线性离散系统分析PPT学习教案

1、会计学1第1页/共93页原理：原理：只有当检流计的指针与电位器接触时，电动机才在采样信号作用下产生运动，进行炉温调节，而在检流计与电位器脱开时，电动机就停止不动，保持一定的阀门开度，等待炉温缓慢变化。在采样控制情况下，电动机时转时停，所以在调节过程中超调现象大为减少，使动态性能得到改善。第2页/共93页第3页/共93页第4页/共93页f(t)f(t)t0t0T)(tf(a)(b)(c)(tfT 第5页/共93页f(t)f(t)t0t0T)(tfT 2T 3T)(tf)(tf第6页/共93页0T 2T3T4Tt0T 2T 3T4Tt零阶零阶保持器保持器)(tf)(tfh)(tfh)(tf第7页/

2、共93页脉冲脉冲控制器控制器保持器保持器被控被控对象对象测量测量元件元件0tttt)(t)(tu)(tuh)(tr)(tc)(tb)(t)(t)(tu)(tr)(tuh000第8页/共93页第9页/共93页A-Analog signals, D -Digital signals。第10页/共93页f(t)f(t)t t0 0t t0 0)(tfT T 2T2T 3T3T 4T4T 5T5Tt t0 0)(tfT T 2T2T 3T3T 4T4T 5T5T0100010010011001011101111010101010111011采样采样整量整量(a)(a)(b)(b)(c)(c) 第11页

3、/共93页f fh h(t)(t)t t0 0t t0 0)(tfT T 2T2T 3T3T 4T4T 5T5Tt t0 0)(tfT T 2T2T 3T3T 4T4T 5T5T0100010010011001011101110010001000110011解码解码信号复现信号复现(a)(a)(b)(b)(c)(c)10001000T T2T2T 3T3T 4T4T 5T5T第12页/共93页数字数字控制器控制器D/A被控被控对象对象测量测量元件元件)(tuh)(tc)(t)(t)(tu)(trA/D数字计算机数字计算机第13页/共93页第14页/共93页脉冲调制器脉冲调制器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页/共93页)()( )()()()(00*nTtLnTenTtnTeLteLsEnnnTsstnTsedtetenTtL0)()(0*)()(nnTsenTesE第16页/共93页第17页/共93页cswTwT152stT401第18页/共93页0T2T3T4Tt0T2T3T4Tt零阶零阶保持器保持器)(tf)(tfh)(tfh)(tf第19页/共93

5、页seesssGTsTsh111)(TTttt000第20页/共93页第21页/共93页0ln0)()()(ln,)()()(nnTzsTsnnTsznTfsFzFTzsezenTftfLsF则令)()(*tfzF为函数)()(*tfZzF)()(tfZzF0)()()(nnTtnTftf第22页/共93页0)()(nnznTfzF第23页/共93页0120( )1111nnF zzzzz 11z111)()( 1 1zzzzFtZ第24页/共93页,2, 1 ,0,)(nenTfanT22101)(zezezezFaTaTnnanT11zeaTaTaTatezzzezFeZ111)(第25页

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

7、1页/共93页ateaTe)(zeFtfeZaTat)(limzFz)(lim)(lim)0(0zFnTffzn第32页/共93页)() 1(lim)()(1lim)()1 (lim)(lim)(1111zFzfzFzzzFznTffzzzn或)(limnTfn第33页/共93页)()(1tfzFZ0)()(nnznTfzF0)()()(nnTtnTftf第34页/共93页nnmmzazazazbzbzbbzF2211221101)(nnzczczcczF22110)()()2()()()(210*nTtcTtcTtctctfn第35页/共93页)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页/共93页15050z.z.125075050z.z.50512.z.z2750z.1250750z.2137501251750z.z.2137508750z.z.38750z. 第37页/共93页niiiniiizzzAzFzzAzzF11)()(z

9、zF)(0)()()(*)()(nnTtnTftftfzF第38页/共93页)(1()1 ()(aTaTezzzezFaTaTaTaTezzzzzFezzezzezzF1)(111)(1()1 ()(011nanTnTtezFZtf)()()()(*atettf)()(1第39页/共93页)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页/共93页)1()()(kfkfkf) 2() 1(2)() 1

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

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

12、 (2) 求求Z域代数方程的解域代数方程的解; (3) 将将Z域代数方程的解经域代数方程的解经Z反变换求反变换求得差分方程得差分方程的时域解。的时域解。第48页/共93页1) 1 (, 0)0(, 0)(3) 1(4)2(xxkxkxkx)()()()0()()1()() 1 ()0()()2(222zXkxZzzXzxzzXkxZzzXzzxxzzXzkxZ0)(3)(4)(2zXzzXzzXz)()()(10nkknzkTfzFznTtfZ第49页/共93页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页/共93页)()()(zRzCzG第51页/共93页(3)()()()(11*zRzGZzCZtc第52页/共93页)5)(2(6)(sssG52)2(2)(sssG)()(222)(525252TTTTTTezezeezezzezzzG第53页/共93页)(1zG)(2zGR(z)C(z)(1zC)()()()(21zGzGzRzC第54页/共93页)()()(21zGGzRzC)(1sG)(2sGR(z)C(z)C(s)R*(s)R(s)C*(s)T)(1sC)()()(s

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

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

16、)(*ssGHsRsssGsHsRs将上式两边离散化第62页/共93页ln/( )( )( ) ( )sz TzR zGH zz令，得( )1( )( )1( )rzzR zGH z*( )( )( )ln/( )( ) ( )CsG sssz TC zG zz令，得第63页/共93页( )( )( )( )1( )crC zG zzR zGH z0)(1zGH)(11)()()(zGzRzzr)(1)()()()(zGzGzRzCzcr第64页/共93页)(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页/共93页)4()()()()()()()()()()(12*112*sGsGsTsGsRsGsGsTsRsT)()()()(*21*1*sGGsTsRGsTTzsln)()()()(211zGGzTzRGzT)(1)()(211zGGzRGzT)()()(*2*sGsTsCTzsln)(1)()()()()(21212zGGzGzRGzGzTzC第66页/共93页GHrcGHrcGHrc)(zC1GHrc2G1G)(1)()(zGHzRzG)()(1)()(zHzGzRzG)(1)(zHGzGR

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

19、93页的，则系统不稳定，有位于单位圆的，则系统不稳定，有位于单位圆周上的，系统周上的，系统临界稳定。临界稳定。0)(1zGHnzzz,21), 2 , 1(nizi), 2 , 1( 1nizi第73页/共93页1K 5K )()(aSSKSGr第74页/共93页)(1()1 ()(aTaTrezzezaKzG)1 ()(1()1 ()(1)()(aTraTaTrezaKezzezaKzGzGz0)1 ()(1()(1aTraTezKezzazG第75页/共93页1rK0368. 0736. 02zz482. 0368. 0482. 0368. 021jzjz16 . 021 zz5rK036

20、8. 0792. 12zz第76页/共93页影响与连续系统类似，影响与连续系统类似，K加大，系加大，系统的稳定性变统的稳定性变差。差。555. 1237. 021zz第77页/共93页否都在单位圆以内，为了能够应用否都在单位圆以内，为了能够应用劳斯判据判断劳斯判据判断离散系统的稳定性，需要通过离散系统的稳定性，需要通过W变换变换（又称双线（又称双线性变换）。性变换）。第78页/共93页jv00jyx1-1u(a)(b)平面z平面第79页/共93页)11(11zzwzzwjvuwjyxz)11(11wwzwwzjvuyxyjyxyxw222222) 1(2) 1(111zzwjyxz第80页/共

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