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# Signal line ： have arrow which shows signal flow direction, signal nearby. - PowerPoint PPT Presentation

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。

• 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。

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) 。

(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

**

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) ：

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

**

Using **，get：

Fig.2-18

feedback interrupted7） 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：

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.2-8 a system,its output and error are

drawing RC circuit block diag. .

From fig.2-20，using kichihoff rule：

Take Laplace transform：

fig2-20

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.2-9

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

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).

2.7.4 block diam. reduction two R- C , such as the fig 2-22 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 2-23 series

Characteristics two R- C , such as the fig 2-22 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 2-22 shown,Then the block diagram is shown as diagram( b). 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.

two R- C , such as the fig 2-22 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 2-22 shown,Then the block diagram is shown as diagram( b). 3）feedback

Fig 2-25 feedback

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

two R- C , such as the fig 2-22 shown,Then the block diagram is shown as diagram( b).

amplificationshrink

shrink amplification

Fig 2-26 comparison point move

two R- C , such as the fig 2-22 shown,Then the block diagram is shown as diagram( b).

left

right

shrink amplification

amplificationshrink

Fig 2-27 branch point（output）move

C two R- C , such as the fig 2-22 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

forwardback

forwardback

Fig 2-26 neighboring point move

G two R- C , such as the fig 2-22 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 2-22 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 2-22 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.2-10 two R- C , such as the fig 2-22 shown,Then the block diagram is shown as diagram( b).

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

series and parallel two R- C , such as the fig 2-22 shown,Then the block diagram is shown as diagram( b).

feedback

Exam 2-11 two R- C , such as the fig 2-22 shown,Then the block diagram is shown as diagram( b).

Simplify fig.2-9.

• simplification hints two R- C , such as the fig 2-22 shown,Then the block diagram is shown as diagram( b). ：

• A move backward

• B move forward

• 1 and 2 move。

Fig 2-29 reduction process

Check methods: two R- C , such as the fig 2-22 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: 2-17