Bài 3 TN DKTD

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Bi 1: Thit k b hiu chnh sm pha

Cho h thng vi hm truyn sau, hy thit k khu hiu chnh sm pha C(s)

Ta bit khu hiu chnh sm pha c dng:

mmn

Trong Matlab c mt cng c gi l SISOtool, cng c ny cung cp cho chng ta mt

giao din dhnh dung hn thun tin cng nh qu trnh thit k cc biu khin tr

nn nhanh v chnh xc hn.

a/. tin hnh thit k khu hiu chnh sm pha. T ca s Command windown ta tin

hnh nhp hm truyn bng lnh sau:

>>G=tf(20,conv(conv([1 0],[1 1]),[1 2])); H=tf(1,1);

kch hot cng c SISOtool ta thc hin lnh sau:

>> sisotool

Ca s thit k Sisotool design v Control and Estimation xut hin nh sau:

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Trong ca s Control and Estimation kch chn System Data nhp d liu cho cng

c sisotool.

Nhp thng snh trn hnh trn. Chn OK. Nh vy trong ca s Sisotool design, by

gis biu din h thng bao gm cc th: QNS, bin v pha vi cc thng s

cha hiu chnh.

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Vo tab Analysis => Respond to step command :Ta sc p ng qu ca h thng.

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Nhn xt:

+ Da vo QNS ta thy rng hm h thng c 2 cc nm bn phi trc o

nn h thng s khng n nh. Cc cc ca h thng l:

>> [cuc,zero]=pzmap(G)

cuc =

0

-2

-1

zero =

Empty matrix: 0-by-1

+ Da vo biu bode v pha ta c cc trnh sau:

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Gm = 0.3000

Pm = -28.0814

wcp = 1.4142

wcg = 2.4253

Nh vy Pm < 0 suy ra h thng khng n nh

+ Da vo p ng nc ca h thng: xt thy th khng n nh nn h

thng kn s khng n nh.

b/.T cu a ta thy h thng cha n nh nn chng ta cn phi hiu chnh cho h thng

n nh v ng thi t cht lng u ra ng nh mong mun:

Thit k h thng vi tiu chun POT lead (l khu hiu chnh sm pha).

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Tin hnh khoanh vng thit k: th tc nh sau: t ca sQNS [Chut phi] =>

Design Requirements => New ca s mi nh sau:

Design requirement type: chn Settling time khoanh vng thit k cho thi gian qu

(vng trng trong QNS l vng tha mn). Design requirement parameters l gi

tr khoanh vng ng vi tiu chun cht lng- chng hn y th gi tr ny bng 8s.

Tng t ta skhoanh vng cho vt l(Percent overshoot). Ta c vng tha mn

yu cu ca h thng nh sau:

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Mt khc v mt ton hc ta c cng thc xc nh cc cp cc quyt nh, t chng

ta ch cn a cc im cc ( vung mu hng) vcc im ny cng gn cng tt:

Mc khc ta c

Vy nn Ta chn : .

V

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Suy ra: wn > 0.7 chn wn = 1.

Ta c cp cc quyt nh nh sau:

Nh vy t ca s Control and Estimation chn tab Compensator Editor ta nhn c

khu hiu chnh sm pha:

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Vy ta c khu hiu chnh sm pha nh sau:

c/. Vo tab Analysis => Respond to step command :Ta sc p ng qu ca h

thng.Tp ng qu ta thy Pot = 10.8% v thi gian xc lp txl = 5s .Ph hp vi tiu

chun ca h thng.

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Nhn xt: So snh vi p ng qu cu a, ta thy h thng sau khi c hiu chnhhot ng n nh.

Bi 2: Thit k b hiu chnh tr pha ca h thng sau:

Ta bit khu hiu chnh tr pha c dng:

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a/. Tin hnh nhp hm truyn vo cng cSISOtool nh bi 1,

>>G=tf(20,conv(conv([1 0],[1 1]),[1 2])); H=tf(1,1);

kch hot cng c SISOtool ta thc hin lnh sau:

>> sisotool

tm thng s ca b hiu chnh t h kn ta tm c nghim ca h kn nh sau:

S1= -5

S2=-1 +jS3=-1-j

V khi cha hiu chnh th:

( ) Sau khi hiu chnh th

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( )

Vy :

Tm cc v zero ca C(s) theo cng thc sau:

| |

Vy ta c hm truyn ca b hiu chnh tr pha nh sau:

Chut phi t ca s QNS, Add => Lag thm mt khu hiu chnh tr pha.

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Do Matlab s t chn ngu nhin cc im cc v zero nn ta s hiu chnh li bng cch

chn chut phi t ca s SISOtool design => chn Edit Compenrator sau tin hnh

hiu chnh

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Sau khi thit k xong khu hiu chnh, ta tin hnh v p ng ca h thng vi u vo

hm dc.

T ca s Sisotool, vo menu Tools => Draw Simulink Diagram v m hnh m

phng Simulink ca b hiu chnh tr pha.

Sa i s khi m phng p ng u vo hm dc nh sau:

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M phng vi thi gian l 10s, nhn c tn hiu u ra nh sau:

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Nhn xt: ta thy c tnh pha lun mca khu hiu chnh tr pha, nn tn hiu ra lun

lun tr pha hn tn hiu vo.C th ni s dng khu hiu chnh tr pha s thu hp bng

thng ca h thng, lm cho h s khuch i ca h thng i vi tn hiu vo tn s cao

gim i, do khu hiu chnh tr pha khng c tc dng ci thin p ng qu .

b/. Tng tnh bi 1, vo tab Analysis => Respond to step command :Ta sc p ngqu ca h thng.

+ p ng qu trc khi hiu chnh

+ p ng qu sau khi hiu chnh tr pha

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Kt lun:Vy khu hiu chnh tr pha khng c tc dng ci thin p ng qu .

Bi 3: Thit k b iu chnh sm tr pha

Hm truyn khu hiu chnh sm tr pha c dng tng qut nh sau:

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a/. Thit k b hiu chnh sm trpha h thng c = 0.5, wn = 5 (rad/s) v h s vn

tc KV = 80.

Thc hin thit k b hiu chnh sm trc.

Vi tiu chun cht lng l = 0.5, wn = 5 (rad/s).

Thc hin tng tnh bi 1 ta thc hin nh sau:

>> G=tf(4,conv(1,[1 0.5]));H=tf(1,1);

>> sisotool

Tin hnh nhp cc thng s cho cng c SISOtool:

Ta c p ngqu khi cha hiu chnh l:

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Tin hnh khoanh vng nh bi 1 ta c vng tha mn iu khin tiu chun cht lng

ca h thng l:

V p ng qu trng thi online vi QNS:

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Xt = 0.5, wn = 5 (rad/s) suy ra:

Ta c thi gian xc lp l:

Nh vy ng qu trn l ph hp vy ta c C1(s) nh sau:

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t G1(s)=G(s)* C(s) ta c

Vi G1(s) ta thit k b hiu chnh tr pha tng t nh bi 2.

>> G=tf(conv(4*3.4259,[0.21 1]),conv([1.1 1],[1 0.5]))

Transfer function:

2.878 s + 13.7

----------------------

1.1 s^2 + 1.55 s + 0.5

Tin hnh nhp cc tham s ca cng c Sisotool, ta c QNS sau:

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Xt = 0.5, wn

= 5 (rad/s) suy ra:

Vy sau khi thm khu hiu chnh tr pha v khoanh vng d liu ta s dch chuyn cc

cc ca G1ti st v tr s1,s2:

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Nhn c khu hiu chnh tr pha nh sau:

Nh vy ta c b iu khin sm tr pha nh sau:

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M phng vi u vo l hm dc.

Nhn thy rng b hiu chnh sm tr pha c c 2 u im ca 2 b hiu chnh trn.

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b.So snh cc p ng qu ca cc khu hiu chnh.

+ Cha hiu chnh

+ Hiu chnh sm pha:

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+ Hiu chnh tr pha:

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+ Sm tr pha:

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Nhn xt:B iu khin sm tr pha c nhng u im ca b iu khin sm pha v c

th gip h thng ci thin p ng qu min tn s cao. V u im ca b hiu

chnh tr pha l gim sai s xc lp min tn s thp. Ging nh mt b lc thng di.

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Bài 3 TN DKTD