第二章 系统数学模型及其相互转换课件.ppt

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1、 本章主要讲解系统数学模型及其相互转换，介绍了系统仿真所使用的各类数学模型的表示以及相互间的转换。2.1 系统的数学模型2.2 实现问题2.3 从系统结构图向状态方程的转换2.4 连续系统的离散化方程ucdtudcdtudcyadtdyadtydadtydadtydannnnnnnnnnnnn22211112221110(2.1.1) ,00000000utuutuytyytyyudtdp ucupcupcyapyaypaypannnnnnn22111110100niiinjnjjnupcypa, 10anjjjnniiinpapcuy010 sUcssUcsUscsUscsYassYasYs

2、asYsnnnnnnnn)()(12211111 sY ty sU tu nnnnnnnnnasasasascscscscsUsYsG1221112211p sG tDutCxty)()()(tButAxtxnl nRtxn mRtum lRtylAnnBmnCnl DDml uyadtdyadtydadtydadtydnnnnnnnn12221111112223121nnnndtydxxdtydxxdtdyxxyxuxaxaxaxauyadtdyadtydadtydadtydxnnnnnnnnnnnnn1211211222111nBuAxxCxy 00110010010010011CBaaa

3、Ann 000000001321nnyxyxyxyx 000000121nnyyyxxxuuxnjjjnniiinxpaxpcuy010uxpajnjjn01jjxxp1, 2 , 1 , 0njuxpaxanjnjjn011010auxaxpnjjjnn101uxxxaaaxxxnnnn100101000010211121nnnjniinxcxcxcxpcy121110 xcccynn11y1xnxxx,21uy,upcypajnijnjnjjn00ucupcupcupcyapyaypaypannnnnnnn221101110nnnnnpxucyapucyapucyap1111100ucya

4、ucyappxnnnnn0122112001nnnnnpxucyapucyapucyapucyaxpxnnnn111ucyaxpxjjjj1njucyaucyapucyapucyapxjjjjjjj, 2 , 1112211200110auaccaccaccaccxxxxaaaaxxxxnnnnnnnnnn0101202101121121121000100001001ucxxxxynn0121001uy,uy 40, 20, 100023127222233uuyyyudtdudtuddtdydtyddtyd uxxxxxx2310001012017321321321001xxxy 100301

5、200700600700100321uyuyyxuyyxyx 1061000321xxx)(),(),(kTxkTykTuT)() 1()() 1()(11kubnkubkyaknyaknynn1q) 1()(1kykyqnjjjnjjjknuqbknyqa10)()(njjjnjjjqaqbknukny01)()(njjjnjjjqaqbkuky01)()(z)0( , 0)()(kkukyz)()()()(11110zUzbzbzYzazaannnn)()()(zUzYzG)(zGnjjjnjjjzazbzG01)(z1z1q)(k)( kh)(k0, 00, 1)(kkk)(ku)(ky

6、kiikhiuky0)()()()()(zHkhZ)()(0kuknxqanjjj), 2 , 1()()(1njkxknxqjnj)()()(01kuknxaknxqanjjj)()()(011kuknxanxanjjnj10a) 1()(kxknxn)()() 1()(11kunxakxknxnjjnjnn)()()()() 1()() 1()() 1()() 1(121113221kukxakxakxakxkxkxkxkxkxkxnnnnnn)()() 1(kGukFxkx1000100001011GaaaFnnnjjjnjnjjjjjnjjjknxqaqbkuqbkyqa0110)()

7、()()()()()(111kxkxbknxqbkynjjnjnjjj11bbbnnsssss226515mpsssss226515mpDuCxyBuAxxEEE)()()()()()1(nDunCxnynBunAxnEx)()()()()()(tDutCxtytButAxtxEDCBAE,)()()()()()()()()()()(tutDtxtCtytutBtxtAtxtE)()()()()()(tDtCtBtjEtAtS1, 0:,)(111kiiikiiikSSSCotSkiSS,kkkkkkDCBjEASDCBjEAS,111111k,1xxx)(sinxAsin 1 , 11 ,

8、1CoAkiSS ,)()()()()()()()()()()(tupDtxpCtytupBtxpAtxpE)(),(),(),(),(pEpDpCpBpA,1nppppnnnnnnnnnnEpEpEpEDpDpDpDCpCpCpCBpBpBpBApApApA110110110110110)()()()()(iiiiiEDCBA,)()()()()()(pDpCpBpjEpApSiiiiiiDCBjEASnnSpSpSpS110)(nSS,0nSS,0)(pS1,)(110innSSSS 7 . 01 . 0,xx 1,)3 . 04 . 0(xx VCidtdiRdtidL22LRC150,

9、100,2 , 1 ,20,10CRLxCRLAxCRLE),(),(0010000001001),(100001000001010),(/CRLLCRLECRLCRCRLAdtdiixTCRL,15L2 . 1R150C sG sZsYsUsZasasasascscscscsUsYsGnnnnnnnnn1221112211tzcdttdzcdttzdcdttzdctytutzadttdzadttzdadttzdadttzdnnnnnnnnnnnnnn12221111222111121nnzxzxzxCxyBuAxx ABC121ccccCnn tuctudtdctudtdctudtdctya

10、tydtdatydtdatydtdatydtdnnnnnnnnnnnnnn12221111222111s 00001221nnnnnnnysyysyssYstydtd 0001111221112211122 11yaysyasasasassuasasasascscscscsYnnnnnnnnnnnnnnn 3212121000000nnsucucyayaysuc 000001211211ucucyayaynnnnn ucxaxucucucucyayayayxucxaxucucucyayayxucxaxucucyayayxucxaxucyayxyxnnnnnnnnnnnnnnnnnnnnnnnn

11、nnn112211111011213221121112212121211111 CxyBuAxx 1211000010000010aaaaAnn121ccccBnn100C 11211323211321000000010101100000nnnnnnnnnnnnyyyyyaaaaaaaxxxxx 112311112232100000000nnnnnnnnnuuuuucccccccc + 4020100023127222233uuyyytudtdudtuddtdydtyddtyd uxxxxxx1327101201000321321 1610420001131110010171712000321

12、xxx012211nnnnnasasasasnn,21 sG nnnnnssscscscscsG2112211 nisGsrisii, 2 , 1lim nnssUsXssUsX1,111nxxx,21CxyBuAxx ndiagA,21TB111nrrrC211kkn sG nkknnnnssscscscscsG1112211 nnkkkkksrsrsrsrsr11111112111 nkkjsGsrkisGsdsdirjsjkiisij, 2, 1lim, 2 , 1lim!1111111 nkkjssUsXssUsXssUsXssUsXjjkkk, 2, 11111111211nxxx,

13、21CxyBuAxx nkA001111111knkkTrrrrrCB11121111100 ,1216716174232ssssssG sG 2316174lim2lim3222222111312211ssssGsrsrsrsrsGss 13lim33154lim2lim21322212sGsrssdsdsGsdsdrsssuxxxxxx110300020012321321321132xxxy 0,01nxx ,0,0,0,0,02yyuuun71016011200As001Bs29114 Cs0Ds图图2.3.1 系统动态结构图系统动态结构图 图图2.3.2 系统的模拟结构图系统的模拟结构

14、图 44433322111111uaxuaxuxabBuBx4343234012011141xxuxxuxuxuuxBaxu00uWWxuKuxiuixk44431, 1 ,aaBdiagK W0W0011110001101001100011WBaWux 000BuAxuKWKWxx0KWBKWA4xy Cxy 1000CKnWnnijWji1111BaW02113WW114W1,11Ba0WjW0j0W, 1, 10201WWK0,WWsK1121sTsTKsKK21122TsTsK1TsK sBAsDCsGsUsXiiiiiiiiiiADC,iB sUsDCsXsBAiiiiiini,2,

15、1 sUDsCsXBsADCBA,nAAAdiagA,21nBBBdiagB,21nCCCdiagC,21nDDDdiagD,21 00UWWXDsCsXBsA 0201sUVUVsRXssXQ0201DWVCWVACWRDWBQ tuVQtuVQtRxQtx0210111 tuVQ011tuVQ021tu0 tu0Q1Q0iD431, 0 ,aaadiagA 4IB431, 1 ,aabdiagC0 , 0 , 0 , 1diagD0,WW000101000010000110000WW21,VVRQ1000010000101001Q4433110000000100aaaabaR00012V0

16、0011bV tuVQtuVQtRxQtx0210111 tutubtxaaaabaaax00010000000000100144331441 tuDtxCtztuBtxAtxiiiiiiiiiiixiuiziAiBiCiD tButAxtx tDutCxtznTnTnTnzzzzuuuuxxxx212121ABCDnAAAdiagA,21nBBBdiagB,21nCCCdiagC,21nDDDdiagD,21n tzPtUQtuiiiiiUiiQiiP tPztQUtuTnUUUU21TnTnPPPPQQQQ2121iy tTUtRzyRT tTUtRzytQUtPztutDutCxtztB

17、utAxtx 72.70585.10038.3387.879527. 011429. 0001417. 0101163. 000135. 0808 .15696. 210125. 01037. 01251251008. 01222321ssssssssGssssGsssGuz tutxtztutxtxtutxtztutxtxtxtztutxtx133133222222111119527. 087.8738.331085.10072.7051096. 28 .156801251259527. 000096. 2000087.870038.330008 .156000801000000100018

18、5.10072.70500100010800000125DCBA tUutztUutztzu23112321 QuPztu100010000001110QP tzy1TURzy00001TRTRQPDCBA,iuzBuAxxT nTutun图图2.4.1 采样控制系统结构图采样控制系统结构图 smaxmax2s sBUsAXXssX0 sBUXsXAsI01 AsI sBUAsIXAsIsX110AteAsI11 dBuexetxttAAt00n1n dBuexenTxnTnTAAnT00 dBuexeTnxTnTnATnA101101ATe dBuenTxeTnxTnnTTnAAT1111

19、nTdttnTBuenTxeTnxTTAAT01nTutnTu nTuTnTxTnTuBdtenTxeTnxmTtTAAT01 ATeT BdteTTtTAm0TTnunTunTutnTu1nTuBdttenTuBdtenTxeTnxTtTATtTAAT001 TnTx TmnTu TmnTu T Tm TmTtTABdtte0 , , 统称为系统的离散系数矩阵。 T Tm TmZZ图图2.4.2 连续系统的离散化连续系统的离散化 sG zG sGsGZzUzYzGh sGh zG表表2.4.1 不同保持器的不同保持器的 zG zG ssG 21TsTssGZ sGZ ssGZ)(sGs1s1

20、 sGs1 sGZzTsseZsGZssGZTs111 sGZzTzG asKsG aTaTezaeKassKZzzzG11111naTnaTnueaKyey zG aTaTezKTezKzzTsGZzTzG11nnaTnKTuyey34527408. 0655. 1009721. 006408. 001187. 0)(zzzzzzhd) 4 . 0)(5 . 0() 2 . 0()(2zzzzzH)103586.13)(3 .637163. 9()104129.28)(273. 6(6556.33)(222ssssssssHcudtdudtuddtudydtdydtyddtyd111710248522332233udtdudtuddtdydtyddtyd23127222233 40, 20, 1000uuyyy 15963152232ssssssG 6515422ssssssG 2322sssUsY 10y 00 y n 311ssGuxxxxxx363300020001321321 T Tm 2322sssG