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 。.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
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。
(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) feedback interrupted
the ratio of error E(s) to input R(s)。
substitute
To equ. Above,canceling G(s) ：
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 a system,its output and error are
drawing RC circuit block diag. .
From fig.220，using kichihoff rule：
Take Laplace transform：
fig220
combine a system,its output and error are（b）and (c) get (d)，fig.(d) is RC network block diag..
drawing a system,its output and error areRC 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 two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b). ——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 two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b). ：the output forward is the input backward
N:series no.
conclusion：The equivalent TF is the products of all the TF.。
（ two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b). 2）parallel
Fig 224 parallel
Characteristics：every component input is the same R(s)，output C(s) is the sum of all the output.
two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b).
n parallel no，including “” 。
conclusion：The equivalent TF is the sum of all the TF.。
（ two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b). 3）feedback
Fig 225 feedback
（4）comparison point and branch point（output）move
two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b).
amplificationshrink
shrink amplification
Fig 226 comparison point move
two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b).
left
right
shrink amplification
amplificationshrink
Fig 227 branch point（output）move
C two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b).
(
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
G two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b). 2
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 two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b). （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 two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b). （s）
C（s）
G1
G2
（a）
+
+
+
+
R（s）
C（s）
G1+1
G2
（b）
+
+
R（s）
C（s）
G1G2+G2+1
（c）
Exam.210 two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b).
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 two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b).
feedback
Exam 211 two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b).
Simplify fig.29.
Fig 229 reduction process
Check methods: two R C , such as the fig 222 shown,Then the block diagram is shown as diagram( b).
assure forward path TF is a constant;
assure feedback loop TF is a constant;
Note :symbol change
Homework: 217