第03章5自动控制理论

1、0122110nnnnnasasasasa102113212321343212753116420feedddcccbbbbaaaaaaaasssssssnnnn,141713131512121311170613150412130211bbaabcbbaabcbbaabcaaaaabaaaaabaaaaabG(s)H(s)E(s)B(s)R(s)C(s) 控制系统框图)()()()(sCsHsRsE)()()(sHsEsE)()()()(sRsHsGsE11)()()()(limlimsHsGssRssEessss100 )1 ()1)(1 ()1 ()1)(K(1G(S)H(S) 2121sT

2、sTsTssssvnvm012 1lims lime 0s0sss)()()()(sHsGsRssE控制系统的稳态误差值时和试求当输入信号分别为传递函数为设单位反馈系统的开环例,sin)()(,wttrttrTs2211G(s) .因而是允许的。际所求一致但与实在坐标原点不解析尽管在数学上由终值定理时时当解, , limsE(s)lime (2) e t T)-T(teTe(t) -1R(s)E(s) (1) R(s) tr(t) (s):1/T)s(s10s0sssss-21/TSTSTST1/T)(SS1S12211S(S)11eTt22223)()()(/ssEsHsGTSG .)( )

3、(lim)(lim)(,)(,sincos)(sincos)( )()()()()(的错误结论否则得出算稳态误差值不能采用终值定理来计所以此时轴上不解析应当注意正弦函数在虚这里0s1e , 0e 11e 111e(t) s11 s1111 s11E(s) sR(s) 322200ssss222222ss222222222222322222222222 TssssEtTTtTTttTTtTTeTTTTsTTTsTTTsssHsGsRssTt位置（阶跃）误差系数位置（阶跃）误差系数 终值定理：终值定理： )(lim)(limssEteestss0)()(lim)()()(lim)(limsGssR

4、sHsGsRssSEessrsssr111000SsR1)(PssssrKsGsGe11111100)(lim)(lim21SsR)( KsSGsSGSessssr11100)(lim)(lim31SsR)(KasGSsGSSessssr11120220)(lim)(lim)(limsGKsP0)(limsSGKs0 斜坡（速度）误差系数斜坡（速度）误差系数抛物线（加速度）误差系数抛物线（加速度）误差系数)(limsGSKas20niimjjsTsTKsG1111)()()(K11sseKsGKsP)(lim0)s(GlimK0sP1n1iim1jj)1ST( S)1ST(K)s (G0sse

5、)s(GlimK0sP21211 1niimjjSTSSTKsG)()()( II II 型系统，阶跃输入时误差系数无穷大型系统，阶跃输入时误差系数无穷大0sse II II 型系统，阶跃输入时没有稳态误差型系统，阶跃输入时没有稳态误差, ,输出最终等于输入输出最终等于输入vK2100KKv20100Kvesstvtr0)(constv020SvsR)()(limsSEesss0)()(limsHsGSvSs1200)()(limsHsSGSvs00Kvv0100vssSKsGsSHKvlim)()(limaK2021tatr)(consta030SasR)()(limsSEesss0)()(

6、limsHsGSaSs1300)()(limsHsGSSas2200Kaas00 lim2020vssSKsHsGSKalim)()(lim32100vvKvKa,302100vvconstKavess,pKKvKa扰动作用下的稳态误差扰动作用下的稳态误差)(1sG)(2sGR(s)E(s)C(s)D(s) 图图3-2 闭环控制系统闭环控制系统)(sCD)(sED)()()(1)()(212sDsGsGsGsCD)()(2)(11)(2)()(sDsGsGsGsDCsDE根据终值定理求得在扰动作用下的稳态误差为)()()(1)()(21200limlimsDsGsGssGssEesDssfKR

7、10 0Rtr0R 000tcKmee,011RKe KKRtcKKRm1100和KRe10 21ssRsC 24141212ssssC tettc2414121 1tr 21KK 、 2221KassKKsRsC 222210KasssKKsCslim21K09021. eMp 75012. npt222122212nnnssKKassKK 125sn. 24. 62,04.2722 . 522nanK0)(Rtrtvtr0)( tatr2021)( KR10Kv0Ka011j cbsssKsG25021.,vvssKKecKcKKv5050.,. pspspsKpsssKKcsbssKsT

8、22222223223)(sG222) 11)(11(ssjsjsKpcpbp22223124bpKc, 2322ssssG1)(sGc ssKsGpc1020501502010523sssssss2015207500201505010123ssss/ )( 1051202ssssKsGsGpc02020501501201052342pppKsKssssKssspppppppppKsKKKKsKKsKsKs2015207503002020750151120152075020201532050140)(; 0pK25260.pK;.537020750ppKK2526040010500.ppKK 01aassRsE,ttr cos)( te assssE22 asCjsBjsAassssE 22222121 aaCjaBjaA, te attjtjeaaejaejate222121 a arctanateaata22221 cos)()()()()(sGsGsRs