自動(dòng)控制原理部分習(xí)題參考答案胥布工

1、自動(dòng)控制原理?局部習(xí)題參考答案第1章1-4有差系統(tǒng)。1-5接線端1接地，2與4相連，3接地，5不需連接。1-8(1)略；(2)無(wú)差系統(tǒng)。第2章2U0(s)R1R2C1C2S(R1C1R?C2)s 1Ui(s)R1R2C1C2s2(R1C1R1C2R2C2)s 112-4G(s) =H2(s)=-R2-其中Qi(s)(R1C1s 1)(R2C2s 1)阻)。2-5 6(司=旦聳=-R2，其中，R和R2分別為在各自Qi(s)R1R2C1C2s2(R1C1R2C1R2C2)s 1工作點(diǎn)的參數(shù)(液阻)。2-1 (a)G(s)(b)G(s)U(s)UC2s(c)G(s)Uo(s)CI_1.1.LsLCI

2、C2S2CIC2C1s C2s2R2R3C1C2s (R2CIR3C2 R3CI)S12-22-3(d)(a)(b)G(s)G(s)G(s)Ui(s)Uo(s)Ui(s)Yo(s)Yi(s)_Yo(s)F(s) (s)G(s)RICISR12C1C2s2(R1C1R1C2)s 1R1C2s(&耳1k1k2f1f22-skk2f1f22- sk1k2(色足全片1k1k2k11Ms2(f1f2)s klM (s) (l2J1J2)s2(l2V -2)s(lN2)N1R和R2分別為在各自工作點(diǎn)的參數(shù)(液22-6dP(t) .Dx0、2g P0Ti2+T0P(t) =Q(t)ix(t)，其中，T=om

3、D,，2gp0 , T0 =- dtP0符號(hào)已略去。,Ti=也,RT2-7歐項(xiàng)而頸訂，其中，軻W)1Tt _ t一RC一丁R為向外散出的熱量與爐內(nèi)外的溫差成正比的比例系數(shù)，即Rq(t)=印)。2-8RS=T2S2+(2T2：K0T/1)s+1和蒙=T2S2+(2：0K+1)s+12-9H(s)_N1KK2K3%_Ur(s) N2CTms2N2Cs N1KK1K2K3Km2-10一、R1C1s 1U2(s)R2C2s 1 Gg(s)= , Gcs)= 2i2 2RC1s(2)搭 F 鬣其中1K =，.=C1R1C2R2, .2C1C2R1R2, TK12R2C1C2-K2KpRC1(TmC2R2

4、) K1KpKmC1C2&R2U1(s)RC2sR1C1K1KmR2C2KKmRCK2K1Km2-112-122-132-14T2T3(a)(b)(c)(d)(e)KKpKmRCQ2(RTpRTm-K2KpTmR2)丁R2CQ2TpTm,T4KKpKmKKpKmLG(s)=1+3e頊4e ; (2) LG(s)】=1+t+e.2G(s)=2; (2) G(s)=弋了2s2(s a)s(s22)G1G2Y(s)/R(s)二1 G1G3G2G3-G2G4-G1G4G-G2Y(s)/R(s)二-1 -G2G3G1 G2Y(s)/R(s) =-1-2-1 GG2G1G2一22G1G2G3G4Y(s)/

5、R(s) =2122 342GQ4G1G3G4G5 G G2G3G4G7 GQ2G3G4G6G4-H1G1G2G4H1G2G4H2G2G3G4G1G2G3Y(s)/ R(s)=-H1G2G1H1G2H2G2G3v,、GG2G3G4R(s) G2G3G4。HG1)D1(S) -6364(1 HQ1)(1 H2G2)D2(S) Y(s)=(1 H1G1)。H2G2)。H3G4) G1G2G3G4H442一G(s) =C(sl - A)B d =U(s)s32s2132-15 (1)(2)2-16 (a)(b)2-17 (a)(b)其中G1G2G3G1G4Y(s)/R(s)=1 G1G2G3G1G4

6、H2G2G3H1G1G2_H1H2G1G2G4當(dāng)1 +H1G1G2=0時(shí)，輸出Y(s)不受干擾信號(hào)D(s)的影響。Y(s)G1G2Y(s)-H1G1G2G2G3-=- - =-R(s) 1 H1G1G2G1G2D(s) 1 H1G1G2G1G2Y(s)G1G2G4G2G4G3G4Y(s)G4= R(s) 1 G2G4G3G4D(s) 1 G3G4G2G4G(s)G(s)2-18Y(s) _G1G2G3G4G5_R(s)一1 H1G3H2G2G3H3G3G4H4G1G2G3G4G5_Y(s) R(s)G1G2G3G4G5G6G3G4G5G6G7GQ6G8(1 G4H2)-HG6G7G8(1G4H

7、2)=1 (LL2L3L4L5)(L1L2L1L3L2L3L2L5)-LL2L3=1 G2H1G4H2G6H3G3G4G5H4-G8H1H4G2G4H1H2G2G6H1H3G4G6H2H3-G4G8H1H2H4- G2G4G6H1H2H3一01001X1(t)-010010X2(t)+00001X3(t)0-24-50-35-10/4 (t)-1u(t)x；(t)1x；(t)x3(t)*(t)_y(t) = 15 17X1(t)3 0X2(t)X3(t)X4(t)2-193-1,八 c /、5(10s 1)1(1)GF(s) =, G B (s)=s(100s +1)(s +1)(0.5s十1

8、)0.1s +15(10s 1),GD(s)-s(s 1)(0.5s 1)GL(s):s(100s 1)(s 1)(0.5s 1)(0.1s 1)5(10s 1)(0.1s 1)TR(s) =、,Q o5s565.05s4160.65s3101.6s251s 55、15s565.05s4160.65s3101.6s2s(2)TRE(s)=頑礦-Gp(s)H(s) T (s)-，-1 GL(S) 5s565.05s4160.65s3101.6s251s 5(3)&s) =5s5+65.05s4+160.65s3+101.6s2+51s +554325s 65.05s160.65s101.6s51

9、s 5-5(100s 1)3-2 1系統(tǒng)在右半s平面無(wú)根，系統(tǒng)穩(wěn)定；2系統(tǒng)是臨界穩(wěn)定的；3系統(tǒng)不穩(wěn)定;63-33-4(4)系統(tǒng)不穩(wěn)定有四個(gè)對(duì)稱坐標(biāo)原點(diǎn)的根s1,2=2土j,s3,4= / j。(1) KA25 ; (2) 0K8 ; (3)K不存在；d0(4) K?0。(1) Kcr=119 ,% =而;(2) 11 CK 353-53-6 301倍。3-73-83-9er(Q)=理sEr(s) =0 ,ed(o)=9%sEd(s) sR(s)ee(二)=lim - =20s)01 GL(s)T1- T2T10, T20,一：K ：12；03-103-113-123-13T1T2.1e(二)=

10、e(二)ed(二)=一6Js2er(二)=lim s2-s、，Js Ks K2SK =s、s：*K (2)STGL(S)一1；(2)-as2s as K3-143-153-163-173-183-193-20ed(二)=如(二)軟(二)=。；(3)ST-Kh2Ts as KhSHST1(a)(a)(3)(b)GL(S)K.T,-L =1 ; (2) SK2TK1K2h =0.01 ; (b) h =0.364 ; (c)S：=3；( b)ST =-2.35 ；Si=0.65; (c)(c) S： =-0.99-500,c、- - ；(3)s2s 500h =0.099 ;SK=0.03S；s(

11、s 1)s(s 1) 500SY1*SK2丫1()=。；Y*)1 K2H23一、=#0 ； (2) 182H1KH,H2 =K2丫1()=0 ；丫1(%)=#0。5Gd(s)1 Gc2(s)Gp2(s)Hm2Gff(s)=_2絲 典GC2(S)GP2(S)GR(S)按擾動(dòng)Mc(s)補(bǔ)償?shù)那梆佈a(bǔ)償方案。 方案(b)。(s)4-2 0.98分鐘。4-3 K0=2,K1=0.54-4T(s)= 10 s 2084-5-e-粉c 1一t*(1)y(t)=2.5 1 - sinQdt +E) =2.5. 1.15e sin(1.73t + ) j一、IT PJT.一，、(2)tr = j j一41 21

12、(s), tp=田1.82(s)3 ts =ft3(s),(A=0.05); 5%=e農(nóng)Y ： X100%=16.3%。財(cái)n(3)K1 =2.54-6八,、553.66GL(s)s(s+21.46)4-74-94-10K1=329 ； K2=3 ; a=18.13。(1) K =25 ,切n=25；(2) 60 / min；60K(1+16.32%) =69.8次/mino圖(a):(1)。=0.25，缶n=2 ,ess=0.25；(2)a =0.5 , esr=0.75；(3)a =0.25 ,K=4圖(b):(1)匚=0.25,con=2 ,ess=0.25 ； (2)a =0.5 , e

13、ssr=0.25 ；(3)a =0.207 ,K=2nssssi4-11(1)圖(a):需要5個(gè)單位時(shí)間；圖(b):需要0.455個(gè)單位時(shí)間；(2)圖(a):擾動(dòng)對(duì)溫度的影響為0.1,且一直保持；圖(b):擾動(dòng)對(duì)溫度的影響為0.00909。4-124-13況=0.167 , 6% =19.46% , ts=0.8025(s)。(1)穩(wěn)態(tài)快差ess為0；(2)% =3 ,=1.2。4-15(1)K=1/T, 0T1/2 ; (2) ess=1/K ；(3)K0=1/K。Kv4-164-17ess=1.4(1)essr = ；(2)essd1=2 ；(3)essd2=0。4-184-21K =10

14、 , v =1 ,T=2。6% =16.32%, ts=6.28(s)(A =0.05)。第5章5-2點(diǎn)(0, j V2)和(-0.42, j0)在根軌跡上，點(diǎn)(,j2)不在根軌跡上。5-55-90 M ：: 3.14Kg=15-100 : Kg0.226g5-115-12a =40.16 Kg1時(shí)穩(wěn)定，K2T1+電1時(shí)不穩(wěn)定，?1曷71+叫=1時(shí)臨界穩(wěn)定虛軸上存在一對(duì)閉環(huán)共軸極點(diǎn)；7穩(wěn)定。6-13c Y芝54 具體數(shù)值取決于阻尼系數(shù) ,:大小，穩(wěn)定；d丫兇55.8 ,穩(wěn)定。6-141無(wú)；2無(wú)6-15相頻特性迅速下降，穩(wěn)定裕度大大降低6-16 1 0K16.3 ; 2 0K0 ;三種情況下，穩(wěn)

15、態(tài)誤差均為；。6-171 % &1rad/s,新充34按漸近特性計(jì)算；2 8% =30% , ts8s；3包2&3.2rad/s ,氣&13按漸近特性計(jì)算，不穩(wěn)定。6-19 6%充18% , ts&1.1s仿真結(jié)果：8%關(guān)3%；ts2.1s6-20 V &70七 ?6.6/ts=66rad/s6-21 1 coc&3.2rad/s ,丫18；2 Mr由3 , co4.8rad/s/s；36% &60% , ts&5.8s；&%整60% , tsR=5.6s6-22精確頻率特性說(shuō)明閉環(huán)系統(tǒng)不穩(wěn)定，有兩個(gè)極點(diǎn)落于右半s平面6-23 0 ：:K 0時(shí),aak(k -2) -ak(k -1)(a -1)2K2時(shí)，0?Ts8；K 2K?2時(shí)，0織ln-。K -2(3)8-148-158-168-188-190 _Ts：二。1 -e七 一K一 W 一,且K a二XX；X(c)|(乂)=也10j,Xd，其中,XJ9-1 (a)f(x)M ,-M ,x 0 x：0M , x _d(b) f (x) = kx, x d；M ,(c) f(x)=0,-M ,-Mf(x)=M-Mx匚x：. ： ；(d)x :x d, x0 x : d , x 0 x -d, x : 0 x ： -d , x :0_k(x-.：)f(x)=0-k(x + A)x二xA ；x _盤(e)f