2.7 Block Diagram 、 signal graph and mason rule. Block Diagram is a kind of tool showing component performance,system construction and signal direction 。. 2.7.1 Block Diagram element （ 1 ） Block :shows function relation between output and input 。.
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2.7 Block Diagram、signal graph and mason rule
Block Diagram is a kind of tool showing component performance,system construction and signal direction。
Signal line：have arrow which shows signal flow direction, signal nearby.
（2）comparison point（Summing Point）
2 or many signal addition or reduction。
“+” addition ，“” reduction 。“+”can be ignored。
note：comparison signal must have same unit。
(3) Branch Point （output point、measuring point）
note：same position has same signal。
2.7.2 some concepts and terms
(1)forward path TF—assuming N(s)=0
when feedback interrupted，the ratio of output C(s) and input R(s) ,or C(s) and E(s)
(2)feedback path TF assuming N(s)=0
the ratio of chief feedback signal B(s) and output C(s) 。
(4) Closedloop Transfer Function(assuming N(s)=0)
the ratio of output C(s) to input R(s) 。
Because of：
modify
**
please remember
That is
(5)error TF(assuming N(s)=0)
the ratio of error E(s) to input R(s)。
substitute
To equ. Above,canceling G(s) ：
(6) TF of output to interference TF assuming R(s)=0
**
Using **，get：
Fig.218
（7） TF of error to interference assuming R(s)=0
**
fig219
Using **，get：
2.7.3 drawing block diag.
(1）considering load effect,write the each part's differential equ. or TF,express in block diag..
(2) according to the signal direction,use the signal line to link every block.
System block diag. is also a kind of system's math model.
Exam.28
drawing RC circuit block diag. .
From fig.220，using kichihoff rule：
Take Laplace transform：
fig220
combine（b）and (c) get (d)，fig.(d) is RC network block diag..
drawing RC circuit block diag. .
（1）according to circuit rule, and write differential equ. and its Laplace transformation, also can directly draw out circuit calculating diagram ( b)(2) according to 4 listing formulas make block diagram;(3) according to signal flow direction,link the every block one by one.
Exam.29
From the fig., R2C2 iis the load of R1C1，affects R1C1output voltage load effect.
If connect a insulation enlarger of high resistance between two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b).
2.7.4 block diam. reduction——equivalent transform in order to write TF,it is necessary to transform block diam..the transformation must obey a principle, namely the transformation keeps TF constant.In control system, any complicated system is mainly composed of series,parallel and feedback.
（1）series
Fig 223 series
Characteristics：the output forward is the input backward
N:series no.
conclusion：The equivalent TF is the products of all the TF.。
（2）parallel
Fig 224 parallel
Characteristics：every component input is the same R(s)，output C(s) is the sum of all the output.
n parallel no，including “” 。
conclusion：The equivalent TF is the sum of all the TF.。
（3）feedback
Fig 225 feedback
（4）comparison point and branch point（output）move
amplificationshrink
shrink amplification
Fig 226 comparison point move
left
right
shrink amplification
amplificationshrink
Fig 227 branch point（output）move
C
(
s
)
C(S)
C
(
s
)
C
(
s
)
R
(
s
)
R
(
s
)
±
±
＋
＋
C
(
s
)
P(s)
Q(s)
Q
(
s
)
P
(
s
)
C(S)
C
(
s
)
C
(
s
)
（5）neighboring comparison point and branch point（output）move
forwardback
forwardback
Fig 226 neighboring point move
G2
G1
R（s）
C（s）
+
( a )
G1
+
+
–
H
Exm. Solve C(s)/R(s) in the system shown in following diag.
G2
R（s）
C（s）
+
G1
+
+

H
C（s）
G1
1+
R（s）
G2
(b)
1+G1H
G1
R（s）
C（s）
G1+G2
(c)
1+G1H
exam. Solve C(s)/R(s) in the system shown in following diag.
R（s）
C（s）
G1
G2
+
+
+
+
R（s）
C（s）
G1
G2
（a）
+
+
+
+
R（s）
C（s）
G1+1
G2
（b）
+
+
R（s）
C（s）
G1G2+G2+1
（c）
Exam.210
Give TF C(s)/R(s)in fig. 228 system
This is a system of many crossing tracks .if do not transform it,it is difficult to reduce with series, parallel and feedback.method is as follows.
Fig 228
series and parallel
feedback
Exam 211
Simplify fig.29.
Fig 229 reduction process
Check methods:
assure forward path TF is a constant;
assure feedback loop TF is a constant;
Note :symbol change
Homework: 217