控制系统的数学模型(2)

2019-08-31 17:09

解 (a)图中有1条前向通路,4个回路

P1?G1G2G3G4,?1?1L1?G2G3H1

L2??G1G2G3H3,L3?G1G2G3G4H4,L4??G3G4H2,??1?(L1?L2?L3?L4)则有

G1G2G3G4?C(s)P ?11?R(s)?1?G2G3H1?G1G2G3H3?G1G2G3G4H4?G3G4H2 P,P2?G3G4,?2?1?L1?1?G1H1,1?G1G2G3,?1?1 L1??G1H1,L2?G3H3,L3??G1G2G3H1H2H3, ??1?(L1?L2?L3)?L1L2,(b)图中有2条前向通路,3个回路,有1对互不接触回路

则有

G1G2G3?G3G4(1?G1H1)??P2?2C(s)P ?11?R(s)?1?G1H1?G3H3?G1G2G3H1H2H3?G1H1G3H3(c)图中有4条前向通路,5个回路

6

P1??G1,P2?G1G2,P3?G2,P4?G2G1, L1?G1,L2??G1G2,L3??G2,L4??G2G1,L5??G1G2, ?1??2??3??4?1,??1?(L1?L2?L3?L4),则有

C(s)P1?1?P2?2?P3?3?P4?4 ?R(s)???G1?G1G2?G2?G2G12G1G2?G1?G2 ?1?G1?G1G2?G2?G2G1?G1G21?G1?G2?3G1G2

(d)图中有2条前向通路,5个回路

P,P2?G3,?2?1,1?G1G2,?1?1 则有

L1??G2H1,L2??G1G2H2,L3??G1G2,L4??G3,L5?G3H1G2H2, ??1?(L1?L2?L3?L4?L5),C(s)P1?1?P2?2 ?R(s)??G1G2?G3

1?G2H1?G1G2H2?G1G2?G3?G3H1G2H2(e)图中有2条前向通路,3个回路,有1对互不接触回路

P,P2??G4G3,?2?1?L1,1?G1G2G3,?1?1 L1??G1G2H1,L2??G3H2,L3??G2H3, ??1?(L1?L2?L3)?L1L2,则有

G1G2G3?G4G3(1?G1G2H1)C(s)P1?1?P2?2 ??R(s)?1?G1G2H1?G3H2?G2H3?G1G2G3H1H2

7


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