方塊圖及訊號流程圖 - 歡迎來到生物電磁 ...bem.bime.ntu.edu.tw/LESSON/AC/BCKUO_2008/Ch03.pdf · chapter 方塊圖及訊號 ... 號處理的換能器。 2

BIME_NTU__Joe-Air Jiang

Automatic Control Systems_B. C. Kuo & F. Golnaraghi

1

CHAPTER

33--1(a) 1(a)

33--1 (a) 1 (a) (b) (b)

1. 1.

--

33--1(b) 1(b)

2. 2.

(3-1)

KK



2

CHAPTER

1. 1.

2. 2.

3. 3. 33--22

33--2 2 (a) (a) (b) (b) (c) (c) (d) (d)

33--2(a) 2(a)

(3-2)

(3-3)

H(s) = 1Error Signal



3

CHAPTER

r(t)R(s) () y(t)Y(s) () b(t)B(s) u(t)U(s)

= e(t)E(s) H(s) = 1H(s) G(s)H(s) L(s) = G(s) M(s) Y(s)/R(s) =

33--3 3

MM((ss) )

( ) ( ) ( )Y s G s U s

( ) ( ) ( )B s H s Y s(3-4)

(3-5)

( ) ( ) ( )U s R s B s

(3-6)

( ) ( ) ( ) ( ) ( )Y s G s R s G s B s (3-7)

( ) ( )( )( ) 1 ( ) ( )Y s G sM sR s G s H s

(3-8)

(3-6) (3-4)

(3-5) (3-7)



4

CHAPTER

1. Basic concepts

i) The product of the transfer functions in the feedforward direction must remain the same.

ii) The product of the transfer functions around the loop must remain the same.

2. Some block diagram reduction rules are summarized in the following table:

Ogata



5

CHAPTER



6

CHAPTER



7

CHAPTER

Consider the system shown in Fig. 3-14(a). Simplify this diagram.

1. See Fig. 3-14 (b)-(d):



8

CHAPTER

2. The numerator of C(s)/R(s) is the product of the transfer functions of the feedforward path.

1 2 1 2 3 2 1 2 3

1 2 1 2 3 2 1 2 3

1 (product of the transfer functions around each loop)

1 ( )1

GG H G G H GG GGG H G G H GG G



9

CHAPTER

pp qq

33--4 4

33--44



10

CHAPTER

(3-9)

(3-10) (3-11)

Y(s) q 1 U(s)R(s) B(s) p 1 G(s) H(s) q p p q

33--5 5

(3-12)

(3-13)

(3-11) (3-10)(3-10) (3-9)

I + G(s)H(s) (3-14)

(3-13) (3-15)



11

CHAPTER

33--1 1 33--55

(3-16)

1. 1.

(3-17)

2. 2.

(3-18)

33--55



12

CHAPTER

(3-19)

(3-20)

(SFG) (SFG)

--

NN

(3-21)



13

CHAPTER

NN

)()(1

kjkjN

k

(3-22)

( ) ( ) (3-23)

(3(3--21) 21)

(3-24)

SFG SFG 1. (nodes) 2. 3.



14

CHAPTER

Ex.

33--6 6 yy22 = = aa1212yy11 2 12 1y a y (3-25)

y1 y2 a12

y1 y2 a12

1 212

1y ya

(3-25)

(3-26) 3-6

33--2 2 SFG

(3-27)

33--77



15

CHAPTER

33--7 (37 (3--27) 27)

(3-27)



16

CHAPTER

1. 2. 3.

4. 5. yk yj yj yk 6. yk yk yj yj

akj akj yk

SFG SFG (())

33--77 yy11

(()) 33--77 yy55



17

CHAPTER

33--8(a)8(a)

33--8 8 yy22 yy33

33--8(b)8(b)

Ex.Ex. 33--8(b)8(b)yy22 33--99 yy22

(3-28)



18

CHAPTER

33--9 9 yy22

(path)(path)

(forward path)(forward path)

3-7(d)

y1 y3 y1 y4 y1 y5

33--7(d) 7(d)

(loop)(loop)



19

CHAPTER

33--7(d)7(d) 33--1010

33--10 10 33--7(d) 7(d)

33--7(d) 7(d)



20

CHAPTER

(path gain)(path gain)

(forward-path gain)

(loop gain)(loop gain)

33--1010 y2 y4 y3 y2 a24a43a32

SFG SFG

SFG SFG ((nontouchingnontouching))

33--7(d)7(d) SFG SFG yy22 yy33 yy22 yy44 yy44

33--7(d) 7(d)

a12a23a34



21

CHAPTER

1.1.

33--11 11

Ex.Ex. 33--1111 yy11

(3-29)

2.

Ex.Ex. 33--1111 SFG SFG

(3-30)

3.3. 33--1212



22

CHAPTER

33--12 12

4.4.

33--1313

33--13 13

SFG SFG SFG SFG 33--1414

( )( )( )

( )1 ( ) ( )

Y sM sR sG sG s H s

(3-8)



23

CHAPTER

33--14 14 33--3 3

SFG SFG SFG SFG NN KK yyinin yyoutout

(3-31)

yin = yout = M = yin yout N = yin youtMk = yin yout k

(3-32)

Masons gain Formula



24

CHAPTER

LLmrmr = = rr (1 (1 r r KK) ) mm ((mm = = iijjkk) )

= 1= 1 (() + () + () ) (() + ) + (3-33)

kk = = kk

SFGSFG

33--3 3 3-14 Y(s)/R(s)

33--14 14 33--3 3

1. 1. RR((ss) ) YY((ss) )



25

33--7(d) 7(d)

CHAPTER

(3-34) 2. 2.

(3-35)

3. 3. 11 = 1= 1

(3-36) (3(3--31) 31)

(3-37) (3-8)

33--4 4 33--7(d)7(d) SFGSFG yy1 1 yy55



26

CHAPTER

1. 1.

2. SFG 2. SFG

3. 3.

(3-38)

33--1010

4. 4. MM11 MM33 11 = = 33 = 1= 1

5. 5. MM22 yy33 yy44 yy44 yy44 yy44

(3-39)



27

CHAPTER

6. y1 y5

(3-40)

Masons Gain Formula: (3-31)

(3-41)

yy22

(3-42)

(3(3--41) 41)

33--55 33--1515 SFGSFG--

2 1 4 1 6 1, , ?y y y y y y

(3-43)



28

CHAPTER

33--15 15 33--5 5

(3-44)

(3-45)

(3-46)



29

CHAPTER

33--1515 SFG SFG yy77//yy22 yin SFG yout y2 yout /y2

/

/

in2

inout

2

out

2in

outin

//

yykk

yykk

MM

yyyy

yy

(3-47)

2in

outin

in2

inout

2

out

//

yykk

yykk

MM

yyyy

yy

(3-48)

33--66 33--1515 SFGSFGyy22 yy77

(3-49)

1. (31. (3--31) 31) --2. 2.



30

CHAPTER

33--16 16 (a)(a)

(b)(b) (a)(a)

33--77 SFG SFG 33--16(a)16(a) YY((ss)/)/RR((ss) = ?) = ?



31

CHAPTER

1. 1. 33--16(b)16(b)

SFG SFG SFG SFG

2. 2.

(3-50)

(3-51)

(3-31)

(3-52)

(3-53) (3-48)

1. 1. 2. 2. SFG SFG 3. 3. SFGSFG



32

CHAPTER

1. x1(t) x2(t)

(3-54)

(3-55) 33--17 17 XX11((ss) = [) = [XX22((ss)/)/ss] + [] + [xx11((tt00)/)/ss] ] 2. 2.

(3-56)

= t0 x2() = 00 < < t0

(3-57)

33--1717 33--1818



33

CHAPTER

33--18 18 XX11((ss) = [) = [XX22((ss)/)/ss] + ] + [[xx11((tt00)/)/ss] ]

1.1.

2.2. ((44--1111) ) 3.3.

4.4.

5.5. 6.6.

1. 1.

(3-58)

(3-59)



34

CHAPTER

33--19 19 (3(3--58) 58)



35

CHAPTER

2. 2. RR((ss))ssnnYY((ss))ssnn11YY((ss))sYsY((ss) ) YY((ss) ) 33--19(a)19(a)

3. 3. 33--19(a)19(a) (3(3--59) 59) 33--19(b)19(b)ssiiYY((ss) ) dd iiyy((tt)/)/dtdt iii i = 0= 01122nn

4. 4. ss11 5. 5. xx11xx22xxnn

33--19(c)19(c)

33--88

33--20 (320 (3--60) 60)

(3-60)

(3-61)

33--2020 xx11 xx22



36

CHAPTER

33--99 33--2020 RR((ss) ) YY((ss) )

(3-62)

BB

(3-63)

(3-64)

x(t) r(t) y(t) abc d



37

CHAPTER

1. 1. s s 11 ss

2. 2. yy((tt) )

3. 3.

4. 4. SFG SFG

33--1010 33--2020

1. 1. 33--2020 33--21212. dx1(t)/dt dx2(t)/dt x1(t)x2(t) r(t) 3. 3.



38

CHAPTER

33--21 21 33--20 20 (3-65)

4. 4. xx11((tt))xx22((tt) ) rr((tt) ) yy((tt) )

(3-66)

33--1111 33--22(a)22(a)

1. 1.

33--22(b)22(b)

3-22(b)

2. dx1(t)/dtdx2(t)/dt dx3(t)/dt r(t) x1(t)x2(t)x3(t)

3. 3. 33--22(b)22(b) --



39

CHAPTER

33--22 22 (a) (a) (b) (b) (a) (a)



40

CHAPTER

(3-67)

(3-68)

MATLAB MATLAB 1. ACSYS MATLAB TFcal

(Transfer Function Calculator)

33--2323

2. (Help for 1st Time User) 3-24 MATLAB



41

CHAPTER

33--23 23

33--24 24 TFcalTFcal MATLAB MATLAB

3. 3. (Transfer Function Calculator)(Transfer Function Calculator) (())



42

CHAPTER

4. 4. 33--2525

33--25 25 TFcalTFcal

33--1212

33--2525

(3-69)

YY((ss)/)/RR((ss))

33--25 (a)25 (a) (Multiply Two Transfer (Multiply Two Transfer Function) Function) (( 33--2323 ))



43

CHAPTER

1. 1. MATLAB MATLAB GG11((ss) ) GG22((ss) )

2. 2.

33--2626

33--26 26 33--1212 33--25 25 (a) (a) TFcalTFcal

(3-70)



44

CHAPTER

3. 3. TFcalTFcal (Add Two Transfer Functions) (Add Two Transfer Functions) (Single Loop Feedback) (Single Loop Feedback) 33--2525 (b)(b) (c)(c)

(b) (b) (3-71)

(c) (c) (3-72)



45

CHAPTER



46

CHAPTER



47

CHAPTER



48

CHAPTER

Documents

方塊圖及訊號流程圖 - 歡迎來到生物電磁 ...bem.bime.ntu.edu.tw/LESSON/AC/BCKUO_2008/Ch03.pdf · chapter 方塊圖及訊號 ... 號處理 的換能器。 2

方塊圖及訊號流程圖 - 歡迎來到生物電磁 ...bem.bime.ntu.edu.tw/LESSON/AC/BCKUO_2008/Ch03.pdf · chapter 方塊圖及訊號 ... 號處理的換能器。 2