基本术语2.前向通路:1.节点:结构图中所有的引出点、比较点从输入到输出,并与任何一个节点相交不多于一次的通路.前向通路中各传递函数的乘积——前向通路增益二、梅逊
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3.回路——起点和终点在同一节点,且与其他节点相交不多于一次的闭合通路.4.不接触回路——相互间没有公共节点的回路回路中所有传递函数的乘积叫回路增益,用L
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示。Pk—从R(s)到C(s)的第k条前向通路传递函数梅逊公式介绍R-CC(s)R(s)=∑Pk△k△:△称为系统特征式△=其中:——所有单独回路增益之和∑Li∑LiLj∑LiLjLz△k称为第k条前向通路的余子式△k求法:去掉第k条前向通路后,用余下的图求△-∑Li+∑LiLj-∑LiLjLz+…1△k=1-∑La+∑LbLc-∑LdLeLf+…—所有两两互不接触回路增益乘积之和—所有三个互不接触回路增益乘积之和R(s)C(s)L1=–G1H1L2=–G3H3L3=–G1G2G3H3H1L4=–G4G3L5=–G1G2G3L1L2=(–G1H1)(–G3H3)=G1G3H1H3L1L4=(–G1H1)(–G4G3)=G1G3G4H1G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)H3(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G1(s)G2(s)G3(s)G1(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)G4(s)G3(s)梅逊公式例R-CH1(s)H3(s)G1(s)G2(s)G4(s)H1(s)H3(s)G1(s)G2(s)G3(s)P1=G1G2G3P2=G4G3△2=1+G1H1△1=1G1(s)G2(s)G3(s)G4(s)H(s)例:G1(s)G2(s)G3(s)G4(s)H(s)R(s)C(s)L1=-G1G2HL2=-G1G4HG1(s)G2(s)G3(s)G4(s)H(s)R(s)C(s)G1(s)G2(s)G3(s)G4(s)H(s)R(s)C(s)G1(s)G2(s)G3(s)G4(s)H(s)R(s)C(s)G1(s)G2(s)G3(s)G4(s)H(s)R(s)C(s)G1(s)G2(s)G3(s)G4(s)H(s)R(s)C(s)G1(s)G2(s)G3(s)G4(s)H(s)R(s)C(s)L2例系统的动态结构图如图所示,求闭环传递函数。G1G2G3H1G4H2___C(s)+R(s)解:系统有5个回路,各回路的传递函数为L1L1=–G1G2H1L2L2=–G2G3H2L3L3=–G1G2G3L4L4=–G1G4L5L5=–G4H2ΣLiLj=0ΣLiLjLz=0Δ=1+G1G2H1+G2G3H2+G1G2G3+G1G4+G4H2P1=G1G2G3Δ1=1P2=G1G4Δ2=1将△、Pk、△k代入梅逊公式得传递函数:G1G2G3+G1G41+G1G2H1+G2G3H2+G1G2G3+G1G4+G4H2=第四节动态结构图L1L2L3H1_+++G1+C(s)R(s)G3G2例求系统的闭环传递函数。解:L1=G3H1L2=–G1H1L3=–G1G2P1=G1G2Δ1=1–G3H1Δ=1+G1G2+G1H1–G3H1R(s)C(s)1+G1G2+G1H1–G3H1G1G2(1–G3H1)=第四节动态结构图ehfgR(s)abcdC(s)C(s)R(s)=1––––++afbgchefhgahfced(1g)–bdabc练习