Ly Thuyet Dieu Khien Tu Dong cu

8/14/2019 Ly Thuyet Dieu Khien Tu Dong cu

1/28

L thuyt KTchuyn thi c

Ngi vit: Bi Trung HiuNgnh iu khin t ng

Khoa in-in tTrng HBK tp H Ch Minh


2/28

Li tha:Nh bit, vi Matlab, cng vic hc tp mn KT tr nnrt n gin v th v. Tuy nhin, i ph vi k thi, d bnl mt ngi hc rt tt l thuyt nhng khng ch trng ncch lm bi vn c th b im thp.

mt ln b nh th, ti nh phi b ra mt khong thigian c th thch nghi vi cng vic tt nhin ca SV: thi c!Trong bi ny, ti trnh by vi cc bn 2 bi ton rt c bnca l thuyt KT.V biu Bode.Thit k mt khu ri rc.

Tt nhin, chng s c trnh by gii vi Caculator, ti sdng FX570MS.


3/28

V gin Bodevi s tr gip ca FX570MS

Vi Matlab, cng vic ny rt n gin dng dng lnh:bode(hm_truyn) vi hm truyn c khai bodi dng:

Hm_truyn=tf(t_s,mu_s)Hm_truyn=zpk(zero,cc, _li)cc thng s ph

Tuy nhin, i ph vi k thi, bn phi v c biu

Bode dng Caculator, l thuyt trong sch KT hng dn cc bn mt cch rt chi tit, ti ch nucch cc bn dng Caculator tnh ra cc kt qu ch:


4/28

V gin Bode bin vi s tr gip ca FX570MS

L thuyt c trnh by chi tit trong sch LT KT nhxut bn HQG tp H Ch Minh trang 112-113.

1i

iT

=

Bc 2: Dng FX570MS Mode 2 (CMPLX) nhphm truyn cn kho st, ch thay bng A*i. Vickho st s cn cc tn s gy, ta ch n gin thaychng kim sot vic v ng hay sai.

Xt v d sau lm r iu :

Bc 1: Xc nh tt c cc tn s gy v

xp chng theo trt t tng dn


5/28

V gin Bode bin vi s tr gip ca FX570MS (v d1)

( ) ( ) ( )0.510

100 1 100 s s

G s e s s s+

= + +Bc 1: Cc tn s gy (lu hm m khngnh hng ti Bode bin )

V biu Bode bin gn ng ca h thng c hm truyn: (thi hc k 2 nm 2004-2005 )

1 2 31, 10, 100 = = =Nhn xt:Hm truyn c mt khu tch phn l tng


6/28


Bc 2: Dng Caculator (FX570MS):Nhn Mode2(CMPLX) tc Complex

Vic tip theo, bn nhn phm Calc, sau thay A bngcc gi tr

Nhp s liu nh sau: (Tnh bng n v dB)

20logAbs(100(Ai+10)(Ai)(Ai+1)(Ai+100))(Ti ly A l bin s trong v d trn)

Calc: A? 0.01= 60Calc: A? 1= 17Calc: A? 10=-17Calc: A? 100=-42

Calc: A? 1000=-80


7/28


Ni cc im trn li, bn s c c bn Bodebin cn v.

Kt qu nh sau:


8/28

Mu xanh: Bode dng Matlab

Mu : V xp x cc gi tr


9/28

V gin Bode pha vi s tr gip ca FX570MS

Trn, ti trnh by cch v Bode bin , cn cchv Bode pha, sn y ti cng xin dn ra:

Trong gio trnh KT, ta khng thy hng dncch v Bode pha, mt mt v cc bc tin hnhca n hi rc ri, m kt qu cho cng khng thtchnh xc (Khng m bo sai s nh Bode bin(


10/28


( ) ( )1

l

ii

=

=

( ) ( ) ( ) ( )11

l l

iii

G j Arg G j G j ==

= = = C s l thuyt:

S dng FX570MS, Mode2 (CMPLX). Nhp hm sdng:

( ) ( )( )1

l

ii

Arg G j =

=


11/28


Lu :

Phi phn r cc tch s ca hm truyn thnh cc tngArg.

Chuyn Arg ca hm m v dng:( ) ( ) ( )arg arg /Ts Tje e T rad s = =

Xt v d sau r hn:

V biu Bode pha ca hm truyn cho V d1


12/28

V gin Bode pha vi s tr gip ca FX570MS (V d 2)

Nhp hm kho st nh sau:(n v: )

Cng vic tip theo:Calc A? 0.01 -90.8Calc A? 0.1 -98.05Calc A? 0.5 -128Calc A? 1 -158Calc A? 2 -200Calc A? 10 -421Calc A? 20 -697Calc A? 50 -1580Calc A? 100 -3000

arg(Ai+10)-0.5A*180/pi-arg(Ai)-arg(Ai+1)-arg(Ai+100)


13/28

Mu xanh: Bode dng Matlab

Mu : V xp x cc gi tr


14/28


Cc sai lm thng gp:

Khi lm vic vi hm m, khng a v dng T mvn dng arg(exp(-Tj)), bn lu l hm m min s phc c chu k tun hon l 2.Khi lm vic vi hm m qun chuyn n v t radsang deg.Khng phn r cc tch ca hm truyn thnh cc tngArg khi gp mt s hm bt thng gy sai kt qu.

Vic tnh ton khi th cc gi tr rt nhanh, khng mt nhiu thi gian, ch khong 3-5 hon thnh bi Bode pha.


15/28

Kt lun v phng php v Bode:Nh phn tch trn, vic v Bode khng phi l cng

vic qu kh khn, tuy nhin, n l cng vic nng v ton hc, vnu bn rt thnh thc vi cch v bng tay, dng l thuyttrang 112-113(Sd), khi bn xc nh cc khu ca hm truyn, c

th bn s khng mt thi gian khi v Bode bin (khong 3),tuy nhin, vi bn khng cn xc nh cc khu ca hm truyn,vn c th v c m khng c trc trc g, bn nn nh rngcch v m yu cu ch l v gn ng.

Tht ra, ti c th v chnh xc n 99% gin Bodenu dng FX570MS. Lc , ti ang lm li ci cng vic camt chic my, v ti cht ngh, lm tt cng vic ca mt ci myth c g phi t ho


16/28

Kho st h ri rc dng PP Kg trng thi:

( ) ( ) ( )10

2 3G s s s= + +

y cng l mt dng bi tp rt thng hay gp trongcc k thi, ti cng th dng FX570MS gii:

Ti ly v d trong sch gio trnh n gin:(trang 280-281)

C(t)+- ( )G s

r(t)e(t) e(kT)

eR(t)T

0.1T s=a. Thnh lp h phng trnh trng thi m t h thng trn.

b. Tnh p ng ca h i vi tn hiu vo l hm nc n v(nhn qu)

ZOH


17/28


0

10 B =

0 4

6 5 A

= ( )1 0C =

Bc 1: Mt cch my mc, ta tm c cc ma trn A, B,D mt h lin tc:

C(s)( )G sER(s)

Ch rng h phng trnh m t h lin tc c dng:

( ) ( ) ( )( ) ( )

r x t Ax t Be t c t Dx t

= +=

&


18/28


( ) ( )( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

1

5 12 3 2 3

62 3 2 3

s s s s s

s sI A s

s s s s

+ + + + + = = + + + +

Bc 2: Tnh ma trn qu .

Cch tm ma trn nghch o:

( )

11 1 11 11

1 1

1

det

n n

n nn n nn

a a A A

A A A

a a A A

= =

K K

M O M M O M

L L


19/28


20/28

Kho st h ri rc dng PP Kg trng thi:( ) ( )( )t InverseLaplaceTransform s = Tnh

( )2 3 2 3

2 3 2 3

3 2

6 6 2 3

t t t t

t t t t

e e e et

e e e e

= + +

Cch tnh Laplace ngc: Gi s phng trnh cn bin i cdng t s/mu s. Vi bc t s b hn bc mu s.

Ta chia ra 3 trng hp sau:

1. Nghim mu s l nghim n.2. Nghim mu s l nghim thc kp.

3. Nghim mu s l nghim phc lin hp.


21/28


( )( )( )

( )

( ) ( )1

k

i

i

Num s Ts s F s

Den s Ms s s s=

= =

1

ik

X t

i

i

n e =

1. Nghim mu s l nghim thc n..

( )

( ) ( )1

?,

i ik

ii

Ts ACalc A X n

d Ms A X X A

dX =


22/28


23/28


( ) ( )( )

( )

( ) ( )( )

2 2

1

k

i ii

Num s Ts s F s

Den s Ms s s =

= =+ +

( ) ( )( )1

cos sinit k

i r i i

et t

= +

( ) ( )( ) ( ) ( )( ) ( )( )

2 2

2 2

1

2i i k

j ji j i

Ts AMode A s F s

Ms A A

=

= + + =+ +

3. Nghim mu s l nghim phc lin hp: s1,2 = -j

( )? i r iCalc A X real Shilft imag = = =


24/28


( )2 2

5

1 3 2 9

s F s

s s s

+= +

( ) ( ) ( ) ( )( )2

30.15 0.4 0.23 0.24cos 3 0.02sin 33

t t t e f t e t e t t = + +

2 2

5 ?1 0.15

1 3 2 9 ,

A Calc A nd X X X A

dX

+ = +

Ti ly mt v d n gin lm r vn ny:

( ) ( )( )

( ) ( )( )

12

22

5 ?3 0.41 2 9

5, ?3 0.23

1 2 9

X Calc X m X X

d X A Calc A m

dX X X

+ = +

+ = +

20.0252 ?2 3

0.241 3

r

i

AMode Calc A i A A

=+ + =


25/28


0

0.042

0.779

T

d Bd B

== 1 0d D D

= =

Tr li v d ca bi ton ri rc, by gi ta tnh cc ma trn Ad ,Bd ,Dd :

0.975 0.0780.468 0.585d A

=

Bc 3: Mt cch my mc, ta th Ad = (T)

Vi lu rng, ta c th dng chc nng tch phn ca FX570MS

Bc 4: H pt trng thi m t h thng ri rc vi tn hiu vo r(kT)

1d d d d

d

x k A B D x k B r k

c k D x k

+ = +

=


26/28

Kho st h ri rc dng PP Kg trng thi:Dng chc nng ma trn ca FX570MS:

( ) ( )( ) ( )( ) ( )( ) ( )

3 2

4 1 1 ? 2 ? 2 ...

4 1 2 ? 2 ?1 ...

4 1 3 ?1 ? 2 ...

Mode times MAT

Shift edit A m n

Shift edit B m n

Shift edit C D m n

:

( ) ( )( ) ( )( ) ( )

4 3 1 ' '

4 3 2 ' '

4 3 3

Shift Mat A

Shift Mat B

Shift Mat C


27/28

Kho st h ri rc dng PP Kg trng thi:Ta tm c phng trnh trng thi: Nhp ma trn A l ma trn va

tm c. Gn ma trn C=(0 0)T sau gn ma trn Ans l ma trnC.(r rng, c th dng ti ma trn cp 3, tc o hm cp 3)

( ) ( ) ( )*Mat A Mat Ans Mat B Ta c nhn nt =n chng no k=n theo yu cu bi ton.

n y, ta gii xong bi ton kho st h ri rc dng pp kg trng thi, tuy cc bc tnh u c th

dng Caculator, nhng bn phi thc hnh vi ln th mi mong c th lm khng sai st.V ti xin nhc li rng, y ch l bin php i ph vi thi c, bn

cn phi c s tm hiu thch hp khi dng Matlab. Hin ti, ti sdng chng trnh matlab 7.0 v Mathematica 5.0, cc chngtrnh trn phc v rt tt cng vic tnh ton .


28/28

Nu bn c hng th trao i vi tiv phng php dng Caculator gii cc

bi tp trong thi c cc mn trng Hxin gi mail v a ch hp th:[email protected], rt vui lng trao

i kinh nghim s dng vi bn.
mailto:%[email protected]:%[email protected]

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Ly Thuyet Dieu Khien Tu Dong cu