电网络课件-信号流图

1、信号流图概念：源点汇点X2X1X3a12a22a13a31a11a3333122213133132121111XaXaXaXXaXaXaXeg:信号流图的变换x1x2a1+a2+.+anx1x2a1a2anx1x3ax2bx1x2ab串联x1x2abbcx4x1x3ax2bcx4x1x3ax2bcx4abx1x2acx4bx1x2aa+bx1x2x1x2ax3bx4cdx1x2ax3bx4cd/bx1x2ax3bx4cd/c并联支路移动节点吸收x1x2ax3bcx1x3abbcx1x2ax3bdcx1x3abbcadcdx1x2x3abcx3x1ab1-cx1xpy2m1px2xmy1ynm2

2、mmn1n2nny2y1ynx1xpm1x2xmm2mmn1n2nn1-p1-p1-p1-p1-p1-peg:x3a1x1x5x2x4a2a4a7a3a6a5消x3消x4节点移动x1x4a3x2x5a1a2a4a7a6a1a5a1a5 +a4x5a1a2a3a6a3+a7x2x1a1a5 +a4x5a1a2a3a7a6a3x2x1H= a1a2a3 +(a4+ a1a5 )(a6a3+a7)x1x2x3x4x5x6H1H2-G2-G1-G3求增益x6/ x121212132211211HHGGHHGHGHGHHH求增益u/ x2ux1x3x2难Mason公式kkPT各支路增益之积条前向通道增益

3、第kPk:3211lll回路增益二重互不接触回路增益三重互不接触回路增益益条前向通道去掉后的增即将第条前向通道的余子式第kkk,:x1x2x3x4x5x6H1H2-G2-G1-G3求增益x6/ x121212132211211HHGGHHGHGHGHHH求增益x6/ x1x1x2x3x4x5x6H1H2-G2-G1-G3求增益x6/ x1bdgfhbfhdgdgabhabcdeH1)1 (x1x2x3x4x5x6bd-g-fhace电网络与信号流图eg:画出下图的信号流图对网络有：)(00000)()()()()()(00000000000000000000000000)()()()()()(

4、13322113332222111332211sUsCsUsIsUsIsUsIRsCsCRRsCsCRRsCsUsIsUsIsUsIS)(00000)()()()()()(00000000000000000000000000)()()()()()(13322113332222111332211sUsCsUsIsUsIsUsIRsCsCRRsCsCRRsCsUsIsUsIsUsIS1sC1sC2sC3sC2sC3sC1R1R2R2R3RSU1I2I3I3U2U1U0UI00RUIIUUUU000sCRsCR1100010000R1GR10001R1R1sCsC0100sCsL1sCsCsC000

5、0sCsCR1s7s11s187n4n3n2n12v2v2222222211111同一网络，变量选择不同，则信号流图不同。为了能快速选择一组独立而充分的流图变量：1 选树支电压和连支电流为变量：电压源支路树支，电流源支路连支受控电压源支路树支，受控电流源支路连支受控源的控制支路： 压控树支，流控连支2 写树支电压和连支电流的表达式（方程）：树支电压=f(连支电流),连支电流=g(树支电压)3以电源为起点，画信号流图eg:画信号流图)()(17sUsUs)(11)(123333IIsCIsCsU)()(5214444IIIRIRsU26)(rIsU树支电压连支电流6437111111)(UUUU

6、sLUsLsI643221)(UUURsI35)(gUsIoates流图Mason公式反映了系统的因果关系，特别使用于控制系统，但是，对于电网络中，网络的方程为u，不很方便。oates流图设方程为u，定义其对应的有向图为：u是输入节点，Xnxxx,21是非输入节点：0ija当时，从ijijaxx 有一条支路，增益为到当0ib时，从iibxu有一条支路，增益为到ux1x4x3-46x28-42106531-2-2-18eg:eg:SUsCsCUUUGGsCsCsCGsCsCsCGsCsCG01102132122221211111123SUsCsCUUUGGsCsCsCGsCsCsCGsCsCG0

7、1102132122221211111uSu1u2u311sC11sC1sC2sC2sCg11sCG 212sCsCG23sCgG1sC3310RUIss32154377577266566511111111111nnnUUUsLGRsCsCsLsCsCsLRRsLRRsLGeg:画出其Coates流图Coates流图增益公式电网络在复频域中的方程为u，设AdetjnjjkkjnjjkkbuXubX111 1即为了能直接从电网络中求增益，先介绍下面的概念1 冷图（Gc)：cold graph从Coates流图中去掉源节点及其所有流出支路后，得到的图。从Coates流图中去掉源节点及其所有流出支路

8、后，得到的图。2 1-因子：符合下列条件的冷图的子图叫1-因子：包含Gc的所有节点每个节点仅含一条入支路，一条出支路。3 1-因子增益：1-因子中各回路的增益之积。冷图为uSu1u2u311sC11sC1sC2sC2sCg11sCG 212sCsCG23sCgG1sCu1u2u31sC2sC2sCg11sCG 212sCsCG23sCgG1sC1-因子：u111sCG u2212sCsCGu323sCgGu2u32sC2sCu111sCG u1u2u31sC2sCgu1u21sC212sCsCGu323sCgG1sC单连接：若节点p和q满足：p节点只有一条出支路，q节点只有一条入支路，其余节点

9、有且只有一条出支路和一条入支路，则p和q支路称为单连接。单连接增益：单连接各支路的增益之积。eg：us到u3的单连接：uSu1u2u311sC1sC2sCuSu1u2u311sC2sC11sCG pbuXjnjjkk11单连接单连接的有向回路数因子因子回路数allnallnpA1111det11的单连接增益因子增益kxu 180046620210130280450104221xxxxeg:求X2ux1x4x3-46x28-42106531-2-2-18x1x4x3x2-42106531-2-2-18冷图1-因子：因子：x1x4x3x26538x1x4x3x2-42-2-1x1x4x3x2101-288x1x4x3x2-43-2x1x4x3x225-18x1x4x3x2106-2-18)2(43126) 1()2(610131) 1()2(81013390461