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《自动控制原理》答案.pdf

1、 1 1-1 1-2 1-3 1-4 1 C n * n u n u 2 I * n u 1 I 0 3 I ct u d u n u * n u n u 2 C ct u d u n u 2 I 0 3 I ct u d u 3 C ct u d u 1-5 1-4 1 * n U 2 7 1-4 1 2 3 4 5 6 7 8 9 0 0 r u c u e u d u 2 0 0 c u r u c u r u e u d u 2 c u r u c u 1-6 1 6 1 6 1 2 3 4 5 6 7 8 “ ” “ ” “ ” “ ” “ ” “ ” gk u gg u f u “

2、 ” “ ” 0 f u gg u u gg u f u u =0 “ ” “ ” = - 0 =0 f u gk u u gk u f u u “ ” “ ” “ ” = “ ” = f u gk u f u gg u 1-7 1 7 1 7 U =- f u f u 1 u 0 1 R R + + 0 r u f u r u f u 1 u 2 u + 0 0 f u r u f u 1 u 2 u 2 2-1 2-1 a b RC c d RC r u( t ) c u( t ) 2 R 2 C c u( t ) + + r u( t ) 1 C 1 R 2 R 2 C c u( t )

3、 + + r u( t ) 1 R 1 C a) r u( t ) 1 R + c u( t ) b R 2 R 2 C r u( t ) 1 R + c u( t ) b R 2 R 2 C 3 C 3 R c) d) 2-1 (a) 2 22 1 2 121 212 12 12 1 () () 11 () ( ) c r R Us sC R CC s C 1 Us RRCCsCC RR sC sC + + = = + + + Ts (b) 2 2 21 2 1 21 1 2 2 2 1212 11 22 12 12 12 1 () () () 11 () ( ) 1 / c r R Us

4、sC RR CC s RC R C s1 Us RRCCs RCRCRCs RR sC sC + + = = Ts + + +(c) 1 2 2 () () 1 c r Us Us R R sC = + 22 12 () 1 () () c r Us RCs Ts Us RCs + = (d) 1 2 2 () () 1 (/ /) c r Us Us R R sC = 2 122 () 1 () () 1 c r Us R Ts Us RRCs = + 2-2 2-2 LC RLC i u( t ) o u( t )i u( t ) + o u( t ) 1 R L C 2 R c u( t

5、 ) + + i u( t ) + o u( t ) 2 L 1 C c u( t ) + + 1 L 2 C + a) b) 2 2 a) LC b) R LC (a) 11 22 12 2 () () () () () () () () () iLc cLo cL L oL Us s LIsUs Uss LIsUs sU I s I s sU I s =+ =+ = = 0 42 1212 11 22 12 () 1 () () ( ) 1 i Us Ts Us LLCCs LCLCLCs = + + +(b) 11 2 12 22 () () () () () () () () () i

6、Rc cRo cR R oR Us RIsUs Uss L IsUs sCU I s I s UR Is =+ =+ = = 0 2 2 11 2 1 () () () ( ) i Us R Ts Us L C Rs RRCLsRR = 2 + + 2-3 T R 60 0.2T R 10000e = 20 C C 00 0.2 0.2 0 10000 2000 ( ) TT R ee T =T 0 20 T = 36.6 930 RT = + 0 60 T = 0.0122 0.793 RT = + 2-4 2-4 a b F(t) 1 x( t ) m 1 f 1 k 2 k 1 x( t

7、 ) 2 x( t ) m F(t) f k 1 x( t ) M 2 x( t ) F(t) 2-4 (a) 2 112 12 2 22 12 2 1 2 1222 () () () () () () () () () () () () () () dxt dxt xt Mk f x t x t F t dt dt dxtxt dxt dxt dxt kf x t x t mF t Mm dt dt dt dt + = += = 2 2 2 2 2 11212 22 1212 2 1 ()() () () () () () () () () ()() () Ms X s ks X s X s

8、 f X s X s F s ksXs Xs fXs Xs msXs Fs MsXs msX += += = 2 1 22 () () ( ) ( ) Xs m sk sf FssM m sMmk sMmf + = +(b) 2 112 11 1 2 2 2 12 1 11 1 2 2 2 2 () () () () () () () () () () () () () () dxt dxt xt mf k x t x t F t dt dt dxt xt dxt 2 2 f kxtxt kxt Ftm kxt dt dt + = += = 2 11121 12 2 121 122 2 12

9、2 () () () () () () () () () () ()() () () m sXs fsXsXs kXsXs Fs fsXs X s kXs X s kX s Fs msXs kX s += += = 11 1 2 32 11 22 1 () () ( ) Xs fskk Fs mfs mk ks kfskk + = + 1 2 i 2-5 2-5 2 u d u( t ) i u( t ) 21 ( ) 2.34 cos ( ) d ut U Kut = 1 K (1) 1i Ku( t ) 3 5 = (2) (3) i u( t ) c M( t ) 1 (t) 2-5 (

10、1) 212 ( ) 2.34 0.82 0.57 ( ) 35 2.34 1.168 0.57 ( ) di ut U Kut U Kut = = 1i (2) (2-5) (2-6) (2-17) 2 12 2.73 ( ) 1.34 ( ) (1) () () () () ( 2 5 ) () () ( 2 6 ) () () () () ( 21 7 ) di aaed ma c U Us K UUs s LsI s RI s C s U s Ms CIs Js s f s M s M s 1 11 = += = += 21 2 12 2 12 () ()/ / / / cc MsMs

11、 irr JJJi fffi = = =+ =+ i(3) + () c M s 1 () s () i Us 2 U 2.73 s Js f + m Ls R C + 1 e C () M s 12 1.34KU ()0 Ms = () 0 Ms = c c 1 32 212 () 1 2.73 1.34 ( ) ( ) ( ) mm i s CU KCUsUs JLs JR fLs fR CCs = + + +m e + ()0 i Us = 1 32 2 () 1 2.73 ( ) ( ) ( ) ( ) mc s CU Ls RM s JLs JR fLs fR CCs = + + +

12、m e 1 32 2 () 1 2.73 ( ) ( ) ( ) ( ) mc s iC U Ls R M s iJLs iJR ifL s ifR iC C s = + + + m e 2-6 2-6 12 CC1 F = 1 R1 6 0 k = 2 R 220k = 3 R1 k = 4 R1 0 0 k = cr U( s ) /U( s ) r u( t ) 1 R + c u( t ) 2 R 2 C + 4 R 1 C 3 R 2-6 11 34 12 12 () () () () , 11 / c r US Us Us US R R RR sC sC = = +2 141 2

13、1 21 1 2 2 131 2 () () () 1 () ( ) ( ) () () () cc rr UsUsUs R RRCCs RCs RCs Ts UsUsUs R RCs + + = 22 12412 141 242 4 132 22 237.5 625 RRRCCs RRCs RRCs R ss RRCs s + = 2-7 2-7 1 2 1 1 K r u( t ) h(t)a R a L + () a ut + + (t) (t) r Q 1 2 + + S U c Q () ht 0 R 1 R () r ut 0 R S U 2-7 (2-8b) (2-58) F (

14、) f ut f K 10 2 11 1 11 () () () () (1 ) ( )( 2 () () () (2 58) () 1 () () rf d d lm m e ff UsUs Us RR Us TT s T s s b C s Ks s K Hs sT s Hs KUs = + = = = + = 8 ) 10 1 2 0 1 2 2 2 a l a a m em L T R JR T CC kH K k FH T k = = = = () f Us () Hs () r Us 1 1 Ks 1 f K 2 1 (1 elm m CTTs Ts) + + 1 0 R R 1

15、1 1 K Ts + 2 1 () () ( 1 ) ( 1 ) f rl m m KK Hs Us sTs TTs Ts K = + + + 11 10 f e KR K KKRC = 2-8 2-8 R(s) 1 G C(s) 2 G 3 G 4 G 1 H 2 H R(s) 1 G C(s) 2 G 3 G 4 G 1 H 2 H + + 3 H 2-8 (a) 3412 1 1234 232 () () 1 GG GG H Ts GGGG GGH + = + (b) 1234 231 342 12343 () 1 GGGG Ts GGH GGH GGGGH = + 2-9 2-9 (1

16、) 1 C(s) T R(s) = (2 ) 2 C(s) T( s ) N(s) = R(s) a C(s) N(s) e b c d g h f 2-9 (1) 1 Ta b c d = 1 1 = 1 Le = 2 Lb =g h 3 Lc = 1231 3 11 LLLL L eb gc he c h = + = + + + + 1 () () () 1 C s abcd Ts R s e bg ch ech = + + +(2) T 1 f c d = g h 1 1 e =+ 1 Le = 2 Lb = 3 Lc = 1231 3 11 LLLL L eb gc he c h =

17、+ = + + + + 2 () ( 1 ) () () 1 Cs fcd e Ts Ns ebgchech + = + + + 2-10 2-10 R(s) C(s) 1 1 1 1 G 2 G 3 G 4 G 1 1 1 1 2-10 11 TG G = 3 4 TG G G = 1 1 = TG G G = 1 1 = LG G = 22 LG G = 31 2 4 LG G G 1 1 = 22 TG G = 2 1 = 31 2 4 42 1 3 11 3 4 = 42 1 LG G G 3 = 51 LG G = 2 ) 13 24 12 3 4 1( 1 GG GG GG G G

18、 = + + + + 13 24 123 124 13 24 12 3 4 () () () 1 ( 1 ) GG GG GGG GGG Cs Ts RsG GG GG GGG + = + 2-11 2-11 a) b) 2-11 (a) 1 1234 TG G G G = 1 1 = 13 4 LG G = 22 3 LG G H = 31 2 3 LG G G H 2 1 = 41 2 3 4 3 LG G G G H = 34 1231 232 12343 1 GG GGGH GGH GGGGH = + + + +1234 34 1231 232 12343 () () () 1 GGG

19、G Cs Ts RsG GG G G HG G HG G G G H = + +(b) 1 1234 TG G G G = 1 1 = 25 2 3 TG G G G = 4 1 LG H = 22 LG H = 32 3 3 LG G H 21 1 GH =+ 11 1 2 = LG G G G H = 55 2 3 4 4 LG G G G H = 41 2 3 4 4 1 2 3 4 5 12 13 15 11 22 233 12344 23454 1212 12313 1234514 1 1 LLLLLL LL LL L GH GH GGH GGGGH GGGGH GGHH GGGHH

20、 GGGGGHH = + + + =+ + + + + +2341 5 151 () () () () GGG G G GGH Cs Ts Rs + = 2-12 2-12 0 0 2 R( s ) 1 C( s ) 1 R( s ) 2 C( s ) 1 C( s ) 1 R( s ) 2 C( s ) 2 R( s ) 21 C( s ) /R( s ) 5 G( s ) 5 G( s ) 1 R( s ) 1 1 C( s ) 1 G( s ) 1 2 G( s ) 1 H( s ) 2 R( s ) 1 2 C( s ) 3 G( s ) 1 4 G( s ) 6 G( s ) 5 G

21、( s ) 2 H( s ) 2-12 112634 () () () () () T GsGsGsGsGs = 1 1 = 2154 () () () T GsGsGs = 2 1 = 1121 () () () LGs Gs Hs = 2342 () () () LGs Gs Hs = 121342123412 1 ()()() ()()() ()()()()()() GsGsHsGsGsHsGsGsGsGsHsHs = + + + 12346145 2 1 121342123412 () () () () () () () () () () ()1()()() ()()() ()()()

22、()()() GsGsGsGsGsGsGsGs Cs Ts R s GsGsHs GsGsH s GsGsGsGsHsH s + = + 5236 () () () () Gs GsGsGs = 3 3-1 5 G(s) s = () () 5 () () 1 () 5 Cs Gs Ts Rs Gs s = = +5111 () ()() 55 Cs TsRs ssss = = = + 5 () 1 1 t t T ct e e = = 0.2 T = 3 0.6( 0.05) s tT = = 4 0.8( 0.02) s tT = = = 3-2 5 G(s) s(0.2s 1) = + 2 () () 2 5 () () 1 () 5 2 5 Cs Gs Ts Rs Gs s s = = + +2 25 n = 5 2 = n 5 n = 0.5 = 2 3 1 3 % 100% 100% 16.3% ee = 2 43 3 0.48 45 1 r n t = 2 23 0.73 15 1 p n t = 3 1.2 ( 0.05) s n t = = 4 1.6 ( 0.02) s n t = = 3-3 3-3

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