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《自动控制原理—胥布工》部分习题参考答案
第1章
1-4 有差系统。
1-5 接线端1接地，2与4相连，3接地，5不需连接。 1-8 （1）略；（2）无差系统。
第2章
2-1 (a) G(s)?U0(s)Ui(s)?R1R2C1C2sR1R2C1C2s22?(R1C1?R2C2)s?1
?(R1C1?R1C2?R2C2)s?11(b) G(s)?U0(s)Ui(s)U0(s)Ui(s)U0(s)Ui(s)?C2s1C1s?1C2s?Ls2?C1LC1C2s2?C1?C
2(c) G(s)?（d）G(s)???R2R3C1C2sR1C1C2s22?(R2C1?R3C2?R3C1)s?1R1C1s
???(R1C1?R1C2)s?1R1C2s
f1f22-2 （a）G(s)?Yo(s)Yi(s)?k1k2f1f2k1k2s2s2?(f1k1f1k1??f2k2f2k2?)s?1f2k1
)s?1?(（b）G(s)?2-3 G(s)?
2-4 G(s)?阻）。
2-5 G(s)?H2(s)Qi(s)H2(s)Qi(s)Yo(s)F(s)?2?1Ms2?(f1?f2)s?kl22
(l?N2N1)
?2(s)M(s)(lJ1?J2)s?(l?1??2)s?R2(R1C1s?1)(R2C2s?1)，其中，R1和R2分别为在各自工作点的参数（液
?R2R1R2C1C2s2?(R1C1?R2C1?R2C2)s?1，其中，R1和R2分别为在各自
工作点的参数（液阻）。
1
2-6 T1~dP(t)dt~?T0P(t)?Qi(t)??x(t)~??Dx02g?P0~VM，其中， ，，????D2g?P0，T?T0?1~RTP0符号?已略去。
2-7
d?(?T)d???(?T)?u(?T)，其中，?(t)??(t)?0，u(t)?u(t)u0，??~tRC?tT，R为向外散出
~(t)??(t)??。 的热量与炉内外的温差成正比的比例系数，即Rq2-8 2-9
Y(s)R(s)H(s)?K0T2s?(2T2?K0T1?1)s?1?N1KK2K3KmN2CTms22和
Y(s)?(s)?K0K1?1T2s?(2T2?K0T1?1)s?12
Ur(s)?N2Cs?N1KK1K2K3Km
R2C2s?1RC2s2-10（1）Gc(s)??1R1C1s?1RC1s243，Gc(s)?2U2(s)U1(s)??
（2）
K??(s)Ur(s)?K(?2s??1s?1)T4s?T3s?T2s?T1s?12，其中
T1?R1C1K1Km?R2C2K1Km?RC1K2K1Km1K1,?1?C1R1?C2R2,?2?C1C2R1R2,2T2?R2C1C2?K2KpRC1(Tm?C2R2)?K1KpKmC1C2R1R2K1KpKmRC1C2(RTp
T3??RTm?K2KpTmR2)K1KpKm,T4?RC1C2TpTmK1KpKm22-11（1）L?1?G(s)??1?3e?2t?4e?3t；（2）L?1?G(s)??1?t?e?t 2-12（1）G(s)?1s(s?a)2；（2）G(s)??s??s(s222??)
2-13（a）Y(s)/R(s)?（b）Y(s)/R(s)?（c）Y(s)/R(s)?（d）Y(s)/R(s)?（e）Y(s)/R(s)?2-14 Y(s)?G1?G21?G1G3?G2G3?G2G4?G1G4G1?G21?G2G3
G1G2G3G422222G1?G21?G1?G2?G1G2G1G4?G1G3G4G5?G1G2G3G4G7?G1G2G3G4G61?H1G2G1?H1G2?H2G2G3(1?H1G1)(1?H2G2)(1?H3G4)?G1G2G3G4H4
G4?H1G1G2G4?H1G2G4?H2G2G3G4?G1G2G3G1G2G3G4R(s)?G2G3G4(1?H1G1)D1(s)?G3G4(1?H1G1)(1?H2G2)D2(s)2
G1G2G3?G1G41?G1G2G3?G1G4?H2G2G3?H1G1G2?H1H2G1G2G4G1G21?H1G1G2?G1G2Y(s)D(s)?1?H1G1G2?G2G31?H1G1G2?G1G2?G41?G3G4?G2G42-15（1）Y(s)/R(s)?
（2）当1?H1G1G2?0时，输出Y(s)不受干扰信号D(s)的影响。 2-16（a）
（b）
Y(s)R(s)Y(s)R(s)?，
?
?G1G2G4?G2G4?G3G41?G2G4?G3G4Y(s)R(s)?，
Y(s)D(s)2-17（a）G(s)?G(s)?G1G2G3G4G51?H1G3?H2G2G3?H3G3G4?H4G1G2G3G4G5Y(s)R(s)?（b）
?G1G2G3G4G5G6?G3G4G5G6G7?G1G6G8(1?G4H2)?H1G6G7G8(1?G4H2)
其中
??1?(L1?L2?L3?L4?L5)?(L1L2?L1L3?L2L3?L2L5)?L1L2L3?1?G2H1?G4H2?G6H3?G3G4G5H44?G8H1H4?G2G4H1H2?G2G6H1H3
?G4G6H2H3?G4G8H1H2H?G2G4G6H1H2H3
?1(t)??0?x????2(t)x0???2-18 ??x?3(t)??0????4(t)???24?x100?50010?35?10??x1(t)??0??????x2(t)00????u(t)，y(t)??15??1??x3(t)??0???????10??x4(t)??1?173?x1(t)???x2(t)?0???x3(t)????x4(t)?
2-19 G(s)?Y(s)U(s)?C(sI?A)B?d?2s32?s?72s?2s?13
第3章
3-1（1）GF(s)?GL(s)?5(10s?1)s(100s?1)(s?1)(0.5s?1)5(10s?1)s(100s?1)(s?1)(0.5s?1)(0.1s?1),GB(s)?
10.1s?1,GD(s)?5s(s?1)(0.5s?1)
TR(s)?5(10s?1)(0.1s?1)5s5?65.05s4?160.65s3?101.6s442?51s?533
2（2）TRE(s)?TDE(s)?11?GL(s)1?GL(s)?5s5s?55?65.05s?160.65s?101.6s2?s?65.05s5?160.65s?101.6s?5(100s?1)43?51s?52
?Gp(s)H(s)5s?65.05s?160.65s?101.6s?51s?5（3）?(s)?5s5?65.05s4?160.65s3?101.6s2?51s?5
3-2 （1）系统在右半s平面无根，系统稳定；（2）系统是临界稳定的；（3）系统不稳定；
3
（4）系统不稳定有四个对称坐标原点的根s1,2?2?j,s3,4??2?j。 3-3 （1）K?25；（2）0?K?8；（3）K不存在；（4）K?0。 3-4 ?d?0
3-5（1）Kcr?119，?n?17；（2）11?K?35 3-6 301倍。
3-7 er(?)?limsEr(s)?0，ed(?)?limsEd(s)??s?0s?01K
3-8 e(?)?lims?0sR(s)1?GL(s)?20
T1?T2T1T23-9 T1?0,T2?0,??0?K?
3-10 e(?)?er(?)?ed(?)?3-11（1）er(?)?lims?s?0216
Js2Js?K1s?K2?1ss（2）ed(?)?ed1(?)?ed2(?)?0 ?0；
?as2T?；（3）ShT?3-12（1）SKs(s?a)s2?as?KT?；（2）Sa?Khs2
?as?K?as?KhT??3-13 SHGL(s)1?GL(s)K1T1
TK1?1；（2）SKTT?3-14（1）SK?2??500s2?s?500T? ；（3）SGs(s?1)s(s?1)?500
3-15（1）（a）h?0.01；（b）h?0.364；（c）h?0.099；
TTT（2）（a）SK（b）SK（c）SK?3；?0.65；?0.03 TT（3）（b）Sh（c）Sh??2.35；??0.99
3-16 SY1K?21?KH1R，SY2K?21?KH22R，H2?2H1?KHK21
25?03-17（1）Y1(?)?0；Y1(?)?3-18 Gff(s)??2318（2）Y1(?)?0?0；
22；Y1(?)?。
Gd(s)[1?Gc(s)Gp(s)Hm(s)]Gc(s)Gp(s)Gp(s)221
3-19 按扰动Mc(s)补偿的前馈补偿方案。 3-20 方案（b）。
第4章
4-2 0.98分钟。
4-3 K0?2,K1?0.5 4-4 T(s)?4
10s?20