1、数学模型数学模型 图图2-1 R-L-C电路dtdiLidtc1iRrcuudtdiLiRidtcuc1rucudtcduRCdtcudLC22（2-1）图图2-1 R-L-C电路图图2-2 R-C滤波网络ruRidtiiC11211)(1dtiiCRidtiC)(112112222cudtiC2211i2ircccuudtduCRCRCRtdudCCRR)(212211222121（2-2）例例2-3 )(tkydttdyf)(22)(dttydm22)()()()(dttydmdttdyftkytF)()()()(22tFtkydttydmdttdyf0)()(sFdtetfst01)(d
2、tstetfL0,10,0)(tttf01tstes0)(1stdessts10)(dteetfLstatatetf)(0)(dtetas0)(1ttaseasas 10)(dttetfLstdteseststtst00101dtesst21s0)(1stetds2)(ttf02)(dtettfLst02)(1stedtsdtetseststtst00221dttesst0232212sssttf0sin)(00sin)(dttetfLst00000cossindtteseststtstsin2200cos20sin0000tLsttsteststest 02)cossin(sin221000
3、00tstesttstLs20200sinstL0)(dtetfst00)(1)(1dtedttdfsetfssttst0)(1)0(1dtedttdfsfsst0)()(dtetfsFst0)()(dtedttdfdttdfLst)0()()(fssFdttdfL)()(ssFdttdfL001ttdttfdttfdttftf)()()()()()(tftfdtd1)()()(sFftfsL011ssFtfL)()(1nnnnmmmmasasasabsbsbsbsG11101110)(nnnnasasasasQ1110)().()().()(srxxqpxxbxaxb220axAaxAaxA
4、sG .)()()(121bxBbxBbxB .)()(121qpxxNxMqpxxNxMqpxxNxM21222211 .)()(srxxSxRsrxxSxRsrxxSxR21222211.)()(6532xxx)(323xxx32xBxA)()(233xBxAx)()(BAxBAx2333231)(BABA65BA6532xxx)(323xxx32xBxA)()(233xBxAxdtduCiccruRiurccudtduRCu)(sUc)(sRCsUc)(sUr11)()()(RCssUrsUcsG)()()()()()()()(111011110trbdttdrbdttrdbdttrdb
5、tcadttdcadttcdadttcdammmmmmnnnnnn因为控制理论着重分析系统的结构、参数与系统因为控制理论着重分析系统的结构、参数与系统的动态性能之间的关系，所以，为简化分析，设的动态性能之间的关系，所以，为简化分析，设系统的初始条件为零。系统的初始条件为零。)()()()()()()()(11101110sRbssRbsRsbsRsbsCassCasCsasCsammmmnnnn在零初始条件下，对上式取拉普拉斯变换得在零初始条件下，对上式取拉普拉斯变换得)()()()(11101110sRbsbsbsbsCasasasammmmnnnnnnnnmmmmasasasabsbsbs
6、bsRsC11101110)()(nnnnmmmmasasasabsbsbsbsG11101110)(01110nnnnasasasarccudtduRCu11)()()(RCssUrsUcsG01 RCsRCs1dtduCiccruRiudtdudtdiRdtducrCidtdiRdtdur)(1)()(sICsRsIssUr01RCs1)()(RCsCssUrsI0s R-L-C电路rcccuudtduRCdtudLC22)()()()(2sUrUsRCsUcsUcLCsSC11)()()(2RCsLCssUrsUcsG012 RCsLCs)()()()(22tFtkydttdyfdtty
7、dm)()()()(2sFskYsfsYsYmskfsmssFsYsG21)()()(02kfsms11)()()(2RCsLCssUrsUcsGkfsmssFsYsG21)()()(niimjjsTsTKsG1111)(niimjjpszsKsG11)()()(KKsRsCsG)()()(1TsKsRsCsG)()()()()()(sGsRsC11TsKs)/()(TssKsC111)1()(/TtceKtx111TsBsATsKssC)()()(11TssBsTsAKTBKAsKsRsCsG)()()(4）微分环节）微分环节sTsRsCsGc)()()(rcccuudtduCRdtudLC
8、22112sTsTTsRsCsGCCL)()()(22222211111nnnCLLCLssLCsLRsLCTTsTsTTsG /)(角频率振荡环节的自然振荡LCn1 振荡环节的阻尼比。LCR21)(txxrcsKesRsCsG)()()(：0()fZUoG sUiZ RsUsUsICr)()()()()(sICssUC1111RSUsUsICr)()()(212RSUsUsICC)()()(sCSIsIsUC1211)()()()()(SIsCsUC221)()()(sRsGsU11)()()(sUsGsU122)()()(sUsGsC23)()()()()(sRsGsGsGsC321)()
9、()()()()(sGsGsGsRsCsG321)()()()(sCsCsCsC321)()()()()()(sRsGsRsGsRsG321)()()()(sRsGsGsG321)()()()()(sGsGsGsRsC321)()()(sEsGsC)()()(sBsRsE)()()(sCsHsB)()()()()(sHsGsGsRsC1)(1sG)(2sGRC)(1sG)(2sGRC)(1sGRC)(2sG)(1sG)(2sGRC)(sGRCY)(sGRCY)(sG序号 法则 原来的框图 等效的法则 4 相加点的 前移 5 引出点的 后移 6 引出点的 前移 7 化简反馈 回路)(sGRCY)
10、(sG)(1sGRCYRCR)(sG)(sGRR)(1sGRCC)(sG)(sGRC)(sGC)(1sG)(2sGRC)()(1)(211sGsGsGRC)()(sRsC343431HGGGGsG)(3434321HGGGGGsG)(42343432343432111GHHGGGGGHGGGGGsG)(2323434321HGGHGGGGG1121221122121sCRCRCRsCCRRsUsUrC)()()()()()()()(sHsGsGsEsB21)(sCR)(sER)(sCR)()()()()()()(sHsGsGsGsGsRsCR21211)()()()()(sHsGsGsRsER2111)()()()(sGsGsEsCRR21)()()()()()()(sHsGsGsGsGsRsCR21211)()()()()()()()()(sHsGsGsGsGsRsGsGsER2121211)(sCD)(sCD)()()(1)()()(212sHsGsGsGsDsCD)()()()()()()(sHsGsGsHsGsDsED2121)()()()()()()(sHsGsGsHsGsDsED2121
