27

CHNG 2: THIT K MCH IU KHIN LOGIC KH NN - IN KH NN

Thit k ra mt mch iu khin t ng tI u v kinh t l ht sc quan trng. Chng ny gii thiu phng php thit k mch iu khin kh nn, in kh nn kh nn bng phng php biu Karnaugh. Trnh t thit k c th hin qua cc v d c th.

2.1. THIT K MCH KH NN CHO QUY TRNH VI 2 XILANH

Gi s quy trnh lm vic ca mt my khoan gm hai xilanh: khi a chi tit vo xilanh A s i ra kp chi tit. Sau piston B i xung khoan chi tit v sau khi khoan xong th piston B li v. Sau khi piston B li v th xilanh A mi li v.

Ta c s kh nn v biu thi gian (biu trng thi) nh sau:

Hnh 2.1. S kh nn v biu trng thi

T biu trng thi, ta xc nh iu kin cc xilanh lm vic: Bc 1: piston A i ra vi tn hiu iu khin A+ A+ = a0.b0 Bc 2: piston B i ra vi tn hiu iu khin B+ B+ = a1.b0

Xilanh A a0

A+

a1

A-

Xilanh B b0

B+

b1

B-

Xilanh A

Xilanh B

bc: 0 1 2 3 4 51

a0

a1 a1

a0

A+

b0 b0

b1

B+ B- A- A+a0 b0

a1 b0

a1 b1

a1 b0

a0 b0

a1

a0 b1

b0

28

Bc 3: piston B li v vi tn hiu iu khin B- B- = a1.b1 Bc 4: piston A li v vi tn hiu iu khin A- A- = a1.b0 Phng trnh logic: A+ = a0.b0 B+ = a1.b0 B- = a1.b1 A- = a1.b0 So snh cc phng trnh trn, ta thy iu kin thc hin B+ v A- ging nhau

Nh vy v phng din iu khin th iu khng th thc hin c. c th phn bit c cc bc thc hin B+ v A- c cng iu kin (a1.b0) th c

2 phng trnh phi thm iu kin ph. Trong iu khin ngi ta s dng phn t nh trung gian (k hiu x v x l tn hiu ra ca phn t nh trung gian).

Phng trnh logic trn c vit li nh sau:

x.b.aA

b.aB

x.b.aB

b.aA

01

11

01

00

====

+

+

tn hiu ra x ca phn t nh trung gian thc hin bc 2 (B+), th tn hiu tn hiu phi c chun b trong bc thc hin trc (tc l bc th 1). Tng t nh vy tn hiu ra x ca phn t nh trung gian thc hin bc 4 (A-), th tn hiu phi c chun b trong bc thc hin trc (tc l bc th 3).

T ta vit li phng trnh logic nh sau:

x.b.aA

x.b.aB

x.b.aB

x.b.aA

01

11

01

00

====

+

+

Trong quy trnh thm mt phn t nh trung gian (Z), ta c tn hiu ra iu khin phn t nh l:

==

+

x.b.aX

x.b.aX

00

11

Nh vy ta c 6 phng trnh khng trng nhau:

Thm

Chun b trc

29

x.b.aX

x.b.aX

x.b.aA

x.b.aB

x.b.aB

x.b.aA

00

11

01

11

01

00

======

+

+

+

Vi 6 phng trnh trn ta c s mch logic nh sau:

Hnh 2.2. S mch logic

Rt gn bng phng php biu Karnaugh: Thit lp biu Karnaugh: ta c 3 bin a1 v ph nh a0 b1 v ph nh b0 x v ph nh x Biu Karnaugh vi 3 bin c biu din nh sau:

&

& S R

X+

X-

&

& S R

&

& S R

A+

A-

B+

B-

Z

x a0 a1 b1 b0 x

A+

A-

B+

B-

A+

B+

X+

A-

X-

X-

4 8

3 7

2 6

1 5b0

b0

b1

b1

a0

a1

a1

a0

x x

b0

b1

a0

a1

a1

a0

Trc i xng

Hnh 2.3. Biu Karnaugh vi 3 bin

30

Cc cng tc hnh trnh s biu din qua trc i xng nm ngang, bin ca phn t nh trung gian biu din qua trc i xng thng ng. Trong iu khin gi thit rng, khi cng tc hnh trnh (v d a0) b tc ng th cng tc hnh a1 s khng tc ng.

Khng xy ra trng hp c 2 cng tc hnh trnh a0 v a1 cng tc ng ng thi hoc c 2 cng tc tc ng ng thi. By gi ta n gin hnh trnh ca xilanh A bng biu Karnaugh: Theo biu trng thi, ta thit lp c biu Karnaugh cho xilanh A:

Hnh 2.4. Biu Karnaugh cho xilanh A Bc thc hin th nht l piston A i ra (A+) v dng li cho n bc thc hin

th 3. Sang bc th 4 th piston A li v (A-). Cc khi 1, 2, 3 v 7 k hiu A+ v cc khi 5, 6 k hiu A-. n gin hnh trnh ca xilanh A (A+) s c thc hin trong ct th nht ( x ). Ta

c phng trnh logic ca A+ l: A+ = a0.b0. x .S0 (vi S0 l nt khi ng) Ct th nht ( x ) gm cc khi 1, 2, 3 v 4, trong khi 4 l trng. A+ = a0.b0. x + a1.b0. x + a1.b1. x + a0.b1. x hay: A+ = (a0 + a1).b0. x + (a1 + a0).b1. x = b0. x + b1. x = (b0 + b1). x A+ = x .S0 Tng t, ta c phng trnh logic ca A-: A- = a1.b0.x n gin khi 5 v 6 A- = a1.b0.x + a0.b0.x = (a1 + a0).b0.x A- = b0.x Phng php tng t nh xilanh A, ta n gin hnh trnh ca xilanh B bng biu

Karnaugh:

1 2 3 4 51

A+ B+ B- A- A+

a1

a0

Bc: A+

A+

A+

A-

A+

A-

4 8

3 7

2 6

1 5 b0

b0

b1

b1

a0

a1

a1

a0

xxKhi ng

31

Hnh 2.5. Biu Karnaugh cho xilanh B Ta c phng trnh logic ban u ca B+: B+ = a1.b0. x n gin khi 2 v 3 B+ = a1.b0. x + a1.b1. x = (b0 + b1).a1. x B+ = a1. x V B- = a1.b1.x n gin ct x gm cc khi 5, 6, 7 v 8, trong

khi 8 l trng. Ta c: B- = a0.b0.x + a1.b0.x + a1.b1.x + a0.b1.x = (a0 + a1).b0.x + (a1 + a0).b1.x = b0.x + b1.x = (b0 + b1).x B- = x n gin phn t nh trung gian (X) bng biu Karnaugh: Biu Karnaugh cho thy rng phn t nh trung

gian v tr SET bt u trong khi 3, gi v tr cho n khi 7 v 6. T khi 5 bt u v tr RESET v gi v tr cho n khi 1 v 2.

Phng trnh logic ban u ca X+: X+ = a1.b1. x n gin X+ min gm cc khi 3, 7,

4, v 8, ta c: X+ = a1.b1. x + a1.b1.x + a0.b1. x + a0.b1.x = ( x + x).a1.b1 + ( x + x).a0.b1 = (a1 + a0).b1 X+ = b1 Phng trnh logic ban u ca X-: X- = a0.b0.x n gin X- min gm cc khi 1, 5, 4 v 8, ta c: X- = a0.b0. x + a0.b0.x + a0.b1. x + a0.b1.x = ( x + x).a0.b0 + ( x + x).a0.b1 = (b0 + b1).a0 X- = a0 (Khi trng 4 v 8 c php s dng chung cho c X+ v X-) Vy phng trnh logic sau khi n gin l:

1 2 3 4 51

A+ B+ B- A- A+

b1

b0

Bc: B-

B+

B+

B-

B-

B-

4 8

3 7

2 6

1 5 b0

b0

b1

b1

a0

a1

a1

a0

xx

X-

X-

X+

X+

X+

X-

4 8

3 7

2 6

1 5b0

b0

b1

b1

a0

a1

a1

a0

x x

Hnh 2.6. Biu Karnaugh cho phn t nh trung gian

32

A+ = x .S0 (S0: l nt khi ng) A- = b0.x B+ = a1. x B- = x X+ = b1 X- = a0 S mch logic c biu din nh sau:

Hnh 2.7. S mch logic sau khi n gin S mch lp rp kh nn c biu din:

S R

X+

X-

&

& S R

& S R

A+

A-

B+

B-

Z

x a0 a1 b1 b0 x

A+

A-

B+

B-(Z: phn t nh trung gian)

S0

33

Hnh 2.8. S mch lp rp S nguyn l lm vic ca mch kh nn n gin nh sau:

Hnh 2.9. S nguyn l mch iu khin kh nn

S0

Xilanh A a0 a1

A- A+

Xilanh B b0 b1

B-B+

X- X+

Z (phn t nh)

b0 b1 a0 a1

x

x

Xilanh A a0 a1

A- A+

Xilanh B b0 b1

B-B+

X- X+

a1b0

b1x x

S0

Z (phn t nh)

a0

34

Vi phng php gii tng t nh trn. Nu ta thay hai van o chiu iu khin bng tn hiu kh nn bng hai van in th ta c s mch in iu khin:

Hnh 2.10. S nguyn l mch iu khin bng in

X-

X+

x

xx

x

b 0 A-

B-x

a 0x

b 1 Z(Rle)

B+

A+S0 x(n

a 1

35

2.2. THIT K MCH KH NN CHO QUY TRNH VI 3 XILANH Gi s, quy trnh ca my lm sch chi tit gm 3 xilanh: chi tit a vo v s c

kp bng xilanh A i ra. Sau xilanh B s thc hin quy trnh lm sch mt pha ca chi tit bng vi phun trong khong thi gian t1. Sau chi tit s c chuyn sang v tr i din bng xilanh C. Ti v tr ny chi tit s thc hin quy trnh lm sch pha th 2 ca chi tit ny bng vi phun trong khong thi gian t1. Sau khi thc hin xong , xilanh C tr v v tr ban u, ng thi xilanh A s li v chi tit c tho ra.

Ta c s kh nn v biu trng thi nh sau:

Hnh 2.11. S v biu trng thi A+: kp chi tit

++21 B,B : qu trnh thc hin lm sch chi tit bt u 21 B,B : qu trnh thc hin lm sch chi tit kt thc

C+: chi tit v tr 1 C-: chi tit v tr 2 A-: tho chi tit

Thit lp phng trnh logic:

Xilanh A a0 a1

A- A+

Xilanh B b0 b1

B- B+

Xilanh C c0 c1

C- C+

Xilanh A

Xilanh B

bc: 1 2 3 4 5 6

a0

a1

a0

A+

b0 b0

b1

+1B C

-

7 8 9 101

Xilanh C

a1

b0

b1

c1 c1

c0

c1

c0

t1 t1

+2B C+

A- 1B 2B

36

Bi v lnh B+ v B- ca piston B trong qu trnh thc hin c lp li 2 ln, cho nn ++21 B,B v

21 B,B s c lin kt bng phn t OR.

Lnh C+ v A- c thc hin ng thi, cho nn phng trnh logic ging nhau. Ta c phng trnh logic cho A+: A+ = a0.b0.c1 Phng trnh logic cho B+:

B+ = (a1.b0.c1) + (a1.b0.c0) Phng trnh logic cho B-:

B- = (a1.b1.c1) + (a1.b1.c0) Phng trnh logic cho C-: C- = a1.b0.c1 Phng trnh logic cho C+, A-: C+ = a1.b0.c0 A- = a1.b0.c0 A- = C+ Phng trnh logic vi cc iu kin: Bi v phng trnh logic cho +1B v C

-, cng nh +2B v C+/A- ging nhau, cho nn

phi thm iu kin ph, l phn t nh trung gian. Lnh SET ca phn t nh trung gian s nm khi gia +1B v

1B . Lnh RESET ca phn t trung gian s nm

khi gia +2B v 2B .

Biu Karnaugh c biu din nh sau:

Hnh 2.12. Biu Karnaugh vi 4 bin

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

X-

2B A

+ X+

1B

c1

C- +2B

A- C+

+1B

c0 c0 c0 c0 c1 c1 c1 c1

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

37

Ta c:

A+ = a0.b0.c1. x

B+ = (a1.b0.c1. x ) + (a1.b0.c0.x)

B- = (a1.b1.c1.x) + (a1.b1.c0. x )

C- = a1.b0.c1.x

C+ = a1.b0.c0. x

A- = a1.b0.c0. x

X+ = a1.b1.c1. x

X- = a1.b1.c0.x

n gin hnh trnh ca xilanh A bng biu Karnaugh (A+, A-) (Ghi ch: i vi nhng quy trnh phc tp, ta n gin biu Karnaugh bng quy tc sau y:

Ni rng ra min ca khi Mi khi ch ghi mt bc thc hin Nhng khi trng c th kt hp vi khi ghi bc thc hin Nhng min c to ra phi i xng qua trc i xng S khi ca min c to ra phi l ly tha ca 2.). Theo quy tc , ta n gin xilanh A nh sau:

Hnh 2.13. Biu Karnaugh cho xilanh A Ta c, phng trnh logic sau khi n gin: A+ = c1.S0 (S0: nt n khi ng) A- = b0.c0. x n gin hnh trnh ca xilanh B bng biu Karnaugh ( ++ 21 B,B v 21 B,B ) Biu Karnaugh cho xilanh B c biu din nh sau:

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

A+

c1

A- A+ A+ A+

A+ A+ A+ A+

38

Hnh 2.14. Biu Karnaugh cho xilanh B Ta c, phng trnh logic sau khi n gin: +1B = a1.c1. x

+2B = c0.x

B+ = (a1.c1. x ) + c0.x 1B = c1.x

2B = c0. x

B- = (c1.x) + (c0. x ) n gin hnh trnh ca xilanh C (C+, C-) Biu Karnaugh cho xilanh C c biu din nh sau:

Hnh 2.15. Biu Karnaugh cho xilanh C Ta c, phng trnh logic sau khi n gin: C+ = b0. x C- = b0.x n gin hnh trnh ca phn t nh trung gian (X+, X-) Biu Karnaugh cho phn t nh trung gian c biu din nh sau:

Hnh 2.16. Biu Karnaugh cho phn t nh trung gian

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

2B

c1

2B

+1B

+1B

+2B

1B 1B

+2B

2B

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

C+

c1

C- C- C+ C+

C- C+ C- C-

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

X+

c1

X- X- X+ X-

X- X+ X+ X+

39

Ta c, phng trnh logic sau khi n gin: X+ = b1.c1 X- = b1.c0 Phng trnh logic ca quy trnh sau khi n gin bng biu Karnaugh: A+ = c1.S0 A- = b0.c0. x

B+ = (a1.c1. x ) + c0.x B- = (c1.x) + (c0. x )

C+ = b0. x C- = b0.x X+ = b1.c1 X- = b1.c0 S mch logic ca quy trnh c biu din:

Hnh 2.17. S mch logic S nguyn l mch iu khin bng tn hiu kh nn:

&

& S R

X+

X-

&

&

&

&

Z

x a0 a1 b1 b0 xc1 c0

&

& S R

A+

A-

&

& S R

C+

C-

0 t11

S R

B+

B-

1

S0

40

Hnh 2.18. S mch kh nn

S0

Xilanh A a0 a1

A- A+

Xilanh B b0 b1

B- B+

Xilanh C c0 c1

C- C+

a0 b0

c1 c0

b0

c0 a1

c1c1

X- X+

b1

c1c0

41

2.3. THIT K MCH KH NN VI 2 PHN T NH TRUNG GIAN Gi s, quy trnh cng ngh c biu din qua biu trng thi sau:

Hnh 2.19. Biu trng thi Phng trnh logic ca quy trnh: T biu trng thi, cc v tr 1, 3 v 5 phng trnh logic ca cc xilanh A+, B+

v C+ ging nhau. Cho nn phn bit c cc hnh trnh trn, ta phi thm 2 phn t nh trung gian (k hiu X v Y). Phng trnh logic ca quy trnh c vit nh sau:

A+ = a0.b0.c0. x . y B+ = a0.b0.c0.x. y C+ = a0.b0.c0.x.y X+ = a1.b0.c0. x . y

A- = a1.b0.c0.x. y B- = a0.b1.c0.x.y C- = a0.b0.c1. x .y X- = a0.b0.c1.x.y

Y+ = a0.b1.c0.x. y Y- = a0.b0.c0. x .y Biu Karnaugh c biu din nh sau: (tn hiu iu khin ca phn t nh

trung gian c biu din i xng qua trc)

Hnh 2.20. Biu Karnaugh vi 2 phn t nh trung gian

Xilanh A

Xilanh B

bc: 1 2 3 4 5 6

a0

71

Xilanh C

a1

b0

b1

c1

c0

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

A+ X+

c1

x

x

y

y

y

y

A-B+

C+

Y- C-

X- B-

Y+

x

x

x

x

y

y

y

y

42

n gin cc hnh trnh bng biu Karnaugh: n gin hnh trnh ca xilanh A+, A- c biu din:

Ta c, phng trnh logic sau khi n gin: A+ = x . y .S0 (S0: nt khi dng) A- = x

Hnh 2.21. Biu Karnaugh cho xilanh A+ v A- n gin hnh trnh ca xilanh B+, B- c biu din:

Hnh 2.22 Biu Karnaugh cho xilanh B+ v B- Ta c, phng trnh logic sau khi n gin:

B+ = a0.x. y B- = y

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

A+

A-

c1

x

x

y

y

y

y

+

--

-

- -

-

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

-

-

c1

x

x

y

y

y

y

-

+B+

-

- -

- B-

43

n gin hnh trnh ca xilanh C+, C- c biu din:

Hnh 2.23. Biu Karnaugh cho xilanh C+ v C-

Ta c, phng trnh logic sau khi n gin: C+ = b0.x.y C- = x n gin hnh trnh ca xilanh X+, X- c biu din:

Hnh 2.24. Biu Karnaugh cho xilanh X+ v X- Ta c, phng trnh logic sau khi n gin:

X+ = a1 X- = c1

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

-

-

c1

x

x

y

y

y

y

-

-

C+

-

-

+

C-

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

-

+

c1

x

x

y

y

y

y

X+

++

+

- -

X- +

44

n gin hnh trnh ca xilanh Y+, Y- c biu din:

Hnh 2.25. Biu Karnaugh cho xilanh Y+ v Y-

Ta c, phng trnh logic sau khi n gin: Y+ = b1 Y- = c0. x

Phng trnh logic ca quy trnh sau khi n gin bng biu Karnaugh: A+ = x . y .S0 B+ = a0.x. y C+ = b0.x.y X+ = a1 Y+ = b1

A- = x B- = y C- = x X- = c1 Y- = c0. x S mch logic sau khi n gin bng biu Karnaugh:

Hnh 2.26. S mch logic

a0 b0

a0 b0

a0 b1

a0 b1

a1 b1

a1 b1

a1 b0

a1 b0

x

x

c0 c0 c0 c0 c1 c1 c1

- -

c1

x

x

y

y

y

y

Y+

+ +

+ Y-

+

-

S R

X+

X-

& S R

& S R

A+

A-

B+

B-

x a0 a1 b1 b0 xS0 y y c1 c0

S R

Y+

Y-

&

& S R

C+

C-

45

S nguyn l mch iu khin bng tn hiu kh nn:

Hnh 2.27. S mch kh nn

Xilanh A a0 a1

A- A+

Xilanh B b0 b1

B- B+

Xilanh C c0 c1

C- C+

Y- Y+

b1

a0 b0S0

c0

X- X+

a1 c1

x

y x

y

Hnh 2.28. S nguyn l mch iu khin bng in

x S 0 A+

X(Rle)a 1 x c 1

A-

x x

y

x

x a 0 B+y

Y(Rle)

c 0y

b 1 y y

y B-

C+yb 0 x

C-x

Mch ng lc K 1 A+

K 2

K 3

K 4

K 5

K 6

A-

B+

B-

C+

C-