2.6闭环传递函数

2.6闭环系统的传递函数1、闭环系统的开环传递函数_H(s)G1(s)G2(s)R(s)C(s)+N(s)闭环控制系统的典型结构闭环系统的开环传递函数是指：反馈信号与偏差的拉氏变换之比，1212(s)G(s)G(s)H(s)(s)(s)H(s)(s)(s)G(s)H(s)(s)(s)(s)kEBCGGEEEE(s)B(s)2、闭环系统的闭环传递函数1)．给定信号R(s)作用闭环传递函数取扰动为零，N(s)=0，(s)=(s)121212KG(s)G(s)G(s)G(s)C(s)=R(s)1+G(s)G(s)H(s)1+G_B(s)H(s)G1(s)G2(s)R(s)E(s)C(s)12(s)G(s)(s)(s)1(s)kGCRG闭环系统传递函数：注意：负反馈分母去+，正反馈-2)．扰动信号N(s)作用的闭环传递函数G1(s)H(s)G2(s)N(s)C(s)令R(s)=0(s)=(s)22n12KG(s)G(s)C(s)=N(s)1+G(s)G(s)H(s)1+G系统闭环传递函数2G(s)(s)(s)1(s)nkCNG3）.给定信号作用下的误差传递函数_R(s)E(s)H(s)G2(s)G1(s)B(s)12(s)11(s)=(s)1(s)G(s)H(s)(s)eKERG1+G1(s)(s)1(s)kERG若单位反馈，H(s)=1，(s)(s)=(s)k1212KGG(s)G(s)C(s)=R(s)1+G(s)G(s)H(s)1+G1(s)=(s)eK1+G若已知单位反馈的闭环函数(s)(s)(s)=(s)kG1+(s)=1(s)e4)．扰动信号N(s)作用的误差传递函数+N(s)G1(s)G2(s)-H(s)E(s)误差函数：偏差信号与扰动信号之比。2(s)H(s)(s)(s)(s)1(s)enkGENG2(k)H(s)(s)(s)(s)(s)1(s)nenkGENNG系统总的输出C(s)为输入和误差同时作用下的结果。122n(s)G(s)G(s)(s)(s)R(s)(s)N(s)(s)(s)1(s)1(s)kkGCRNGG122(s)G(s)R(s)1G(s)N(s)1G和当(s)(s)(s)RCH表明一定条件下，输出只取决输入信号和反馈信号，不受扰动影响，较好抗干扰能力。系统总的输出E(s)为输入和误差同时作用下的结果。2en(k)H(s)1(s)(s)R(s)(s)N(s)(s)(s)1(s)1(s)ekkGERNGG闭环传递函数具有相同的分母[1+Gk(s)],因为具有相同的信号流图特征式，12(H)aLGG12k111+G(s)aLGGHk1+G(s)0称为闭环系统特征方程式注意：叠加原理求系统输出量C(s)和E(s)，先求各种情况下的C(s)和E(s)，然后叠加。例题1求C(s)/R1(s)，C(s)/R2(s)1bcde1a-f-g-h1lR2(s)R1(s)C(s)1bcde1a-f-g-h1R1(s)C(s)解：当R1(s)作用时，R2(s)=01234pbcdepadepbcpa，，，。1bcde1a-f-g-h1R1(s)C(s)a1234L=L+L+L+L=-(eg+cf+bcdeh+adeh)1234LegLcfLbcdehLadeh，，，。bcLLegcf11abcLLLegcfbcdefadehegcf12341,1,1,1egeg1(s))1(sCbcdeadeabcaegcfbcdehadehegcegbceRfgbcde1a-f-g-h1R2(s)C(s)l当R2(s)作用时，R1(s)=0123,,pleplehbcplehabcde1a-f-g-h11R2(s)C(s)1234,,,LegLcfLbcdehLadeh1231,1,1cf2(s)(1cfhahbc)(s)1cfegbcdehCaleRdehcefg