内容教程案例pitino

BasicAutomaticControl,prof.LucaFerrarini

POLITONG-SHANGHAI

BASICAUTOMATICCONTROLProf.LUCAFERRARINI

AcademicYear2008/09Teston27March2009

NAME(characters)

NAME(pinyin)

ITALIANNAMEMATRICULATIONNUMBER

SIGNATURE

Donotreadanybook,anynote,anydidacticmaterialduringtheexamination.

Beclearandconciseinyouranswers.

BasicAutomaticControl,prof.LucaFerrarini

POLITONG

,2009/03/27,POLITONG

page

2/4

EXERCISEA

Giventhetime-invariantdynamicsystemdescribedbythefollowingequations(p1,p2ep3arerealparameters):

x&

x&x&

y(t)x2(t)

(t)u(t)

u(t)

t)

Forwhichvaluesoftheparametersp1,p2ep3isthesystemasymptoticallystable?Motivateyouranswer.

Isthefirststatevariableobservablethroughtheoutput?

Forthesystemabove,considerthistimeonlythepartassociatedtothestatevariablesx2ex3.

Findtheexpressionofthetransferfunctionfromutoyfortheconsideredsubsystem.

Isthereanyvalueoftheparametersp1ep2forwhichthesystemdescribedbyG(s)isnotcompleycontrollableandobservable?Motivateyouranswer.

ForthetransferfunctionG(s)obtainedinthepoint2.1,considerthistimetheparametervaluesp1=3andp2=1.

Findthepoles,zeros,gainandtypeofthetransferfunction.

DrawtheasymptoticBodeplotsandpolarplotofthefrequencyresponseassociatedtothetransferfunction.Semilogchartsareprovidedatofthistext.

EXERCISEB

Givenatime-invariantlinearsystemwiththefrequencyresponseillustratedbelow:

Findthepoles,zeros,gainandtypeofthesystemtransferfunction.

Findtheexpressionofthesystemtransferfunction.

Drawthepolarplot(qualitative)ofthefrequencyresponseassociatedtothetransferfunctionobtainedinthepoint4.2.

Findastate-spacerepresentationforthetransferfunctionobtainedinthepoint4.2.

degrees

EXERCISEC

Considerthelinearsystemdescribedbythefollowingblockdiagram:

+

+

n(t)

G(s)

H(s)

F(s)

r(t) +

-

y(t)

where

F(s) ,G(s)Ts1and

H(s).

BodeDiagram-Phase

frequency

BodeDiagram-Magnitude

Ts1 s1

Findtheexpressionofthetransferfunctionfromthedisturbancentotheoutputyandfromthereferencesignalrtotheoutputy.

Studythestabilityoftheoverallsystemasafunctionofα,supposingthatμ>0,τ>0andT>0.

Calculatethefinalvalueofy(t)forn(t)=step(t)andr(t)=4step(t)asαvaries.Justifytheanswer.

Whichistheorderofthesystemfromr(t)toy(t)?Andtheonesystemfromn(t)to