線性離散系統(tǒng)分析PPT學(xué)習(xí)教案

1、會(huì)計(jì)學(xué)1第1頁(yè)/共93頁(yè)原理：原理：只有當(dāng)檢流計(jì)的指針與電位器接觸時(shí)，電動(dòng)機(jī)才在采樣信號(hào)作用下產(chǎn)生運(yùn)動(dòng)，進(jìn)行爐溫調(diào)節(jié)，而在檢流計(jì)與電位器脫開(kāi)時(shí)，電動(dòng)機(jī)就停止不動(dòng)，保持一定的閥門開(kāi)度，等待爐溫緩慢變化。在采樣控制情況下，電動(dòng)機(jī)時(shí)轉(zhuǎn)時(shí)停，所以在調(diào)節(jié)過(guò)程中超調(diào)現(xiàn)象大為減少，使動(dòng)態(tài)性能得到改善。第2頁(yè)/共93頁(yè)第3頁(yè)/共93頁(yè)第4頁(yè)/共93頁(yè)f(t)f(t)t0t0T)(tf(a)(b)(c)(tfT 第5頁(yè)/共93頁(yè)f(t)f(t)t0t0T)(tfT 2T 3T)(tf)(tf第6頁(yè)/共93頁(yè)0T 2T3T4Tt0T 2T 3T4Tt零階零階保持器保持器)(tf)(tfh)(tfh)(tf第7頁(yè)/

2、共93頁(yè)脈沖脈沖控制器控制器保持器保持器被控被控對(duì)象對(duì)象測(cè)量測(cè)量元件元件0tttt)(t)(tu)(tuh)(tr)(tc)(tb)(t)(t)(tu)(tr)(tuh000第8頁(yè)/共93頁(yè)第9頁(yè)/共93頁(yè)A-Analog signals, D -Digital signals。第10頁(yè)/共93頁(yè)f(t)f(t)t t0 0t t0 0)(tfT T 2T2T 3T3T 4T4T 5T5Tt t0 0)(tfT T 2T2T 3T3T 4T4T 5T5T0100010010011001011101111010101010111011采樣采樣整量整量(a)(a)(b)(b)(c)(c) 第11頁(yè)

3、/共93頁(yè)f fh h(t)(t)t t0 0t t0 0)(tfT T 2T2T 3T3T 4T4T 5T5Tt t0 0)(tfT T 2T2T 3T3T 4T4T 5T5T0100010010011001011101110010001000110011解碼解碼信號(hào)復(fù)現(xiàn)信號(hào)復(fù)現(xiàn)(a)(a)(b)(b)(c)(c)10001000T T2T2T 3T3T 4T4T 5T5T第12頁(yè)/共93頁(yè)數(shù)字?jǐn)?shù)字控制器控制器D/A被控被控對(duì)象對(duì)象測(cè)量測(cè)量元件元件)(tuh)(tc)(t)(t)(tu)(trA/D數(shù)字計(jì)算機(jī)數(shù)字計(jì)算機(jī)第13頁(yè)/共93頁(yè)第14頁(yè)/共93頁(yè)脈沖調(diào)制器脈沖調(diào)制器f(t)t0)(t

4、TT2T3T-T-2T-3Tf(t)(tf0t)(tT)(tf*0( )(0) ( )( ) ()(2 ) (2 )( ) ()()()nf tftf Tt TfTtTf ntt nTf nTt nT*0( )()()nftf nTtnT第15頁(yè)/共93頁(yè))()( )()()()(00*nTtLnTenTtnTeLteLsEnnnTsstnTsedtetenTtL0)()(0*)()(nnTsenTesE第16頁(yè)/共93頁(yè)第17頁(yè)/共93頁(yè)cswTwT152stT401第18頁(yè)/共93頁(yè)0T2T3T4Tt0T2T3T4Tt零階零階保持器保持器)(tf)(tfh)(tfh)(tf第19頁(yè)/共93

5、頁(yè)seesssGTsTsh111)(TTttt000第20頁(yè)/共93頁(yè)第21頁(yè)/共93頁(yè)0ln0)()()(ln,)()()(nnTzsTsnnTsznTfsFzFTzsezenTftfLsF則令)()(*tfzF為函數(shù))()(*tfZzF)()(tfZzF0)()()(nnTtnTftf第22頁(yè)/共93頁(yè)0)()(nnznTfzF第23頁(yè)/共93頁(yè)0120( )1111nnF zzzzz 11z111)()( 1 1zzzzFtZ第24頁(yè)/共93頁(yè),2, 1 ,0,)(nenTfanT22101)(zezezezFaTaTnnanT11zeaTaTaTatezzzezFeZ111)(第25頁(yè)

6、/共93頁(yè)f*(t)f(t)F(s)F(z)采樣L-1Z第26頁(yè)/共93頁(yè))()(assasFassassasF11)()(aTaTaTaTezezezezzzzzF)1 ()1 (1)(21L)( 1)(ttf1Latetf)(第27頁(yè)/共93頁(yè)1zz2)1(zTz32)1(2)1(zzzTaTezzaTsln)/1(1azz22tas1第28頁(yè)/共93頁(yè))()()()(2121zFzFtftfZ)()(zaFtafZ第29頁(yè)/共93頁(yè))()(zFznTtfZn)()()(10nkknzkTfzFznTtfZ0) 1()() 0 (TnfTff)()(zFznTtfZn第30頁(yè)/共93頁(yè)第3

7、1頁(yè)/共93頁(yè)ateaTe)(zeFtfeZaTat)(limzFz)(lim)(lim)0(0zFnTffzn第32頁(yè)/共93頁(yè))() 1(lim)()(1lim)()1 (lim)(lim)(1111zFzfzFzzzFznTffzzzn或)(limnTfn第33頁(yè)/共93頁(yè))()(1tfzFZ0)()(nnznTfzF0)()()(nnTtnTftf第34頁(yè)/共93頁(yè)nnmmzazazazbzbzbbzF2211221101)(nnzczczcczF22110)()()2()()()(210*nTtcTtcTtctctfn第35頁(yè)/共93頁(yè))5 . 0)(1(5 . 0)(zzzzF43

8、219375. 0875. 075. 05 . 0)(zzzzzF)4(9375. 0)3(875. 0)2(75. 0)(5 . 0)(TtTtTtTttf9375. 0)4(,875. 0)3(,75. 0)2(, 5 . 0)(TfTfTfTf110.5( )lim(1) ( )lim(1)1(1)(0.5)zzzfzF zzzz 第36頁(yè)/共93頁(yè)15050z.z.125075050z.z.50512.z.z2750z.1250750z.2137501251750z.z.2137508750z.z.38750z. 第37頁(yè)/共93頁(yè)niiiniiizzzAzFzzAzzF11)()(z

9、zF)(0)()()(*)()(nnTtnTftftfzF第38頁(yè)/共93頁(yè))(1()1 ()(aTaTezzzezFaTaTaTaTezzzzzFezzezzezzF1)(111)(1()1 ()(011nanTnTtezFZtf)()()()(*atettf)()(1第39頁(yè)/共93頁(yè))35(25) 1(21)35)(1(1)(zzzzzzF解：)35)(1()(zzzzF)()53(1 21)()53(21)( 121)()53(2) 1(2)35(25) 1(2)(0*/nTttfttfzzzzzzzzzFnnTt第40頁(yè)/共93頁(yè))1()()(kfkfkf) 2() 1(2)() 1

10、()()1()()()(2kfkfkfkfkfkfkfkfkf)()()(111kfkfkfnnn第41頁(yè)/共93頁(yè))() 1()()() 1(2)2()() 1()() 1()()()() 1()(112kfkfkfkfkfkfkfkfkfkfkfkfkfkfkfnnn第42頁(yè)/共93頁(yè)0)()(22tcxdtdxbdttxda120( )(1)(2)()( )()nnc kac ka c ka c knb r kb r kmTkxTkxkxTTkTxkTxtttxtxdttdx)()()()()()()()(12222TkxdttdxTkxdttdx)()()()(第43頁(yè)/共93頁(yè)012

11、)()()(kxkxkx整理，得：0)()() 1()() 1(2) 2(2kcxTkxkxbTkxkxkxa)()()() 1()()() 1(2)2()()(22222kxtxTkxkxTkxdtdxTkxkxkxTkxdttxd0)()(22tcxdtdxbdttxda第44頁(yè)/共93頁(yè))()21 ()()4532(21321zRzzzCzzz)2(2) 1()() 3(4)2(5) 1(3)(2krkrkrkckckckc)(453221)(32121zRzzzzzzC第45頁(yè)/共93頁(yè) )(2)(2 . 0) 1(krkckc第46頁(yè)/共93頁(yè)6661212.)(c第47頁(yè)/共93頁(yè)

12、 (2) 求求Z域代數(shù)方程的解域代數(shù)方程的解; (3) 將將Z域代數(shù)方程的解經(jīng)域代數(shù)方程的解經(jīng)Z反變換求反變換求得差分方程得差分方程的時(shí)域解。的時(shí)域解。第48頁(yè)/共93頁(yè)1) 1 (, 0)0(, 0)(3) 1(4)2(xxkxkxkx)()()()0()()1()() 1 ()0()()2(222zXkxZzzXzxzzXkxZzzXzzxxzzXzkxZ0)(3)(4)(2zXzzXzzXz)()()(10nkknzkTfzFznTtfZ第49頁(yè)/共93頁(yè)35 . 015 . 0)3)(1()(zzzzzzzzX,2, 1 ,0,)3(5.0)1(5.0)()()3(5.0)1(5.0)

13、(0kkTxnTttxkknkk或TtTttx/)(.)(.)(3501500nnTtnTftf)()()(*第50頁(yè)/共93頁(yè))()()(zRzCzG第51頁(yè)/共93頁(yè)(3)()()()(11*zRzGZzCZtc第52頁(yè)/共93頁(yè))5)(2(6)(sssG52)2(2)(sssG)()(222)(525252TTTTTTezezeezezzezzzG第53頁(yè)/共93頁(yè))(1zG)(2zGR(z)C(z)(1zC)()()()(21zGzGzRzC第54頁(yè)/共93頁(yè))()()(21zGGzRzC)(1sG)(2sGR(z)C(z)C(s)R*(s)R(s)C*(s)T)(1sC)()()(s

14、GsGZzGG2121 第55頁(yè)/共93頁(yè) )(1sG)(2sGR(z)C(z)C(s)R*(s)R(s)C*(s)T)(1sC)(*1sC)(1zC)()()()(21zGzGzRzC第56頁(yè)/共93頁(yè))(1()1 (1)(21aTaTrrezzezaKasKsZzGG)()()(2121zGzGzGG1212( )( )( )( )G z G zZ G sZ G sasKsGssGr)(,1)(21)()()(2121sGsGZzGG)(1(1)()(221aTrrezzzKasKZsZzGzG第57頁(yè)/共93頁(yè)sesGTsh1)()(0sGTT第58頁(yè)/共93頁(yè))()()1()()()(

15、)(*2*21sRsGesRsGsGsCTs)()()()()()()1()(*2*2*2*sRsGesRsGsRsGesCTsTs得：則令,/lnTsezTzs)()()1 ()()()()()(21212zRzGzzRzGzzRzGzCssGZzzzGzzRzC)(1)()1 ()()(021TsesG1)(1ssGsG)()(02TT第59頁(yè)/共93頁(yè)第60頁(yè)/共93頁(yè))(t)(*t)(tb)(*tb)(tc)(*tc)(tr)(*tr第61頁(yè)/共93頁(yè)( )( )( )( )( ) ( )( )( )( )sR sB sB sH s C sC sG ss)()()()()()()()(

16、)(*ssGHsRsssGsHsRs將上式兩邊離散化第62頁(yè)/共93頁(yè)ln/( )( )( ) ( )sz TzR zGH zz令，得( )1( )( )1( )rzzR zGH z*( )( )( )ln/( )( ) ( )CsG sssz TC zG zz令，得第63頁(yè)/共93頁(yè)( )( )( )( )1( )crC zG zzR zGH z0)(1zGH)(11)()()(zGzRzzr)(1)()()()(zGzGzRzCzcr第64頁(yè)/共93頁(yè))(1)()()(2121ZGGZGZRGZC 1*2( )( )( )(1)( )( )( )(2)( )( )( )(3)sR sC s

17、T ssG sC sTsG s)(2sGTR(s)C(s)(1sG)(s)(*sT)(sT第65頁(yè)/共93頁(yè))4()()()()()()()()()()(12*112*sGsGsTsGsRsGsGsTsRsT)()()()(*21*1*sGGsTsRGsTTzsln)()()()(211zGGzTzRGzT)(1)()(211zGGzRGzT)()()(*2*sGsTsCTzsln)(1)()()()()(21212zGGzGzRGzGzTzC第66頁(yè)/共93頁(yè)GHrcGHrcGHrc)(zC1GHrc2G1G)(1)()(zGHzRzG)()(1)()(zHzGzRzG)(1)(zHGzGR

18、)(1)()(1212zHGGzRGzG第67頁(yè)/共93頁(yè)1GHrc2G1GGHrc1GHrc2G)()(1)()(zHzGzRzG)(1)()(zGHzRzG)()(1)()(1212zHGzGzRGzG)()(1)()()(2121zHGzGzRzGzGGHrc第68頁(yè)/共93頁(yè)sTeZ jSTjTTjsTeeeez)(TsTeeZTeZsT第69頁(yè)/共93頁(yè)TeTTsTeeZ01z01z01z第70頁(yè)/共93頁(yè)j00s平面z平面(a)(b)u-11jv第71頁(yè)/共93頁(yè)( )( )1( )crG zZGH z)(t)(*t)(tb)(*tb)(tc)(*tc)(tr)(*tr第72頁(yè)/共

19、93頁(yè)的，則系統(tǒng)不穩(wěn)定，有位于單位圓的，則系統(tǒng)不穩(wěn)定，有位于單位圓周上的，系統(tǒng)周上的，系統(tǒng)臨界穩(wěn)定。臨界穩(wěn)定。0)(1zGHnzzz,21), 2 , 1(nizi), 2 , 1( 1nizi第73頁(yè)/共93頁(yè)1K 5K )()(aSSKSGr第74頁(yè)/共93頁(yè))(1()1 ()(aTaTrezzezaKzG)1 ()(1()1 ()(1)()(aTraTaTrezaKezzezaKzGzGz0)1 ()(1()(1aTraTezKezzazG第75頁(yè)/共93頁(yè)1rK0368. 0736. 02zz482. 0368. 0482. 0368. 021jzjz16 . 021 zz5rK036

20、8. 0792. 12zz第76頁(yè)/共93頁(yè)影響與連續(xù)系統(tǒng)類似，影響與連續(xù)系統(tǒng)類似，K加大，系加大，系統(tǒng)的穩(wěn)定性變統(tǒng)的穩(wěn)定性變差。差。555. 1237. 021zz第77頁(yè)/共93頁(yè)否都在單位圓以內(nèi)，為了能夠應(yīng)用否都在單位圓以內(nèi)，為了能夠應(yīng)用勞斯判據(jù)判斷勞斯判據(jù)判斷離散系統(tǒng)的穩(wěn)定性，需要通過(guò)離散系統(tǒng)的穩(wěn)定性，需要通過(guò)W變換變換（又稱雙線（又稱雙線性變換）。性變換）。第78頁(yè)/共93頁(yè)jv00jyx1-1u(a)(b)平面z平面第79頁(yè)/共93頁(yè))11(11zzwzzwjvuwjyxz)11(11wwzwwzjvuyxyjyxyxw222222) 1(2) 1(111zzwjyxz第80頁(yè)/共

21、93頁(yè)0122 yx0Re122uwyx0Re122uwyx0Re122uwyx第81頁(yè)/共93頁(yè)15 . 0234)(232zzzzzzcr)(zcr015 . 0223zzz11wwz01)11(5 . 0)11(2)11(23wwwwww第82頁(yè)/共93頁(yè)01317323www01017315117330123wwww第83頁(yè)/共93頁(yè)1arcK)(1()1 () 1()(1)(22aTaTaTaTrrezzaTeezaTeaKaSSKZzzzG第84頁(yè)/共93頁(yè))1 ()1 () 1()1 () 1()(1)()()(2222aTaTaTraTaTraTaTaTreaaTeeKzeaaTeKzaaTeezaTeKzGzGzRzC)( 1, 1STa0368. 0264. 0)368. 1368. 0(2rrKzKz11wwz0104. 0736