自动控制原理孙炳达课后答案1-4章.pdf

1.18c SM_ 1 Q 2 Q f i * c() * c() * c 1. 4.11. 4.11. 4.1 M 220 1.19 T () ( ) 1.4.5 - 1.4.5 1.3 TR) o Tx6 ()00 ioi 1.4.51.4.5 oii TG o TX i SMTG 1.4.6 1.4 1.4.4 1.5 (a)(b)(a) 110 v(b) (a)uKSM G f i (a)110V (b)uK f iG 0 f i (b)(b)110V 2.1(a) 2 121 2 () ooi d xdxdx mfff dtdtdt () (b) 12121 () oi o dxdx f KKK K xK f dtdt (c) 121 () oi oi dxdx fKKxfK x dtdt 2.2 2 f 0 x i x 2 K 1 K 1 f 1 u 0 u 1 C 2 R 2 C 1 R x A B (a) 22 212121122 2 1212112212 1 1 2 2 1 1 1 ( )()1 1 ( )()1 1 1 o i R UsC sR R C C sRCR C s U sR R C C sRCR CRC s R C s R C s R C s (b)A 221 ()()() ioo io dxdxdxdx fKxxf dtdtdtdt 1 B 11 () o dxdx fK x dtdt 2 12 221 ()() io io dxdx fKxxK x dtdt 3 3x2 22 121121212 22 121221212 ()() ooii oi d xdxd xdxf fffff fff xx K KdtKKKdtK KdtKKdt a(b) C sC s ( )()1( )()1 1 1 ( )()1( )()1 212121122212121122 1 1 C sR R C C sRCR C sC sR R C C sRCR C s 212121122212121122 0 x x 212121122212121122 1 1 1 2 1 1 1 ( )()1( )()1( )()1 1 1 1 C sR R C C sRCR C sC sR R C C sRCR C s 212121122212121122 ( )()1( )()1 1 R C sC s 1 1 C s R R 111122 11 11 ,KKfRfR CC 2.3 0 2 K QP P 2.4 2 2 42 ( ) 32 ss G s ss 12 12 ( )1( )2 12 tt g tLtee ss 2.5 12 1 1 1 11 2 2 2 2 212 (1) (2) (3) (4) i hh q R d h Cqq dt h q R d h Cqq dt 22 2 1122112221 ( ) ( ) ( )()1 i HsR G s Q sRC R C sRCR CR C s 2.6 ( )10 ( ) ( )35 C s G s E ss 2 ( ) 41 H s s 2 ( )10 ( )100(41) ( )1( )( )122325 C sG ss R sG s H sss 2 2 ( )1010(12235) ( )1( )( )122325 E sss R sG s H sss 2.7 12 001100111 01 0 0 0 0 1 ( )()1 1 ( ) 1 o i R UsR C RC sR CRC sC s U sR C s R C s R C s 2.81 0 30180 / 11 330 180 m E KVrad ( )( )H sH s ( )( )( ) ( )10 ( )100(41)( )10 ( )100(41) ( )1( )( )122325( )1( )( )122325 ( )10 ( )100(41)( )10 ( )100(41)( )10 ( )100(41) ( )1( )( )122325( )1( )( )122325( )1( )( )122325( )1( )( )122325( )1( )( )122325( )1( )( )122325 1122112221 ( )()1( )()1( )()1( )()1 1122112221 ( )()1( )()1( )()1( )()1( )()1( )()1 1122112221 4141s41414141 2 ( )10 ( )100(41)( )10 ( )100(41) ( )1( )( )122325( )1( )( )122325 2 ( )10 ( )100(41)( )10 ( )100(41) ( )1( )( )122325( )1( )( )122325( )1( )( )122325 2 2 ( )10 ( )100(41)( )10 ( )100(41)( )10 ( )100(41) ( )1( )( )122325( )1( )( )122325( )1( )( )122325 2 2 ( )1010(12235)( )1010(12235) ( )1( )( )122325 ( )1010(12235)( )1010(12235) ( )1( )( )122325 12 3,2KK 2 m T ( ) ( )1 m am Ks UsT s m K 1 ()/rad sV t K 1 /()Vrad s 2 23 01230123 1 1 1 o mmt i mm TK K K K ss K K K K KK K K K K 2.9 0123mmmm 1 1 1 mmtmmt 2 2 1TKTK 2 TKTK1 1 mmtmmt 2 1 1 ssss mmtmmtmmt K K K K KK K K K KK K K K KK K K K K mmtmmtmmt TKTKTK mmtmmtmmtmmtmmtmmt ssssssss mmtmmtmmt 01230123mm01230123 23mmtmmt2323 K K 232323232323K Kmmtmmtmmt K K mmt ssss K K K K KK K K K KK K K K KK K K K K 012301230123 mmtmmt2323 ssssss mmtmmt2323 2.10 3.10.62/ n rad s%9.5% 2 3 2 ,2.5 1 ps n n tsts 2 8 ( ) 2.44 s ss 3.2 2 44 ( ) 64(0.8)(5.2) s ssss 5.2 1,4 0.8 1 33 1.253.75 s tTs 4111.140.17 ( ) (0.8)(5.2)0.85.2 C s ssssss 0.85.2 ( )1 1.140.17 tt c tee 3.30.434.3/ n rad s 2 2354 ( ) 27.41177 s ss 3.4 15%0.520.84.6/ n rad s 1 2 11 ( ) (1) t K s sK K sK 2 1 21.2 n K0.18 t K 2 1 0.73 0.3 ,0.54 ,1.25 1 drs nn n tststs 3.5 123 3.6 1 22 j 3j 45j 3.7 1 1,2.5K 3.8 nnnn drsdrs 0.3 ,0.3 ,0.3 ,0.3 ,0.3 , drsdrsdrsdrsdrs 0.3 ,0.3 , nnnn 0.3 ,0.3 ,tsts 1111 (1)(1) 1111 (1)(1) 11 (1)(1)(1) 11 0.3 ,0.3 ,0.3 ,0.3 , drsdrs 0.3 ,0.3 ,0.3 ,0.3 ,tsts drsdrsdrsdrs nn n drsdrsdrsdrsdrs 2 drsdrs 2 2 nnnnnn n nn1nnnnnn1nn 0.80.8 11 2 1 1n K K1 1 2 tststststststs drsdrs 3 3.9 114K 21sz 32 0.0250.2750.3750.6750zzzK4.8K 3.10 2 12(21) ( ) (1) s G s ss ,12 pva KKK 2 12(21) ( ) (24) s G s s ss ,0.5,0 pva KKK 3.11 0.75K0, 1.33 3.12 10.11/ n rad s%72.9% 3 3.2 ,30 ps n tsts 20.51/ n rad s%16.3% 3 3.6 ,6 ps n tsts 3.14 K K 12(21)12(21) ( )( )G sG s ( )( ) ss G s 3.15 1 2 212 (1) EN K s T sK K 1 10 ( )10, ( )10 , ssn ssn n te K n tte 2 21 TT 2 2 2121 (1)(1) EN K s s T sK K Ts 2 2 K K s T sK Ks T sK K 1 ( )10,0 10 ( )10 , ssn ssn n te n tte K 4 4.1 4.2sujv 112 ()()()(21)szspspk (2)()(1)(21)ujvujvujvk (21) 21 vvv arctgarctgarctgk uuu 1 xy arctgxarctgyarctg x y 2 2 (21) 2 vuvv arctgarctgk uuuv 2 2 2 2 (21) 2 1 2 vuvv uuuv arctgk vuvv uuuv 2 2 0 2 vuvv uuuv 22 420uuv 222 (2)( 2)uv 4.3 4.4 - 300- 250- 200- 150- 100- 50050100 - 200 - 150 - 100 - 50 0 50 100 150 200 Root Locus Real Axis 2150K 321d | 21| | 21 50| | 21 100| 9.6 5000 K 2nm9.6K - 108- 21- 21 9.6 Root LocusRoot Locus 4.5 1 2 (4) 420 b s ss - 9- 8- 7- 6- 5- 4- 3- 2- 10 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 Root Locus Real Axis - 8.5 2 30 (40) b s s - 40- 35- 30- 25- 20- 15- 10- 50 - 15 - 10 - 5 0 5 10 15 System: sys Gain: 13.3 Pole: - 20 - 0.0466i Damping: 1 Overshoot (%): 0 Frequency (rad/sec): 20 Root Locus Real Axis - 20 4.64.7 4.8 Frequency (rad/sec): 20 - 25- 25 Frequency (rad/sec): 20 - 12- 10- 8- 6- 4- 20