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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 。. 2.7.1 Block Diagram element ( 1 ) Block :shows function relation between output and input 。.

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Signal line have arrow which shows signal flow direction signal nearby

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。

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。


Signal line have arrow which shows signal flow direction signal nearby

note:comparison signal must have same unit。

(3) Branch Point (output point、measuring point)

note:same position has same signal。


Signal line have arrow which shows signal flow direction signal nearby

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) 。


Signal line have arrow which shows signal flow direction signal nearby

(3) Open-loop Transfer Function(assuming N(s)=0). when feedback interrupted, the ratio of chief feedback signal B(s) and error E(s) 。

(4) Closed-loop Transfer Function(assuming N(s)=0)

the ratio of output C(s) to input R(s) 。

Because of:

modify

**

please remember

That is


Signal line have arrow which shows signal flow direction signal nearby

(5)error TF(assuming N(s)=0)

the ratio of error E(s) to input R(s)。

substitute

To equ. Above,canceling G(s) :


Signal line have arrow which shows signal flow direction signal nearby

(6) TF of output to interference TF assuming R(s)=0

**

Using **,get:

Fig.2-18


Signal line have arrow which shows signal flow direction signal nearby

(7) TF of error to interference assuming R(s)=0

**

fig2-19

Using **,get:


From addition when both input r s and interference act on a system its output and error are

From addition,when both input R(s)and interference act on a system,its output and error are:

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.


Signal line have arrow which shows signal flow direction signal nearby

Exam.2-8

drawing RC circuit block diag. .

From fig.2-20,using kichihoff rule:

Take Laplace transform:

fig2-20


Signal line have arrow which shows signal flow direction signal nearby

combine(b)and (c) get (d),fig.(d) is RC network block diag..


Signal line have arrow which shows signal flow direction signal nearby

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.2-9

From the fig., R2-C2 iis the load of R1-C1,affects R1-C1output voltage ---load effect.


Signal line have arrow which shows signal flow direction signal nearby

If connect a insulation enlarger of high resistance between two R- C , such as the fig 2-22 shown,Then the block diagram is shown as diagram( b).


Signal line have arrow which shows signal flow direction signal nearby

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 2-23 series


Signal line have arrow which shows signal flow direction signal nearby

Characteristics:the output forward is the input backward

N:series no.

conclusion:The equivalent TF is the products of all the TF.。


Signal line have arrow which shows signal flow direction signal nearby

(2)parallel

Fig 2-24 parallel

Characteristics:every component input is the same R(s),output C(s) is the sum of all the output.


Signal line have arrow which shows signal flow direction signal nearby

n parallel no,including “-” 。

conclusion:The equivalent TF is the sum of all the TF.。


Signal line have arrow which shows signal flow direction signal nearby

(3)feedback

Fig 2-25 feedback

(4)comparison point and branch point(output)move


Signal line have arrow which shows signal flow direction signal nearby

amplificationshrink

shrink amplification

Fig 2-26 comparison point move


Signal line have arrow which shows signal flow direction signal nearby

left

right

shrink amplification

amplificationshrink

Fig 2-27 branch point(output)move


Signal line have arrow which shows signal flow direction signal nearby

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

forwardback

forwardback

Fig 2-26 neighboring point move


Signal line have arrow which shows signal flow direction signal nearby

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


Signal line have arrow which shows signal flow direction signal nearby

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

+

+

+

+


Signal line have arrow which shows signal flow direction signal nearby

R(s)

C(s)

G1

G2

(a)

+

+

+

+

R(s)

C(s)

G1+1

G2

(b)

+

+

R(s)

C(s)

G1G2+G2+1

(c)


Signal line have arrow which shows signal flow direction signal nearby

Exam.2-10

Give TF C(s)/R(s)in fig. 2-28 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 2-28


Signal line have arrow which shows signal flow direction signal nearby

series and parallel

feedback


Signal line have arrow which shows signal flow direction signal nearby

Exam 2-11

Simplify fig.2-9.


Signal line have arrow which shows signal flow direction signal nearby

  • simplification hints:

  • A move backward

  • B move forward

  • 1 and 2 move。

Fig 2-29 reduction process


Signal line have arrow which shows signal flow direction signal nearby

Check methods:

assure forward path TF is a constant;

assure feedback loop TF is a constant;

Note :symbol change

Homework: 2-17


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