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1、SolutionstoSkill-AssessmentExercisesToAccompanyControlSystemsEngineeringth4EditionByNormanS.NiseJohnWiley&SonsCopyright©2004byJohnWiley&Sons,Inc.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyfromorbyanymeans,electronic,mechanical,
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SolutionstoSkill-AssessmentExercisesChapter22.1.1TheLaplacetransformoftisusingTable2.1,Item3.UsingTable2.2,Item4,2s1F(s)=.2(s+5)2.2.ExpandingF(s)bypartialfractionsyields:ABCDF(s)=+++2ss+2(s+3)(s+3)where,105101010A==B==-5C==,and()ss++23()29
5、2s(s+2)3S®0s(s+3)S®-2S®-32dF(s)40D=(s+3)=dss®-39TakingtheinverseLaplacetransformyields,5-2t10-3t40-3tf(t)=-5e+te+e9392.3.TakingtheLaplacetransformofthedifferentialequationassumingzeroinitialconditionsyields:322sC(s)+3sC(s)+7sC(s)+5C(s)=sR(s)+4sR(s)+3R(s)Collectingterms,322(s+3s+7s+5
6、)C(s)=(s+4s+3)R(s)Thus,2SolutionstoSkill-AssessmentExercises2C(s)s+4s+3=32R(s)s+3s+7s+52.4.C(s)2s+1G(s)==2R(s)s+6s+2Crossmultiplyingyields,2dcdcdr+6+2c=2+r2dtdtdt2.5.1s1ABCC(s)=R(s)G(s)=*==++2s(s+4)(s+8)s(s+4)(s+8)s(s+4)(s+8)where111111A==B==-,andC==(s+4)(s+8)32s(s+8)16s(s+4)32S®0S®
7、-4S®-8Thus,11-4t1-8tc(t)=-e+e3216322.6.MeshAnalysisTransformingthenetworkyields,Now,writingthemeshequations,Chapter23(s+1)I(s)-sI(s)-I(s)=V(s)123-sI(s)+(2s+1)I(s)-I(s)=0123-I(s)-I(s)+(s+2)I(s)=0123SolvingthemeshequationsforI2(s),(s+1)V(s)-1-s0-12-10(s+2)(s+2s+1)V(s)I(s)==22(s+1)-s-1
8、s(s+5s+2)-s(2s+1)-1
