1、二章自动控制系统的数学模型2022-11-29mFkxmkxdtdxfFdtdxfkxFdxmtd22Fkxdtdxfdxmtd22 弹簧弹簧-质量质量-阻尼器系统阻尼器系统2022-11-29MJkftddtdMdJ1122MdtddJkftd1122 机械转动系统机械转动系统 2022-11-29+-eaia负载LaRaMc+-（1）电枢回路ueRiiLaaaaaadtd（2）反电势Ceea（3）电磁力矩iCamM icMamdc（4）轴上动力学方程McMdtdJ)(22MMTKKTtdTTccamummcdtdUadtddRLTaaa，CCRTmeamJ，CKeu1，JTKmm 电枢控制
2、的他励直流电动机电枢控制的他励直流电动机2022-11-29yyy0y0ABx0 xx0)()()()()(000000 xyxxxdtdyyxdtdyfxfyxfyxxxx 2022-11-29功率功率放大放大运放运放I运放运放II反馈联接反馈联接测速发电机测速发电机减速器减速器负载负载uru1u2Mcuf+-+-转速自动控制系统原理图转速自动控制系统原理图ua2022-11-29X运算放大器I运算放大器II功率放大器电动机测速电机+-urueu1u2uaMcuf2022-11-29 ；uKuuKuefr111)()(1122uuKudtduKua23KuffMKKuuTcmrrmdtddt
3、dKdtd)()(0MKKKTcmmUrdtdUrKdtdt)()1()(00KKKKKu321KKKKKK054321MKuKTcmaumdtd（忽略电枢电阻，电抗）忽略电枢电阻，电抗）2022-11-29i(t)1111)()()()()(0)()()(TsRCssssssRCsttUdttdRCuuuuuuuioiooioo初始条件下在11)()()(,11)(TssGssTssGuuio则令：)(suiG(s)(suo+uo(t)ui(t)-2022-11-29)()()()()()(01110111txdtxdtxtydtydtybtdbtdbatdatdammnmmmnnnnnn
4、y(t)-输出量 x(t)-输入量asasabsbsbnnnnmmmmsXsYsG011011)()()(2022-11-29ui(t)R1R2C2uO(t)CRTCRSTSUUGSCRSCRZZUUSCRZRZsssssioio212221221222211,1)()()(1)()(1比例比例积分控制器积分控制器PIPI控制器控制器2022-11-29ui(t)C1R2uO(t)R1CRRRCRRRZZUUGRZSCRSCRZKsKSSSSio11121112122211111,)1()1()()()(11比例比例微分控制器微分控制器PD控制器控制器2022-11-29ui(t)C1R2uO
5、(t)R1C2(a)yiy0 xf1f2k1k2(b)ab2022-11-292022-11-29 只适应线性定常系统；只适应线性定常系统；由系统（元件）的参数、结构决定，是系统的动态数学模型；由系统（元件）的参数、结构决定，是系统的动态数学模型；n m,n n m,n 为系统的阶数为系统的阶数 单输入单输入单输出单输出 传递函数写法：传递函数写法：012201asasabsb)s(G有理分式有理分式:)as)(as()bs()s(G010零零极点形式极点形式:)1sT)(1sT(1s)s(G21时间常数形式：时间常数形式：2022-11-29 常数ksXsYsGtkxty)()()(),()
6、(TssksXsYsGdttxkty1)()()(,)()(2022-11-29 11)()()()()()(TssXsYsGtxtydttdyTT:时间常数)(tx)(ty)(tx1632.00T1斜率Ttety1)(Ttetyttx1)()(1)(时，当tTetYTsssTssXsGsY11)(111111)()()(过程：2022-11-29)(tx)(ty)(tx)(ty2022-11-290)()()(22)(22ttxtydttdyTdttydT，,12221)(TSSTsG2222)(,1nSnSnsGTn则令的相点是一对共轭复数时)(,10sG)(2222)(sXnnsnsYs
7、nnsnsYssX12222)(,1)(则当2022-11-29)1gtt1sin(1e1)t(y212n2tny(t)y(t)x(t)txxnj21jS平面2022-11-29sT1TsTs)s(G1s2sK)s(G1sK)s(GKS)s(G)t(xdt)t(dx2td)t(xdK)t(y)t(xdt)t(dxK)t(ydt)t(dxK)t(y1222221sT1实现微分环节纯微分环节一阶微分环节二阶微分环节2022-11-29 时滞环节，滞后环节，时延环节时滞环节，滞后环节，时延环节)t(x)t(ye)s(X)s(Y)s(Gsx(t)tty(t)2022-11-29G(s)C(s)R(s)
8、R(s)R(s)-B(s)B(s)+-2022-11-29 步骤步骤:典型环节表示系统中的具体元件典型环节表示系统中的具体元件 按信号传递顺序连接各典型环节按信号传递顺序连接各典型环节,从而构成整个系统结构图从而构成整个系统结构图2022-11-29K1K2(s+1)K3-Km/（TmS+1）Ku/（TmS+1）运算放大器运算放大器运算放大器运算放大器功率放大器功率放大器电动机电动机测速电动机测速电动机Ur+-UfUeU1U1U2U2UaMcUaUf+Kf2022-11-29K1K2(s+1)K3Ku/（Tms+1）Ur(s)Ue(s)U1(s)U2(s)Ua(s)-Mc(s)Uf(s)(s
9、s)+-+Kf-Km/（Tms+1）2022-11-29 )s(G)s(G21)s(Xc)s(Xr)s(G1)s(G2)s(Xr)s(Xc)s(X1)s(G)s(G)s(X)s(X)s(X)s(X)s(X)s(X)s(G)s(G)s(X)s(X),s(G)s(X)s(X),s(G)s(X)s(X211cr1rcrc21c1r1则：又2022-11-29)s(G1)s(G2)s(Xr)s(X1)s(X2+)s(Xc)s(G)s(G21)s(Xr)s(Xc)()()()()()()()()()()(),()()(),()()(2121212111ssssssssGsXcssssssssGGXXXX
10、XXXGXXGXXrrccr则：又 2022-11-29)s(G)s(H)s(XrB(s)+-E(s)s(Yc)s(H)s(G1)s(G)s(Xr)s(Yc)s(Y)s(H)s(B)s(B)s(X)s(G)s(Ycrc)s(X)s(G)s(Y)s(H)s(G)s(Y)s(H)s(X)s(G)s(Yrccrc)()(1)()()(sHsGsGssXYrc 2022-11-29+-)s(GYX1X2)s(G)s(GX1X2Y)s(X)s(X)s(G)s(Y21)s(X)s(G)s(X)s(G)s(Y21)s(GX1X2Y+-)s(GYX1X2)s(G1XX)s(G)s(Y21X)s(G1X)s(G
11、)s(Y21 +-+-2022-11-29G(s)YX1X1G(s)s(G1YX1G(s)YYG(s)YX1G(s)Y 2022-11-29)s(G1)s(G4)s(G2)s(G3)s(H)s(C)s(R+-)s(G1)s(G4)s(G2)s(G3)s(H)s(C)s(R+-+)s(G22022-11-29)s(G1)s(G4)s(G2)s(G3)s(H)s(G2)s(C)s(R+-+GGG421HGG1G323)s(C)s(RHGG1GGGGG3243321)s(C)s(R2022-11-29)s(G1)s(G4)s(G2)s(G3)s(H)s(C)s(R+-)s(G1)s(G4)s(G2)
12、s(G3)s(H)s(C)s(R+-+)s(G22022-11-29)s(G1)s(G4)s(G2)s(G3)s(H)s(G2)s(C)s(R+-+GGG421HGG1G323)s(C)s(RHGG1GGGGG3243321)s(C)s(R2022-11-29G1G3G2G4H2H3H1)s(R)s(C+-G1G3G2G4H2H3H1)s(R)s(C+-G142022-11-29G1GG43G2H3H1)s(R)s(C+-GH42HGGGGHGGHGG1GGGG)s(R)s(C1432134323243212022-11-29)s(R+-R11R12)s(C1C2s1C1s2022-11-29
13、2022-11-29)()()()()(21sHsGsGsRsB表示)(sGkR(s)G2(S)+)(1sGH(S)N(S)+B(S)E(S)C(S)2022-11-29)()()(1)()()()(2121SHSGSGSGSGSRSC)()()(1)()()(212sHsGsGsGsNsC)()()(1)()()()()(1)()()()(2122121sHsGsGsNsGsHsGsGsRsGsGsC2022-11-29XYGXYG。2022-11-292022-11-29NREPQCG1G2-H1 同结构图2022-11-29n1kkkP*1)s(GfedcbaLLLLLL1n P k aLcbLLuedLLLk2022-11-29)(sR)(1sG)(2sG)(3sG)(4sG32111GGGP)(sC)(sH不存在不接触的回路不存在不接触的回路HGGGGGGGPPsRsCsG324332122111)(1)()()(前向通路前向通路3421,2GGPn1HGGL3211)(13回路回路HGGL3212HGGL3211)(141,12152022-11-292022-11-29)t(GL)s(G)s(GL)t(g1当，输入)t(g)t(C),t()t(X例例:).s(G,e4)t(g2t求1s28s4e4L)s(G212t2022-11-29
