1、题2-1 90.9*0.005*20=9.09(mm/MPa)3.5*9.09=31.8(mm)题2-2已知：求幅值误差。代入公式得幅值误差1幅值误差2幅值误差31231212223230.35,1,2,511()10.58658.6%1(*2/)11()10.32732.7%1(*2/)11()10.08468.46%1(*2/)s Ts Ts TsATATAT ,题2-3已知：幅值比相位差幅值比相位差系统稳态输出1122121122121(),0.005,10,01 0.005100,451()0.9991(0.005*10)()(0.005*10)2.861()0.891(0.005*1
2、00)()(0.005*100)26.57()0.5*0.999cos(102.86)0.oooorH ssssrsAtgAtgy tt ,求稳态响应.2*0.89cos(10071.57)0.5cos(102.86)0.18cos(10071.57)ooottt题2-4已知：3000米时即可忽略瞬态项，测量值滞后时间为时间常数得到3000/5600()44*1560()1tsso=15s,v=5m/sc时实际高度=3000-v*=2925(m)题2-5已知：由公式：幅值误差得到时间常数幅值误差相位差11122121222122100,2*100(),5%,?50,2*50(),?()?11(
3、)10.051()0.0005211()10.0131.3%1()()()9.28orfHzsrfHzsAsAtgc 幅值误差幅值误差题2-7已知：1(),cos1H sts求的输出响应y(t).传递函数输入拉氏变换输出拉氏变换可分解成系数c计算系数a,b计算得到系数a,b222222221222222222222222221(),()11()()()11111(1)111()11111,11ssjsjsH sX ssssY sH s X ss ssasbcs sssscss ssasbss sjajbjjab 2222222122/22221/211()111()()cossin11cos(
4、)cos 1()1arctan(),sin,cos1()1()1()1()()()cos()()()costttsY ssssy tLY stteteAy tAty tAe 12()()()y ty ty t代入得：全响应：稳态响应+衰减响应其中记为：稳态响应衰减响应全响应：/22221/21/212()sin(0)1()sin()sin1()1arctan(),sin,cos1()1()1()1()()()sin()()()sin()()cos()()()cos()()()tttx tt ty tteAy tAty tAey tAty tAey ty ty t 正弦全响应：稳态响应+衰减响应
5、其中正弦稳态响应衰减响应余弦稳态响应衰减响应或参考一阶系统单位频率（单位正弦）输入响应题2-8一价系统二阶系统一阶与二阶串联比较有原式为2n22nn222nnnn2nn211(),(j)1(j)1()21()2j12j13155072*0.01j1 1577536176j1760.01,15775361256,0.072*115775362*,0.01j1 1577536176jnH sHsH sssHrss 系统灵敏度2S 输入：求总稳态响应一阶响应幅值比一阶响应相位差二阶响应幅值比二阶响应相位差总响应幅值总响应相位差总稳态响应12122 222nnn22n1212()10*sin62.8,
6、62.81(62.8)0.851(62.8)arctan()32.131(62.8)1.01()4()2()(62.8)arctan0.41()10*2*(62.8)*(62.8)17(62.8)(62.8)32.53(ooorx ttsAAAAy t ）)17sin(62.832.53)ot题2-9一价系统传递函数二阶系统传递函数一阶化为标准式二阶标准式一阶与二阶串联总灵敏度2n22nn2n22nn1()1()21.513*0.53.51 741*1.43*41123H ssH sssssss题2-10 已知二阶响应幅值比二阶响应相位差二阶响应幅值比减小，接近于1，失真小二阶响应相位差增大n
7、n2 222nnn2n2 222nn800,2,0.14,400,2,()?()?0.7,()?()?10.14,()1.311()4()2()(62.8)arctan10.571()10.7,()0.981()4()2(62.8)arctannofHzffHzf AAAA n2n()43.031()o 测得第1个超调量为1.5,系统静态增益3，应用公式超调量M=1.5/3=0.5，可按式求得阻尼比，即 2121e,0.211lnMM题2-11u(t)=12nn22n222nnn2 222nnnn2n26.23,121.03()11.03()3*3*20.421.021()3*,1()4()1()3*3*2.387.1422()()arctan901()()7.14*sin(1.03)2ddddonTsTrsTH sssssAAy tt 已知无阻尼固有频率传递函数无阻尼固有频率处幅值无阻尼固有频率处相位差无阻尼固有频率处频率响应
