自动控制原理第四版习题答案教学适用

部分习题答案部分习题答案2-2(a)()()()(21txftxtxftxmooio-即：即：)t(xf)t(x)ff()t(xmi1o21o (b)t(xfk)t(xkk)t(x)kk(fi2o21o21 (c)()()()()(121txktxftxkktxfiioo+=+2-3(a)t(u)t(u)CRCRCR()t(uCCRRooo+2122112121(b)t(xkk)t(x)kfkfkf()t(xffooo2112211121+2-4(a)t(uR)t(uCRR)t(u)RR()t(uCRRi2i21o21o21 (b)t(u)t(u)RCRC()t(uCCRooo+122122（2-2题题2-4题）题）（仅供参考，不对之处敬请批评指正，谢谢！）（仅供参考，不对之处敬请批评指正，谢谢！）)()(2)(121tutuRCtuCRCiii )t(xkk)t(x)kfkf()t(xffiii21122121+=)t(u)CRCR()t(uCCRRii 22112121+=1听雨书屋2-5(1)运动模态：运动模态：t5.0e tettx5.022)(-(2)tsine23t5.0 tsine)t(x23t5.0332 (3)(1+t)e-tte)t1(1)t(x 2-6PQoQ22k 2-7y11.12F 2-8)(sinEeooodd 2-9)2s)(1s(2s4s(s)2 tt2ee2)t(dt)t(dc)t(k 2-10零零初态初态响应响应t2ee21)t(ct1 零零输入输入响应响应tt22e2e)t(c 总输出总输出tteetctctc221241)()()(（2-5题题2-10题）题）运动模态：运动模态：运动模态：运动模态：2听雨书屋（2-11题题2-15题）题）2-1125s23s12)1s4(100)s(R)s(C2 25s23s12)5s23s12(10)s(R)s(E22 2-12(a)sCR)10sCR)(1sCR()s(U)s(U1ooo11io (b)1sCR(RR)s(U)s(Uooo1io (b)1sC)RR()1sCR(RR)s(U)s(U22122o1io 2-132123o22113o21ioRRsCRsCCRRRR)s(U)s(U 2-141sTK)s(U)s(m1am 1sTK)s(M)s(m2am 2-1511132k3)1sT(skmm 3skt111i o iuouu 1u2uautum3mt32miokk26.31s)kkk31(sT26.31)s()s(3听雨书屋（2-17题题2-21题）题）2-17(a)3221GG1GG)s(R)s(C (b)21112121HHHG1)HH1(GG)s(R)s(C (c)22112231HGGHG1G)GG()s(R)s(C (d)3311332211321HGHGHGHGHG1GGG)s(R)s(C (e)232121123214HGGHGGHG1GGGG)s(R)s(C (f)121231HGG1G)GG()s(R)s(C 2-18(a)1212121HGGGG1GG)s(R)s(C 1212112123HGGGG1)HGG1(GG)s(N)s(C (b)434243421GGGG1GGGG)G1()s(R)s(C 43424GGGG1G)s(N)s(C 2-19与与2-17同同 2-20与与2-18同同 2-21(a)23112132123111134321HGHGHHGGGHGHG1)HG1(GGGGG)s(R)s(C 2311213212311123423HGHGHHGGGHGHG1HHGG)HG1()s(R)s(E (b)21212121GG3GG1GG2GG)s(R)s(C 212121GG3GG1GG1)s(R)s(C 4听雨书屋（2-22题）题）2-22(a)23234313543216HGGHGGHG1GGGGGG)s(R)s(C (b)9个单独回路：个单独回路：5654321545434363242121HGGGGGGL,HGGGL,HGL,HGL,HGL 1489568178568175654376HHGL,HGGHGL,HGGGL,HGGGGGL 6对两两互不接触回路：对两两互不接触回路：L1L2 L1L3 L2L3 L7L2 L8L2 L9L2三个互不接触回路三个互不接触回路1组：组：L1L2L34条前向通路及其余子式：条前向通路及其余子式：P1=G1G2G3G4G5G6,1=1;P2=G7G3G4G5G6,2=1;P3=-G7H1G8G6,3=1+G4H2;P4=G1G8G6,4=1+G4H2;91a61321cba41kkkLLLLLL1P)s(R)s(C(c)128.1539590)s(R)s(C (d)afchehgfchbgaf1)bg1(edabcd)s(R)s(C (e)adehcefgbcdehegcf1)eg1)(bca(adebcde)s(R)s(C1 adehcefgbcdehegcf1lehalehbc)cf1(le)s(R)s(C2 (f)fgdegf1)cicfdejcfdh()idegbbdejbdh(aegiaej)fg1(ah)s(R)s(C1 fgdegf1fjifdejfdh)s(R)s(C2 fgdegf1egiej)fg1(h)s(R)s(C3 5听雨书屋（3-1题题3-9题）题）3-1Tte1)t(hTT 3-2(1)10)t(k t10)t(h 3-2(2)t4sine425)t(kt3 )13.53t4sin(e451)t(hot3 3-3 (1)25.1s0125.0)s(2)16s)4s(50s5)s(22 (3)1s3(s1.0)s(3-4s917.2ts96.1t%478.9%26.0spn 3-5686.15.2z5.010066.1r2dn%99.17%s0133.6ts156.3ts45.1tspr 3-65.2443.1n 3-7311.0k44.1k21 3-8 (a)10n 系统临界稳定系统临界稳定(b)s51.7t%8.29%15.01ss1s)s(sn2 (c)s08.8t%3.16%15.01ss1)s(sn2 (b)比比(c)多一个零点多一个零点,附加零点有削弱阻尼的作用。附加零点有削弱阻尼的作用。3-9 (1)2.0es5.3t%09.35%101015k)1s5.0(s5)s(Gsssn (2)249.11r10z1010110k)1s(s)1s1.0(10)s(Gdn 1.0es3t%06.37%2sss 6听雨书屋（3-11题题3-20题）题）3-11劳斯表变号两次，有两个特征根在劳斯表变号两次，有两个特征根在s右半平面右半平面,系统不稳定。系统不稳定。3-12 (1)有一对纯虚根：有一对纯虚根：2js2,1 系统不稳定。系统不稳定。(2)5s1s1s2js654,32,1 系统不稳定。系统不稳定。(3)有一对纯虚根：有一对纯虚根：5js2,1 系统不稳定。系统不稳定。3-137.1k0 3-1400 3-15 (1)ssssee20k(2)sssse2.0e10k(3)20e0e1.0kssss 3-16(1)(3)(2)0k0k50kavp 0k200kkkavp 1kkkavp 3-18 (1)(2)(3)0essr 0e1ssn 0e2ssn 3-20k1)1sT(sk12 1sT12 RuBCE(s)=R(s)-C(s)由题意得：由题意得：2122112o2TTkTTk)T(k1 7听雨书屋（4-4题题4-5题）题）-0.8810j7=k-0.293-1.707-0.9-4.236op135=op0=8听雨书屋（4-6题题4-10题）题）4-6(1)11k=(2)30*k=63.630199z=-0.4042.73*k=036.1=op73.92=6j+-2-210j260*k=-3.2921j96*k=oop135,45=150kc=62.9ko=-21.137.70=9听雨书屋（4-11题题4-12题）题）s1=-9.98s2,3=-2.46354.3j-4系统始终不稳定！系统始终不稳定！55.2j=75.22*k=75.22*k0时稳定时稳定10听雨书屋（4-13题题4-14题）题）)3s2s(s)2s(k)s(G2+=)2s)(1s(s)10s(k)s(G+=-0.434j1.6976k=-8.47224)2s()4s(b)s(G+=)40s(sb30)s(G+=11听雨书屋（4-15题题4-19题）题）2j2*k=-0.732536.0*k=2.732464.7*k=整条实轴为根轨迹整条实轴为根轨迹2 12*k0k*12时系统稳定时系统稳定系统始终不稳定系统始终不稳定12听雨书屋（4-20题题4-21题）题）主导极点离虚轴太近！主导极点离虚轴太近！主导极点离虚轴太近！主导极点离虚轴太近！6)24.3)(3.23()20(10)(221 ssssksGt6)24.3)(3.23()20(10)(2222 ssssksGt6)24.3)(3.23(10)(2223 sssksGt2 1k 0k1系统稳定，系统稳定，c(t)振荡收敛，振荡收敛，5.0)(cn 13听雨书屋（5-2题题5-8题）题）5-213j)36(36)j()9s)(4s(36)s(2 5-3)57.26t2cos(79.0)4.48tsin(632.0)t(eooss 或：或：)90t2cos(707.0)4.3tsin(447.0)t(cooss )t(c)t(r)t(essss 5-4848.1653.0n 5-50j0jT T5-60j0j0j0j1 v2 v3 v4 v5-7)1s20(s)1s05.0(10)s(G 5-8o4.1539.17)5.0 j(G o53.327383.0)2j(G 61 14听雨书屋（5-9题题5-13题）题）j-10 2 20o90)0 j(G o4.153)2j(G o4.333)2j(G o3600)j(G 5-95-11(1)02.620 125.025.040 dB)(L dB05-11(2)40 60 80 861.02611.2 dB0dB)(L 5-11(3)06.3802.261.01243.5 20 40 60 707.0r dB25.1Lm dB020 40 60 20 4006.78 dB0 11.020dB)(L 5-11(4)5-135-5：T时系统稳定，时系统稳定，5-6：=1时系统稳定，时系统稳定，其余不稳定。其余不稳定。T时系统不稳定。时系统不稳定。15听雨书屋（5-14题题5-23题）题）5-14(1)Z=0-2(-1)=2 不稳定不稳定 (2)z=0 稳定稳定 (3)z=0-2(-1)=2 不稳定不稳定(4)z=0 稳定稳定 (5)Z=0-2(-1)=2 不稳定不稳定 (6)z=0-2(1-1)=0 稳定稳定 (7)z=0 稳定稳定(8)z=0 稳定稳定 (9)Z=1 不稳定不稳定 (10)z=2 不稳定不稳定 5-15z=0-2(-1)=2 不稳定不稳定 5-16(1)k1.5 (2)T1/9 (3)k-11/T5-17 z=0-0=0 稳定稳定5-18（左图）原系统稳定，改变（左图）原系统稳定，改变k值。使值。使c 2 时系统稳定时系统稳定,（右图）原系统（右图）原系统z=0-2(-1)=2不稳定。改变不稳定。改变k值，使值，使c 0时应有时应有 0k2.64 ;k0时应有时应有 -1k05-203686.10 5-2184.021a4 5-22oc156.6594455.1 5-23on17.5324.2517.0 o21180)()(其中其中其中其中o1180)(5-24o4o3o2o156.33608.15190 16听雨书屋（6-1题题67题）题）6-1 (1)1667.11623.30521.4924.26 hkxoc1249.383.77673.298473.3 hxoc(2)6-2 (1)57 k(2)11.227572673.2 vskst(3)%2.3%7.02226.28)01.0()091.0)(3()(stkssssGsvc6-3 取取820 cksssGc04.014.01)(验算得：验算得：oc1.62,93.7 6-5(1)sssGc004.0119.01)(验算得：验算得：dBho7.161.30 (2)118016.2)(sssGc验算得：验算得：dBho3.304.50 6-6ococ5131.747962.025.14969.1 6-7(1)取取5.05 cvk1200120)(1 sssGc验算得：验算得：oc4.53,45.0 (2)13.0161200120)(sssssGcoc3.51,05.2 验算得：验算得：17听雨书屋(6-8题题6-15题题)6-8 (1)1s101s)s(Gc+=(a)(b)系统不稳定系统不稳定1s01.01s1.0)s(Gc+=oc5.346.36 44.89 hx(c)1s025.0)(1s10()1s5.0()s(G2c+=oc2.4810=dB7.21h,8.58x 6-8 (2)采用采用(c)6-140k0.045时系统为过阻尼时系统为过阻尼;k10s)s(Gr=时时ess=0,其中其中0k+=0k,ks1)s(G111c0k,0TTkTk1k0,sk)s(G221oo2c+=18听雨书屋(6-16题题6-17题题)6-1695.2466.0)()3747.1()(12 kssGsssGcn6-17100)2()12.0(505024.12.0)(12223 sssssssse04.0028.012=(Ts+1)寄生因子不影响系统稳定性寄生因子不影响系统稳定性,且因为它为非主导极点且因为它为非主导极点,所以也不太影响动态性能所以也不太影响动态性能,但附加极点有增大阻尼的作用。但附加极点有增大阻尼的作用。19听雨书屋（7-3题题7-10题）题）7-3(1)e(nT)=10(2n-1)T2t(7)Tt(5)t(3)nTt()3n2()t(*e0n(2)7-5 )(e0)(e (1)(2)7-756)4(c15)3(c4)2(c 7-8(1)nTt()46122131()t(*c0)1(cTtTt0n 7-9T7T5T222ez)ee(zz10)z(G (a)(b)ezzezz(310)z(GT5T2 7-10(a)z(G)z(G)z(GG1)z(G)z(31211 (b)z(GGG1)z(GRG)z(GGG)z(RG)z(C43h4243h1 (c)z(GGG)z(D1)z(NG)z(GGG)z(D)z(D)z(R)z(C21h1221h21 7-4(1)1nnnn20nnn11a3a,z3a)z1(z31)z(E (2)25.2)5.0)(1n3(5.1)n(enn (2)1(1)1n(4T)nT(cn (3)nnn)3(5)2(7)1(11)n(c 20听雨书屋（7-11题题7-21题）题）)nTt()37.047.01()nT(cn 7-11 7-13 (1)0067.0z0587.1z8987.2z8467.2zz0384.0z16.0)z(c23423 (2)T4t(415.1)T3t(94.0)T2t(4938.0)Tt(16.0)t(*c(3)因为系统不稳定，所以因为系统不稳定，所以 不存在。不存在。)(c 7-15(1)不稳定不稳定 (2)不稳定不稳定 (3)不稳定不稳定7-16(1)不稳定不稳定 (2)0k3.31时时稳定稳定7-17 1.0)(e4.0k)1z(8.0z2.1)z(Ga2 7-18 1)(e0k1.0kkavp 7-19 0k2.272时系统稳定；时系统稳定；ess0.1时时k应大于应大于10，此时系统不稳定，此时系统不稳定，所以所以k无值可取。无值可取。7-21 1z58.058.1z632.0368.0z)z(D 7-22)1z(k1z2)z(D 21听雨书屋（8-12题题8-19题）题）8-12(2)的准确性高的准确性高8-14(a)()(1)(11sGsHsG (b)(1)()()(111sGsHsGsG 8-15(a)aAAaAkaAakkAN 2)(12arcsin2)(b)bAAbAaAMAN )(1)(14)(22(c)khAA)(1AM4)A(N22kh8-163.52215)2(jG有自振有自振ttxsin3.5)(8-17320 k时系统稳定时系统稳定时系统不稳定时系统不稳定 k2232 k时有自振，时有自振，tkktxsin246)(8-18ttcttx91.3sin16.0)(91.3sin8.0)(8-19ttcttyttx2sin398.0)(2sin4)(2sin796.0)(22听雨书屋