodes University Systems Engineering

ol Systems Engineering, International Adaptation, 8th Edition by Nise

Typology: Exams

2025/2026

Available from 02/26/2026

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Copyrightk©

k

2011kbykJohnkWileyk&kSons,kInc.



O

k

N

k

E

Introduction

ANSWERSkTOkREVIEWkQUESTIONS

1.

Guidedkmissiles,kautomatickgainkcontrolkinkradiokreceivers,ksatellitektrackingkantenna

2.

Yesk-kpowerkgain,kremotekcontrol,kparameterkconversion;kNok-kExpense,kcomplexity

3.

Motor,klowkpasskfilter,kinertiaksupportedkbetweenktwokbearings

4.

Closed-

loopksystemskcompensatekforkdisturbanceskbykmeasuringkthekresponse,kcomparingkitktokthekinputk

responsek(thekdesiredkoutput),kandkthenkcorrectingkthekoutputkresponse.

5.

Underkthekconditionkthatkthekfeedbackkelementkiskotherkthankunity

6.

Actuatingksignal

7.

Multipleksubsystemskcanktimeksharekthekcontroller.kAnykadjustmentsktokthekcontrollerkcankbe

kimplementedkwithksimplyksoftwarekchanges.

8.

Stability,ktransientkresponse,kandksteady-statekerror

9.

Steady-state,ktransient

10.

Itkfollowskakgrowingktransientkresponsekuntilktheksteady-

statekresponsekisknoklongerkvisible.kTheksystemkwillkeitherkdestroykitself,kreachkankequilibriumkstate

kbecausekofksaturationkinkdrivingkamplifiers,korkhitklimitkstops.

11.

Naturalkresponse

12.

Determinekthektransientkresponsekperformancekofktheksystem.

13.

Determineksystemkparametersktokmeetkthektransientkresponsekspecificationskforktheksystem.

14.

True

15.

Transferkfunction,kstate-space,kdifferentialkequations

16.

Transferkfunctionk-kthekLaplacektransformkofkthekdifferentialkequation

State-spacek-krepresentationkofkanknthkorderkdifferentialkequationkasknksimultaneouskfirst-

orderkdifferentialkequations

Differentialkequationk-kModelingkaksystemkwithkitskdifferentialkequation

SOLUTIONSkTOkPROBLEMS

50kvolts

1.

Fivekturnskyieldsk50kv.kThereforekKk=

5kxk2

k

r

ad

Discover Exams of Systems Engineering Rhodes University

Partial preview of the text

Download ol Systems Engineering, International Adaptation, 8th Edition by Nise and more Exams Systems Engineering in PDF only on Docsity!

O k N k E

Introduction

ANSWERS k TO k REVIEW k QUESTIONS

1. Guidedkmissiles,kautomatickgainkcontrolkinkradiokreceivers,ksatellitektrackingkantenna

2. Yesk-kpowerkgain,kremotekcontrol,kparameterkconversion;kNok-kExpense,kcomplexity

3. Motor,klowkpasskfilter,kinertiaksupportedkbetweenktwokbearings

4. Closed-

loopksystemskcompensatekforkdisturbanceskbykmeasuringkthekresponse,kcomparingkitktokthekinputk

responsek(thekdesiredkoutput),kandkthenkcorrectingkthekoutputkresponse.

5. Underkthekconditionkthatkthekfeedbackkelementkiskotherkthankunity

6. Actuatingksignal

7. Multipleksubsystemskcanktimeksharekthekcontroller.kAnykadjustmentsktokthekcontrollerkcankbe

kimplementedkwithksimplyksoftwarekchanges.

8. Stability,ktransientkresponse,kandksteady-statekerror

9. Steady-state,ktransient

10. Itkfollowskakgrowingktransientkresponsekuntilktheksteady-

statekresponsekisknoklongerkvisible.kTheksystemkwillkeitherkdestroykitself,kreachkankequilibriumkstate

kbecausekofksaturationkinkdrivingkamplifiers,korkhitklimitkstops.

11. Naturalkresponse

12. Determinekthektransientkresponsekperformancekofktheksystem.

13. Determineksystemkparametersktokmeetkthektransientkresponsekspecificationskforktheksystem.

14. True

15. Transferkfunction,kstate-space,kdifferentialkequations

16. Transferkfunctionk-kthekLaplacektransformkofkthekdifferentialkequation

State-spacek-krepresentationkofkanknthkorderkdifferentialkequationkasknksimultaneouskfirst-

orderkdifferentialkequations

Differentialkequationk-kModelingkaksystemkwithkitskdifferentialkequation

SOLUTIONS k TO k PROBLEMS

50 kvolts

1. Five k turns k yields k 50 k v. k Therefore k K k =

5 kxk 2 k r

ad

= k 1.

1 - 2 k k Chapterk1:k k Introduction

Amplifierkand Heater

Thermostat k valves

controls

Dancerk dynamics Dancer positionksen sor transducer Motorka ndkdrive Amplifier system

Desiredk

temperature

Temperature

k difference

Voltagek

difference

Fuelk flo

w

Actualk t

emperature

k+

Desired

k rollk

angle

Input

k voltag

e

Error

k voltag

e

Aileron

k positio

n

Roll

k rat

e

Rollk a

ngle

Desiredk speed Inputk voltage

Speed kErrorkv oltage Actual kspee d Voltagekpr oportional tokactualkspeed

1 - 3 k SolutionsktokProblems

Amplifier

Motork

andk dr

ivek sy

stem

power

Transducer

Sensork&k

transducer

Transducer

Desired

Input

k voltag

e

Power

k Error

k voltag

e

Rodk

position

Actual

k pow

er

Voltagek pr

oportional

tokactualkpower

Desired Population

Desired

k stude

nt

Actual

Graduatingk

and

drop-

outk rate

Netkrate

Actualk stude

nt

studentk popula

tion +

error rate^ student^ -

ratek k +

ofkinflux population

Desired Voltagek proportional tokdesired volume Volumek error Voltagekrepresentin g actualkvolume (^) Actual volume volume +

Effective volume + Voltagekpro portionalktok speed Transducer

Speed

Administration Integrate

Volume kcontrolkcircuit Radio

Admissions

Reactor

1 - 5 k SolutionsktokProblems

Desiredk + Controllerk

Desired

k force

Actual

Desired

k positio

n

Force Depth

Commandedkb loodkpressure (^) + Isofluranekco ncentration bloodkpr essure

Vaporizer Patient

1 - 6 k k Chapterk1:k k Introduction

Retinak+kOptical

Internalkeye

kmuscles

Desired^ Brain

k Light

a.

Nervousk

systemk e

lectricalk

impulses

Retina’s

k Light

Intensity Intensity

b.

Desiredk Lig

htk Intensity

Nervousk

systemk e

lectricalk

impulses

Retina’sk Lig

htk Intensity

External

k Light

Ifk thek narrowk lightk beamk isk modulatedk sinusoidallyk thek pupil’sk diameterk willk alsok varyksinusoidallyk(withkakdelaykseekpartkc)kinkproblem) c. k Ifkthekpupilkrespondedkwithknoktimekdelaykthekpupilkwouldkcontractkonlyktokthekpointkw herekaksmallkamountkofklightkgoeskin.kThenkthekpupilkwouldkstopkcontractingkandkwoul dkremainkwithkakfixedkdiameter.

Retinak+kOpticalkNe

rves

Internalkeye

kmuscles

Brain

1 - 8 k k Chapterk1:k k Introduction

24 solutionkiski(t)k =k Ae-(R/L)tk+k k 1 k

.kSolvingkforkthekarbitrarykconstants,ki(0)k=kAk+k

k 1

=k 0.kThus,kAk =

R 1 k 1

.kThekfinalksolutionkiski(t)k= R

--k

k 1 k e-(R/L)tk=k k 1 k (1kk e (k^ R /k^ L ) t k). R R R R

c.

18. (^) a. Writingkthekloopkequation,k Ri kk L k^ kdi k k^ k^1 k^ k idt kk v (^) (0)kk v ( t ) dt C k^ ^ C d k^2 i k  di b. Differentiatingkandksubstitutingkvalues, 2 k^25 i kk^0 dt k^2 dt

Writingkthekcharacteristickequationkandkfactoring,

M k^2 kk 2 M k k 25 kk( M k  1  24 i )( M k  1  24 i )k.

Thekgeneralkformkofktheksolutionkandkitskderivativekis

i kk Ae  t kcos(k 24 t )kk Be  t ksin(k 24 t ) di k k(k A kk dt 24 B ) e  t kcos(k k 24 t )kk(k k 24 k A kk B ) e  t ksin(k k 24 t ) Usingk i (0)kk0;k di k (0)kk vL k(0)k k 1 k k 1 dt L L

i k 0 k =k A k = 0

di k (0)kkk A kk dt 24 B k= 1 Thus,k A kk 0 kandk B k. 24

Theksolutionkis

i k 1 e  t ksin(k 24 t )

1 - 9 k SolutionsktokProblems

c.

a. Assumekakparticularksolutionkof

Substitutekintokthekdifferentialkequationkandkobtain

Equatingklikekcoefficients,

Fromkwhich,kCk=k

35 k k

andkDk=k

10 k

Thekcharacteristickpolynomialkis

Thus,kthektotalksolutionkis

Solvingkforkthekarbitrarykconstants,kx(0)k=kAk+ 53 k =k0.kTherefore,kAk=k-k 53 k .kThekfinalksolutionkis

b. Assumekakparticularksolutionkof

1 - 11 k SolutionsktokProblems

dt

dxk =k 3 kBk- 4 kC k cos 3 kt k - k 4 kBk+k 3 kC k sin 3 kt k e-^4 k^ t

Solvingkforkthekarbitrarykconstants,kx(0)k =k3Bk–k4Ck=k0.kTherefore,kBk=k-8/15.kThekfinalksolutionkis

x ( t )kk 2 k k e ^4 t k kk^8 k sin(3 t )kk 2 k cos(3 t k) 5 k 15 5 

a. Assumekakparticularksolutionkof

Substitutekintokthekdifferentialkequationkandkobtain

Equatingklikekcoefficients,

Fromkwhich,kCk=k-k

1 k k

andkDk=k-k

k 1 kk

Thekcharacteristickpolynomialkis

Thus,kthektotalksolutionkis

Solvingkforkthekarbitrarykconstants,kx(0)k=kAk-k

1 k

=k2.kTherefore,kAk=

11

.kAlso,kthekderivativekofkthe

5

solutionkis

Solvingkforkthekarbitrarykconstants,kx(0)k =k-kAk +kBk-k0.2k=k-3.kTherefore,kBk= k 3 k

.kThekfinalksolution

5

is

x ( t )kkk 1 k cos(2 t )kk k 1 k sin(2 t )kk e  t k k^11 cos( t )kk 3 k sin( t ) 5 10 k^5 5 

b. Assumekakparticularksolutionkof

xpk=kCe-2tk+kDtk+kE

Substitutekintokthekdifferentialkequationkandkobtain

kdx kdt

1 - 12 k k Chapterk1:k k Introduction

Equatingklikekcoefficients,kCk=k5,kDk=k1,kandk2Dk+kEk=k0.kFr

omkwhich,kCk=k5,kDk=k1,kandkEk=k-k2.

Thekcharacteristickpolynomialkis

Thus,kthektotalksolutionkis

Solvingkforkthekarbitrarykconstants,kx(0)k=kAk+k 5 k-k 2 k=k 2 kTherefore,kAk=k-1.kAlso,k thekderivativekofkthe

solutionkis

dx k k(k A kk B ) e k^ t k k Bte  t k k 10 e ^2 t k k 1 dt

ol Systems Engineering, International Adaptation, 8th Edition by Nise, Exams of Systems Engineering

Related documents

Partial preview of the text

Download ol Systems Engineering, International Adaptation, 8th Edition by Nise and more Exams Systems Engineering in PDF only on Docsity!

O k N k E

Introduction

ANSWERS k TO k REVIEW k QUESTIONS

1. Guidedkmissiles,kautomatickgainkcontrolkinkradiokreceivers,ksatellitektrackingkantenna

2. Yesk-kpowerkgain,kremotekcontrol,kparameterkconversion;kNok-kExpense,kcomplexity

3. Motor,klowkpasskfilter,kinertiaksupportedkbetweenktwokbearings

4. Closed-

loopksystemskcompensatekforkdisturbanceskbykmeasuringkthekresponse,kcomparingkitktokthekinputk

responsek(thekdesiredkoutput),kandkthenkcorrectingkthekoutputkresponse.

5. Underkthekconditionkthatkthekfeedbackkelementkiskotherkthankunity

6. Actuatingksignal

7. Multipleksubsystemskcanktimeksharekthekcontroller.kAnykadjustmentsktokthekcontrollerkcankbe

kimplementedkwithksimplyksoftwarekchanges.

8. Stability,ktransientkresponse,kandksteady-statekerror

9. Steady-state,ktransient

10. Itkfollowskakgrowingktransientkresponsekuntilktheksteady-

statekresponsekisknoklongerkvisible.kTheksystemkwillkeitherkdestroykitself,kreachkankequilibriumkstate

kbecausekofksaturationkinkdrivingkamplifiers,korkhitklimitkstops.

11. Naturalkresponse

12. Determinekthektransientkresponsekperformancekofktheksystem.

13. Determineksystemkparametersktokmeetkthektransientkresponsekspecificationskforktheksystem.

14. True

15. Transferkfunction,kstate-space,kdifferentialkequations

16. Transferkfunctionk-kthekLaplacektransformkofkthekdifferentialkequation

State-spacek-krepresentationkofkanknthkorderkdifferentialkequationkasknksimultaneouskfirst-

orderkdifferentialkequations

Differentialkequationk-kModelingkaksystemkwithkitskdifferentialkequation

SOLUTIONS k TO k PROBLEMS

50 kvolts

1. Five k turns k yields k 50 k v. k Therefore k K k =

5 kxk 2 k r

ad

1 - 2 k k Chapterk1:k k Introduction

Amplifierkand Heater

Thermostat k valves

controls

Desiredk

temperature

Temperature

k difference

Voltagek

difference

Fuelk flo

w

Actualk t

emperature

Desired

k rollk

angle

Input

k voltag

e

Error

k voltag

e

Aileron

k positio

n

Roll

k rat

e

Rollk a

ngle

1 - 3 k SolutionsktokProblems

Amplifier

Motork

andk dr

ivek sy

stem

power

Transducer

Sensork&k

transducer

Desired

Input

k voltag