现代控制理论基础第2版王孝武课后答案15章.pdf

1 2 2 1 2 1 11 2 1 2 11 2 1 2 21 2 1 1 1 1 1 2 1 22111 2 2 2 2 21 1 2 12 2 2 1 1 1 2 1 1 1 1 11 10 1 0 11 1 11 u u )t (i )t (i RRu u u L LL )t (i )t (i L RR L R L R L R dt )t (di dt )t (di u)t (iR)t (iRu u L )t (i L RR )t (i L R dt )t (di L u L u L )t (i L R )t (i L R dt )t (di A A 1- 1 1 u 2 u 1 R 1 L A u 2 L 2 R 1 i 2 i 3 1- 2 1 2 1 2 1 22 12 2 1 2222 12121 21 2 1 112 1 22 2 22 1 22 2 1 12 2 12 1 121 211 01 1 1 11 1 111 11 u u u u u CR CR u u CRCR CRCRR RR dt du dt du : uuu u CR u CR u CRdt du u CR u CR u CRR RR dt du C C c C C C C CC C CC C 1 u 1 R 2 R 2 C 1 C 2 Uc 1Uc 2 u 4 1- 5(1) 2 1 2 1 2 1 212 21 32211 01 2 0 712 10 2712 2127 x x y u x x x x uxxx xx yxxyxxyx yy uyyy 5 1- 5(2) 3 2 1 3 2 1 3 2 1 22110003 120112 0221 30 22311201 001 0 21 21 0023 100 010 0 21 21 0 32 x x x y u/ / x x x / x x x aaab /aab /ab b: uxxuxxuyx uuyy 6 1- 6(1) 21121121 2 21 12 2 21 21121121 2 21 2112 21 2 1 21 211 2 21 1 12 2 11 1 1 2 1 1 1 2 21 11 21 2 1 21 211 2 21 1 12 1 1 2 1 1 1 2 21 1 2 21 2 1 1 1 1 1 1 1 11 2 11 2 21 2 1 1 1 1 1 10 )( )( 1 0 11 )( )( )( )(10 1 0 11 RRsLRsLRsLRsLL LRsLL RRsLRsLRsLRsLL RRsRL LL R LL RRR s L RR L R s L LL L R s L R L R L RR s RR sg LL R LL RRR s L RR L R s L R s L R L R L RR s L RR s L R L R L R s s ssgRR L LL L RR L R L R L R AI DBAICDC BA 7 1- 6(2) 127 2 127 2 0 12 17 01 )( 127 12 17 712 1 )( 001 2 0 712 10 2127 22 2 1 1 1 ssss s s sg ss s s s s s ssg uyyy AI DBAIC DCBA 8 1- 6(3) 3223 0 21 21 2323 23 1 001 23 2323 23 1 023 10 01 0001 0 21 21 0023 100 010 32 3 2 3 2 2 2 3 2 2 2 1 1 1 s ss /s / / s/s ss/ ss )s(g /s s/s ss/ ss s/ s s s s)s(g / / / uuyy AI DBAICDC BA 9 1- 10 )k(x )k(x )k( y )k(u )k(x )k(x )k(x )k(x )k(u)k(x)k(x)k(x )k(x)k(x )k(x)k( y)k(x )k(x)k( y)k(x )k( y)k(x )k( y),k( y )k(u)k( y)k( y)k( y 2 1 2 1 2 1 212 21 32 21 1 01 1 0 32 10 1 1 321 1 21 11 1 2132 10 1- 13 200 010 000 02121 100 02121 010 101 101 010 101 101 0 1- 1 0 1 0 0 0 0 1 1 0210 021 100 011 011 1 1 1 321 333222 111321 PAPQP qqqQ qqAIqqAI qqAI AI A / / )(detdet 11 1- 15 10 11 ) 11 01 ( 11 10 01 11 ) 11 01 ( 01 11 ) 1 0 ( 0 1 1- 1 0 1- 01 21 1 1 1 1 21 22121 111 21 2 PAPJQP qqQ qqqqAI qqAI AIA )(detdet 12 1. 1- 1 u(t)uc(t) uR(t) ,uC(t) )(tu C 1- 1 )t (ut)t ( i C )t (u)t (u)t (Ri t )t ( i L C C d 1 d d )t( i Ct )t(u L )t(u L )t(u )t( i L R t )t( i C C 1 d d d d )t (u RCt )t (u )t (u L R )t (u L R )t (u L R t )t (u R C CR R 1 d d d d 13 1- 1 )t (u L R )t (u )t (u RC L R L R t )t (u t )t (u C R C R 00 1 d d d d 10 0 R 1 10 0R 10 0R 1 PP xx CC R C R C u i u u u u , u i )t(u )t(u tu C R C 10)( 14 2. uDDxCDxC uDxCDxCyy uDBxCBxA uDxCBxAuBxAx 2122111 2221111 2122111 22211111111 )( )( u B DB x x A0 CBA x x 2 21 2 1 2 211 2 1 uDD x x CDCy 21 2 1 211 S2S1 1 2 1 u 1 22 15 3. 3322111 3333222211111 xCyxCyxCy uBxAxuBxAxuBxAx 32 32 S1S2S3 (1) 111 2222 2211111111 xCyy uBxAx xCBxAuBxAx 2 1 1 2 2 1 2 211 2 1 x x 0Cy u B 0 x x A0 CBA x x 16 4. 3322111 3333222211111 xCyxCyxCy uBxAxuBxAxuBxAx 32 32 S1S2S3 222 222112 1122222222 2211111111 )( xCyy uBxAxCB xCuBxAuBxAx xCBxAuBxAx 2 1 2 2 1 212 211 2 1 x x C0y u B 0 x x ACB CBA x x 2 (2) 17 5. 3322111 3333222211111 xCyxCyxCy uBxAxuBxAxuBxAx 32 32 S1S2S3 111 33333333 3322222222 2211111111 xCyy uBxAuBxAx xCBxAuBxAx xCBxAuBxAx 3 2 1 3 3 2 1 3 2 1 x x x 00Cy u B 0 0 x x x A00 CBA0 0CBA x x x 1 3 322 211 (3) 18 2- 1(1) )tsin(tsin tsin)tsin( e tsinetcosetsine tsinetsinetcose se)t ( s s sss s sse)t ( t ttt ttt t t 0 0 2 222 222 11 2 1 111 60 2 3 2 3 2 3 60 2 3 3 2 2 3 3 1 2 3 2 3 3 2 2 3 3 2 2 3 3 1 2 3 1 11 1 1 11 1 AIL AIAIL A A 19 2- 2(1) tttt tttt tttt tttt tt e.e.e.e. e.e.e.e. eeee eeee ee)t ( )(detdet 55 55 55 55 1 1 1 21 251250251251 250250250251 555 5 4 1 50 01 51 11 65 10 11 15 4 1 11 15 4 1 51 11 51 051 65 1 PP PAP QP Q AI A A 20 t ttt tttt t tt tt t t t t e eee eeee tataet ee ee e e e e )t (a )t (a detdet 3 3 33 10 3 3 3 11 2 1 1 0 21 0 4 1 4 1 30 11 ) 4 1 4 1 ( 10 01 ) 4 1 4 3 ( )()()( 4 1 4 1 4 1 4 3 31 11 1 1 31 0)3)(1( 30 11 2 1 AI AI A A 2- 4(1) 21 )()( (0), 5 2 )( 12 10 00 1 txt- tx xtx, xx 2- 5 )()( 11 txt- tx )()()()( 1100 txt- ttxt- t )()0( )()()0()0( )()()0()0( 11 11 11 tx- t txt- t- tx txt- txt- s s sss s s 2 11 2 1 12 1 2 1 1 AI tt tt tt tt ee ee ee ee txt 2 2 2 2 1 23 3 3 )69( 3 )39( )()( 2 3 2 1 3 1 2 3 2 1 3 2 2 3 1 1 3 1 2 3 1 1 3 2 )2)(1( 2 11 ssss ssss ss s s 3 )2( 3 )(2 3 )( 3 )2( 22 22 11 tttt tttt eeee eeee s)t (AIL 22 tt eet BA Cx Cx xBAxx )( (0) 2- 7 CICICx xBAxBCCACx Cx BA BABABA BA 00 (0) )( )( ee eeeeee dt d eet tttttt tt 23 2- 11 t tttt tttt t tttt tttt t e eeee eeee e)t ( eeee eeee ss s ss ssss s set s s sss s s 2 1 1 2 3 2 1 2 3 2 3 2 1 2 1 2 1 2 3 11 2 3 2 1 2 3 2 3 2 1 2 1 2 1 2 3 3434 3 34 1 34 4 )( 3 14 34 1 43 1 33 33 33 33 22 22 111 2 1 1 BCH LAIL AI A A 24 2- 17 )k( . . )k( . )k( . . T T T T T de .T e t s ss s s se t uxx BH G LLAIL T A AT A 10 0050 10 101 1 10 0050 2 1 0 0 2 10 101 10 1 10 1 1 0 11 0 1 22 0 2 1 1 111 25 3- 1(1) nrank c c 1 00 11 Q AbbQ 3- 1(2) nrank c c 3 804020 4122312 060401 Q BAABBQ 2 3- 2(1) 3- 2(2) nrank O O 2 24 11 Q cA c Q nrank o o 3 141 202 021 101 010 001 2 Q CA CA C Q 26 3- 3 3- 5 1ab 2 1 11 1 11 : rankrank bab a co oc QQ cA c QAbbQ ,bbx0 22212 0 11 c 7 3- 6 nrank c c 3 240100 101010 402101 173 2 Q HGGHHQ3- 11 3- 12 cbA T 123 0 1 1 200 010 000 0 1 1 011123 1 2 3 200 010 000 200 010 000 T T T TT 27 3- 13(1) u, aaa nrank cc 1 0 32 10 1 0 32 10 45 25 10 1 55 24 55 24 01 13 105 22 13223 20 01 2 105 22 1 1 2 1 210 2 xxPbbPAPA PppP AI QABBQ 1 3- 14 xyxx cPcPbbPAPA PppP AI cA c Q 1 10 3 0 21 50 10 3 0 21 50 21 11 3 1 11 12 11 12 14 11 01 12 2552 11- 2-3 14 11 11 1 1 2 10 2 u, aa o 28 3- 15 321 1 1 1 1 2 010 0 0 1 300 031 120 010 0 0 1 300 031 120 010 031 103 610 1101 600 931 100 310 010 031 103 931 100 310 010 031 103 32 310 1131 603 xxxxy xx cPcbPb APPA PP QbAAbbQ cc cc cc , u, rank cc 29 3- 16 321 1 1 1 1 2 001 0 1 0 201 021 010 001 0 1 0 201 021 010 412 201 100 452 100 010 001 120 012 001 120 012 412 201 100 001 120 012 32 252 120 012 xxxxy xx cPcbPb APPA PP Q cA cA c Q , u, rank oo oo oo oo 30 1.1- 1 u(t)uc(t) )(tu C 1- 1 . u u , u i C R C xx 1 PPPxx 31 2.S2S1 22222 222222 11111 111111 uDxCy uBxAx uDxCy uBxAx S S uDDxCDCy u B DB x A0 CBA x uDxCy uBxAx uDDxCDxCuDxCDxCy uDBxCBxAuDxCBxAx 21211 2 21 2 211 22222 22222 212211122221111 212211122221111 1122 )( )( yyuyuu 32 2.S2S1 22222 222222 11111 111111 uDxCy uBxAx uDxCy uBxAx S S tttt tttt eeee eeee 22 22 2 222 3. 4. A tt eet BA Cx Cx xBAxx )( (2)(0) (1) 33 3. tt eet BA Cx Cx xBAxx )( (2)(0) (1) (2)(0) 0,)( (1) (1)( 00 CICICx Cx xBAxBCCAx Cx BA BA BABA BA ee teet eeee eet tt tttt tt 34 31 20 AA tttt tttt eeee eeee 22 22 2 222 4. A 10 01 2 222 0 22 22 tttt tttt eeee eeee t 35 5. 4 3 2 1 4 3 2 1 4 3 2 1 0300 5000 00 01 00 20 3000 1300 0030 0013 x x x x y u x x x x x x x x 2 4 1 3 2 4 1 3 2 4 1 3 0003 0500 00 00 20 01 3000 0300 1030 0103 x x x x y u x x