《自动控制原理》胡寿松+习题答案(附带例题课件)

:6456864412345167123341234567123452678120180300456BodeNyquist12345Bode67123341MATLABMATLAB22MATLAB23MATLABNyquistBode24MATLAB25030%470%20%10%2001200565MATLABMATLABMATLAB6MATLABNyquistBodeMATLAB200771141-21-62222-4(a)2-5(b)3224322-2(1)(2)2-82-95322-62-10(c)2-11(a)6422-12(b)2-13(a)2-14(c)74285210523-211623-312623-413723-73-111472158116831804-217920°4-124-13818924-44-64-84-1519102201025-4(2)(4)211125-3(4)5-5(2)(3)221125-10231225-75-9241222513226132271426-1281426-22915230152311627-2321627-77-89121-3123451-2H10zzzControllerzzzzzz1112224-61-6∫+=ttdxqty010)(5)0(3)(ττ0)(5)0(3)(22+=ttxqty0)(5)0(3)(23+=ttxqty0)(lg)0(3)(24+=ttxqty13)]0(3[q])(5[0∫tdxττ)]0(3[q)](5[tx141532122-4a2-5b2.12.1.112342.1.2/2.22.2.1123ABC4562.2.2116dt)t(duC)t(ic=∫=dt)t(iC1)t(uc2dtdiLtL=)(uL∫=dttuLtiLL)(1)(3∫==vdtkkyFdtdFk1v=kFyv4dtdyffvF==fFdtdffTθω==ωθT2.2.31--)t(F)t(y[]m1Ftyt)t(Fk)t(Ff2m322idtydmmaF==∑22fkdtydm)t(F)t(F-F(t)=−4)t(Ffdtdyf)t(F),t(ky)t(Ffk==5)t(Fk)t(Ff22dtydmdtdyfky(t)-F(t)=−6F(t)ky(t)dtdyfdtydm22=++kfT,kmTf2m==)t(Fk1ydtdykfdtydkm22=++)t(Fk1)t(y=k12R-L-C)t(ur)t(uc[]1)t(ur)t(uc)t(i)t(Ff)t(FkFm1723rcuuRidtdiL=++4)t(i)t(ucdtduCic=5)t(i)t(ircc2c2uudtduRCdtudLC=++3auaiaiDM1auωLM2CIf=3aaaaaauEiRdtdiL=++LD22MMdtdJdtdJ−==ωθ4ωeakE=ekamDikM=mk5DaMEaiLMLmeaLmeaaemea22meaMkkRdtdMkkLuk1dtdkkJRdtdkkJL−−=++ωωωmeamkkJRT=aaaRLT=LmLmaaem22maMJTdtdMJTTuk1dtdTdtdTT−−=++ωωωLMaem22mauk1dtdTdtdTT=++ωωω2.2.4-1-2-1-2012-1012-1-1-2-1-2nnnmmmnnmnnnmmmdcdcdcdcdrdrdrdraaaaacbbbbbdtdtdtdtdtdtdtdt+++++=+++++mr1iajb2mn1842342-2122-82-92.32.3.1AxyA)y,x(A00)y,x(00x∆y∆)y,x(00)y,x(∆∆)y,x(00x∆“”y∆2.3.21)x(fy=)y,x(00xKx)x(fy0∆=∆′=∆)x(fK0′=)y,x(00αtg)x(fK0=′=)x(fy=xKx)x(fy0∆=∆′=∆θsiny=00=θπθ=0θsiny=00=θπθ=0100=θ0siny0000===θθ)0,0()y,(00=θθθθθθθ∆=∆=∆′=∆=000|cos)(yyy∆yθ∆θθy)0,0()y,(00=θθ∆y∆θ=y2πθ=00siny000===πθθ)0,()y,(00πθ=θθθθθπθ∆−=∆=∆′=∆=0|cos)(yy019θ−=y2n)x,,x,x(fyn21=n21x,,x,x)x,,x,x(fyn02010=1122nnyKxKxKx∆=∆+∆++∆0002211XnnXXxfKxfKxfK∂∂=∂∂=∂∂=n=22211xKxKy∆+∆=∆202101202101xxxx22xxxx11====∂∂=∂∂=xfKxfK1234y),x(∆∆xyy,x∆∆2.42.4.1LaplacesLaplaceC(s)c(t)2.4.2TransferFunction1LaplaceLaplace)s(C)s(R-1-2-1-2012-1012-1-1-2-1-2nnnmmmnnmnnnmmmdcdcdcdcdrdrdrdraaaaacbbbbbdtdtdtdtdtdtdtdt+++++=+++++mrLaplaceLaplaceLaplaceLaplace)t(c)s(C)t(r)s(R)s(R)bsbsbs(b)s(C)asasas(am1-m1-m1m0n1-n1-n1n0++++=++++n1-n1-n1n0m1-m1-m1m0asasasabsbsbsb)s(R)s(CG(s)++++++++==RLCRsrtLaplaceLaplaceCsCSSCS20rcc2c2uudtduRCdtudLC=++Laplace)s(U)s(U)s(RCsU)s(ULCsrccc2=++1RCsLCs1)s(U)s(U)()s(U)s(1)URCs(LCs2rcrc2++==⇒=++sG)t(Fkyy)ff(ym21=+′++′′Laplacek)sff(ms1)s(F)s(Y)()s(F)s(k)Y)sff((ms212212+++==⇒=+++sG2123456dtdP=ssdtdP→=)s(R)t(r),s(C)t(c→→)s(G7)s(G)t(g)t(g)s(G↔)t(g)]t(g[L)s(G=8mnnmt-2tee1)t(c−+−=)2s)(1s(24sss11s12s1s1)]t(l[L)ee1(L)s(R)s(C)s(G2t2t++++=+++−=+−==−−tteets−−−−+==212)()](G[L)t(gδtteet−−−+==22)(dt)t(dc)t(gδ)2s)(1s(24ss1s12s21]2)(L[)]t(g[L)s(G22++++=+−++=−+==−−tteetδ21524631)s(N)s(Masasasabsbsbsb)s(R)s(CG(s)n1-n1-n1n0m1-m1-m1m0=++++++++==mn0)s(M=m21,z,,zz0)s(N=12,,,nppp2)ps()ps)(ps()zs()zs)((zs(KasasasabsbsbsbG(s)n21m21gn1-n1-n1n0m1-m1-m1m0−−−−−−=++++++++=00gabK=)1s2TsT)(1sT()1s2s)(1s(KasasasabsbsbsbG(s)222221222221n1-n1-n1n0m1-m1-m1m0++++++=++++++++=ξςτττnmabK=KgKmmi12mi1ggnn12njj1(1)z(z)(z)(z)KKK(p)(p)(p)(1)p==−−−−==−−−−∏∏3s“○”“×”)22ss)(3s()2s()s(G2++++=)j1s)(j1s)(3s()2s()s(G−+++++=41)s(Gn21ppptptptpneee2122iiijpωσ±=tcoseitiωσtsineitiωσmiptptptpeeeiii1mtt−miiijpωσ±=tcosettcosetcoseit1-mititiiiωωωσσσttsinettsinetsineit1-mititiiiωωωσσσt2●st●StS3“”“”“”4K2.51)t(Kr)t(c=K)s(G=2)()()(trtcdttdcT=+0011)(ωω+=+=sTssGT10=ωTT1−)()(tultr=()[(0)]tTctucue−=+−)0(ccRC323)()(trdttdcT=∫=tdttrTtc0)(1)(ssG1)(=0)(tr)(tc4dttdrTtc)()(=TssG=)(1)(+=TssG5)()()(2)(222trtcdttdcTdttcdT=++ξ222222222121121)(nnnssTTssTTssTsGωξωωξξ++=++=++=Tn1=ω10≤ξ6)()(τ−=trtcsesGτ−=)(sseτ−∞=s245272-62-10c2-11a2.71211)()()(21++==sGeΩsTsTTKsmamsUaaaKsEsUsG==)()()(2)()()(sUsUsETr−=TTKssUsG=Ω=)()()(33131RC2Laplace25Laplace⎪⎩⎪⎨⎧==−=⇒⎪⎪⎩⎪⎪⎨⎧==−=∫scsIsURsUsIsUsUsUdttiCtuRtutitututuRRRR)()()()()()()()(1)()()()()()(221221)1(1)()()(12+==RCssUsUsG2RCLaplace⎪⎪⎪⎩⎪⎪⎪⎨⎧=−==−=⇒⎪⎪=)(1)(dttitu⎪1C⎩∫222C⎪⎪1⎪⎨⎧−==−=∫222121111111211111111)()()()()()()()()()()]()([)()()()()()(sCsIsUsCsIsIsURsUsIsUsUsUdttitituRtutitututucRcRcRcR1]1)([1)()()(2122112221112++++==sCRCRCRsCRCRsUsUsG41series∏====niinsGsGsGsGsRsCsG121)()()()()()()(2parallel26∑==+++==niinsGsGsGsGsRsCsG121)()()()()()()(3Feedback()()()1()()()1()()()1()()BECsGsEsssRsGsHsRsGsHΦ==Φ==±+s5312423()(()()())()1()()()GsGsGsGsGsGsGsHs+∴=+6)()()(sRsCsG=27)()()()(121sGsGsEsC=2)()()(sHsCsB=3)()()()()()(sBsG210sHsGsGsE==4)]()()(1[()()()()(sHsGsGsGsGsRsCs2121c+==Φ5⎩Φ)(sN⎨+−==)]()()(1[)()()()()]()()21221sHsGsGsHsGsRsNsHsGE⎧+==Φ(1[1)()()(sGsRsEs60)(1)()()(1021=+=+sGsHsGsG123428727b2-122-13a2-14c2.8Mason146342312aaaa221261234“-”5216“”1x6x3223aa22a293∑=∆∆=nKKKPP11KPP2)(sGKfedfedcbcbaa)(1∆+−+−=∑∑∑LLLLLL1+−+−=∆K∆KK∆KPP∆41[]()(1djfkbifkbidjbcdefgmfdjbi)()bidjfkk−++++++−=∆=∆111=abcdefghP)()()(11108bidjfkdjfkbifkbidjbcdefgmfkdjbix−++++++−=∆=2abcdefghPx∆[])()(1773366337722662277663322HGHGHGHGHGHGHGHGHGHGHGHG+++++++−=∆77661432111HG