BI TH NGHIM 1

NG DNG MATLAB PHN TCH CC H THNG IU KHIN T NGI. MC CH MATLAB l mt trong nhng phn mm thng dng nht dng phn tch, thit k v m phng cc h thng iu khin t ng. Trong bi th nghim ny, chng ta s dng cc lnh ca MATLAB phn tich h thng nh xt tnh n nh ca h thng, c tnh qu , sai s xc lp II. CHUN B thc hin yu cu trong bi th nghim ny, chng ta cn phi chun b k trc cc lnh c bn ca MATLAB. Khi khi ng chng trnh MATLAB 6.5, ca s Command window xut hin vi du nhc lnh >>. thc hin cc lnh, chng ta s g lnh t bn phm theo du nhc ny. Chng ta cn tham kho v hiu r cc lnh c bn v nhn chia a thc, biu din hm truyn h thng v kt ni cc khi h thng. Ngoi ra, phn tch c tnh ca h thng, chng ta cn phi hiu k cc lnh nh: bode(G), nyquist(G), rlocus(G), step(G),grid on.. III. TH NGHIM III.1. Tm hm truyn tng ng ca h thng - Mc ch: Gip chng ta lm quen cc lnh c bn kt ni cc khi trong mt h thng. - Th nghim: Bng cch s dng cc lnh c bn conv, tf, series, parallel, feedback tm biu thc hm truyn tng ng G(s) ca h thng sau:

G1 = ( s + 3)( s + 5) , G2 = 2 , G3 = , H1 = s + 2s + 8 s s+2 Thc hin:

s +1

s

1

1

>> G1 = tf([1 1],conv([1 3],[1 5])); % Nhp hm truyn G1 >> G2 = tf([1 0],[1 2 8]); % Nhp hm truyn G2 >> G3 = tf(1,[1 0]); % Nhp hm truyn G3 >> H1 = tf(1,[1 2]) ; % Nhp hm truyn H1 >> G13 = parallel(G1,G3); % Tnh hm truyn tng ng ca G1, G3 >> G2H1 = feedback(G2,H1) % Tnh HTT ca G2, H1 >> G13G2H1 = series(G13,G2H1) % Tnh HTT ca G13 v G2H1 >> G = feedback(G13G2H1,1) % Tnh HTT ca h thng Ta c: G(s) =2s 4 + 13s3 + 33s 2 + 30 s S 6 + 12s5 + 62 s4 + 193s3 + 356 s2 + 270 s

III.2. Kho st h thng dng biu Bode - Mc ch: T biu Bode ca h h G(s) ta tm c tn s ct bin, d tr pha, tn s ct pha, d tr bin ca h thng h. Da vo kt qu tm c xt tnh n nh ca h thng hi tip m n v vi hm truyn vng h l G(s). - Th nghim: Kho st h thng phn hi m n v c hm truyn vng hG(s) = K ( s + 0, 2)( s 2 + 8s + 20) a. Vi K=10, v biu Bode bin v pha h thng trn trong khong tn s

(0.1,100) >> Ts= 10 % Nhp t s ca G(s) >> Ms = conv([1 0.2],[1 8 20]) % Nhp mu s ca G(s) >> G = tf(Ts,Ms) % Tnh hm truyn G(s) >> Bode(G,{0.1,100}) % V biu Bode ca G(s) trong khong tn (0.1 100) >> Grid on % K li Ta c kt qu:

b. Da vo biu Bode, tm tn s ct bin, d tr pha, tn s ct pha, d tr bin ca h thng

Tn s ct bin = 0,455 (rad/s) d tr pha = 1800 76,80 = 103,20 Tn s ct pha = 4,63 (rad/s) d tr bin = 24,7 (dB)c. H thng trn n nh v d tr bin v d tr pha >0 d. V p ng qu ca h thng trn vi u vo hm nc n v trong

khong thi gian t = 0 -> 10s >> Gk = feedback(G,1) % Tm hm truyn vng kn ca G(s) >> step(Gk,10) % V p ng qu ca h thng vi u vo hm nc n v trong khong thi gian (010s) >> grid on % K li Ta c kt qu sau:

e. Vi K = 400, thc hin li cc yu cu cu a -> d >> G = tf(400,conv([1 0.2],[1 8 20])); >> bode(G,{0.1,100}); >> grid on

Da vo biu trn ta tm c: Tn s ct bin = 6,7 (rad/s) d tr pha = -230 Tn s ct pha = 4,68 (rad/s) d tr bin = -7,12 (dB)

H thng trn khng n nh v d tr bin v d tr pha < 0 V p ng qu ca h thng trn vi u vo hm nc n v trong khong thi gian t = 0 10s >> Gk = feedback(G,1) >> step(Gk,10) >> grid on

III.3. Kho st h thng dng biu Nyquist - Mc ch: T biu Nyquist ca h thng h G(s) ta tm d tr bin, d tr pha ca h thng vng kn hi tip m n v. Da vo kt qu tm c xt tnh n nh ca h thng kn. - Th nghim: Kho st h thng phn hi m n v c hm truyn vng h nh phn III.2 G(s) = ( s + 0.2)( s 2 + 8s + 20) a. Vi K= 10, v biu Nyquist ca h thng: >> G = tf(10,conv([1 0.2],[1 8 20])) >> Nyquist(G) >> Grid On % Nhp hm truyn G(s) % V biu Nyquist ca G(s) % K liK

Ta thu c biu :

b.

III.4. Kho st h thng dng phng php qu o nghim s - Mc ch: Kho st c tnh ca h thng tuyn tnh c h s khuch i K thay i, tm gi tr gii hn Kgh ca K h thng n nh. - Th nghim: H thng hi tip m n v c hm truyn vng h: G(s) = ( s + 3)( s 2 + 8s + 20) a. V qu o nghim s ca h thng >> G = tf(1,conv([1 3],[1 8 20])) >> Rlocus(G) >> Grid On Ta thu c kt qu: % Nhp hm truyn G(s) % V QNS % K liK

Da vo biu trn ta tm c Kgh (l v tr ct nhau gia QNS vi trc o). Gi tr Kgh = 425 nh hnh v sau:

b. h thng c tn s dao ng t nhin n = 4 th K = 51,9

c. h thng c h s tt = 0,7 th K = 20,2

d. h thng c vt l POT = 25% th K = 76,7

e. h thng c thi gian xc lp (tiu chun 2%) txl = 4s th K = 185

III.5. nh gi cht lng ca h thng - Mc ch: Kho st c tnh qu ca h thng vi u vo hm nc tm vt l v sai s xc lp ca h thng. - Th nghim: Vi h thng nh phn III.4

a. Vi gi tr K = Kgh = 425, v p ng qu ca h thng vng kn vi u vo hm nc n v. >> Gk = feedback(425*G,1) % Tm vng truyn hm kn vi K=425 >> Step(Gk,10) % V p ng nc t 0 10s >> Grid On % K li Ta thu c kt qu:

d. Vi K = 76,7 (gi tr tm c cu III.4.d) ta c p ng qu ca h thng vng kn vi u vo hm nc n v trong khong thi gian t = 0 5s. T hnh v ta xc nh c vt l v thi gian xc lp. >> Gk = feedback(76.7*G,1) % Tm hm truyn vng kn ca G(s) vi K = 76,7 >> Step(Gk,5) % V p ng nc t 0 5s >> Grid On % K li Ta c:

c. Vi K = 185 (gi tr tm c cu III.4.e) v p ng qu ca h thng vng kn vi u vo hm nc n v trong khoang thi gian t = 0 5s >> Gk = feedback(185*G,1) % Tm HTVK ca G(s) vi K = 185 >> Step(Gk,5) % V p ng nc t 0 5s >> Grid On % K li

d. V 2 p ng qu 2 cu b v c trn cng 1 hnh v

BI TH NGHIM 2

NG DNG SIMULINK M PHNG V NH GI CHT LNG H THNG I. MC CHSIMULINK l mt cng c rt mnh ca MATLAB xy dng cc m hnh mt cch trc quan v d hiu. m t hay xy dng h thng ta ch cn lin kt cc khi c sn trong th vin ca SIMULINK li vi nhau. Sau tin hnh m phng h thng xem xt nh hng ca b iu khin n p ng qu ca h thng v nh gi cht lng h thng. II. CHUN B thc hin yu cu trong bi th nghim ny, chng ta cn phi chun b k v hiu r cc khi c bn cn thit trong th vin ca SIMULINK. Cc khi trong bi th nghim ny l: Step, Signal Generator, Mux, Scope, XY Graph, Sum, Gain, Tranfer Fcn, Relay, PID controller, Saturation III. TH NGHIM III.1. Kho st m hnh h thng iu khin nhit III.1.a. Kho st h h, nhn dng h thng theo m hnh Ziegler-Nichols - Mc ch: c trng ca l nhit l khu qun tnh nhit. T khi bt u cung cp nng lng u vo cho l nhit, nhit ca l bt u tng ln t t. nhit l t ti gi tr nhit cn nung th thng phi mt mt khong thi gian kh di. y chnh l c tnh qun tnh ca l nhit. Khi tuyn tnh ha m hnh l nhit, ta xem hm truyn ca l nhit nh l mt khu qun tnh bc 2 hoc nh l mt khu qun tnh bc nht ni tip vi khu tr. Trong bi th nghim ny ta xem m hnh l nhit nh l mt khu qun tnh bc 2. - Th nghim: Dng SIMULINK xy dng m hnh h thng l nhit vng h nh sau:

a. Chnh gi tr ca hm nc bng 1 cng sut cung cp cho l l 100%. Chnh thi gian m phng Stop time = 600s. M phng v v qu trnh qu ca h thng trn.

b. Ta xc nh c cc thng s L = 22, T = 178

III.1.b. Kho st m hnh iu khin nhit ON OFF - Mc ch: Kho st m hnh iu khin nhit ON-OFF, xt nh hng ca khu rle c tr. - Th nghim: Xy dng m hnh h thng iu khin nhit ON-OFF nh sau:

a. Chnh thi gian m phng Stop time = 600s. Kho st qu trnh qu ca h thng vi cc gi tr ca khu Relay l Output when on =1, Out put when off = 0 V: Switch On = +1 Off Point = -1

Suy ra:

+e1 = 100 98 = 20 e2 = 100 105 = 50

T = 60 (s)

Switch On = +5

Off Point = -5

Suy ra:

+e1 = 100 92 = 80 e1 = 100 112 = 120

T = 95 (s)

Switch On = +10

Off Point = -10

Suy ra:

+e1 = 100 88 = 120 e2 = 100 119 = 190

T = 130 (s)

Switch On = +20

Off Point = -20

Suy ra:

+e1 = 100 78 = 220 e2 = 100 130 = 300

T = 170 (s) b. Tnh sai s ng ra so vi tn hiu t v thi gian ng ngt ng vi cc trng hp ca khu Relay cu a. Vng tr +1/-1 +5/-5 +10/-10 +20/-20+e1 e2

Chu k ng ngt 60 95 130 170

2 8 12 22

5 12 19 30

Nhn xt: Gi tr vng tr cng nh th sai s ng ra nh nhng chu k ng ngt s tng ln lm gim tui th ca b iu khin ON-OFF

c. 2 gi tr +e1v e2 c th hin nh hnh v sau

d. sai s ca ng ra xp x bng 0 th ta thay i gi tr vng tr 0. Chu k ng ngt lc ny ca Relay l lin tc. Trong thc t ta khng th thc hin b iu khin ON-OFF nh vy c

III.1.c. Kho st m hnh iu khin PID - Mc ch: Kho st m hnh iu khin nhit dng b iu khin PID, cc thng s ca b PID c tnh theo phng Ziegler-Nichols. T so snh cht lng ca h thng 2 b iu khin PID vi b iu khin ON-OFF - Th nghim: Xy dng m hnh h thng iu khin nhit PID nh sau:

a. Theo III.1.a ta c L = 22, T = 178 Suy ra: Kp = KI =1, 2T 1, 2.178 = = 0,014 LK 22.300 Kp 0,014 = = 3, 22.103 2L 2.22

KD = 0,5KpL = 0,5.0,014.22 = 0,154 b. Chn stop time = 1500s. Ta thu c kt qu sau:

c. Nhn xt: Ta thy sai s ca phng php PID l rt ln cht lng ng ra ca phng php ny km hn phng php ON-OFF, nhng phng php ny li c thi gian chu k ng ngt ln hn nn b iu khin s c tui th lu hn ONOFF. III.2. Kho st m hnh iu khin tc , v tr ng c DC

Trong phn ny, chng ta tm hiu cch xy dng m hnh ng c t hm truyn m t ng c DC. Sau , kho st m hnh iu khin tc v v tr ng c DC vi b iu khin PID. III.2.a. Kho st m hnh iu khin tc ng c DC - Mc ch: Trong phn ny, chng ta s xy dng m hnh iu khin tc ng c DC dng b iu khin PID c tnh n s bo ha ca b iu khin. Kho st nh hng ca b iu khin PID n cht lng p ng ng ra vi tn hiu u vo l hm nc. - Th nghim: Xy dng m hnh h thng iu khin PID tc ng c DC nh sau:

Trong : - Tn hiu t u vo hm nc u(t) = 100 - Khu bo ha Saturation c gii hn l +30/-30 - Transfer th hin m hnh tc ng c DC a. Chnh thi gian m phng Stop time = 10s. Thc hin kho st h thng vi b iu khin P (KI = KD = 0) ta c bng sau: Kp POT exl txl 1 10 20 Khng c Khng c Khng c 16,7 2 1 0,8 0,8 0,8 50 0,23% 0,4 0,8 100 0,3% 0,2 0,8

Nhn xt: Khi Kp nh th h thng khng c hin tng vt l nhng sai s xc lp li ln. Tng Kp, m bo c cht lng h thng c sai s xc lp nh nhng hin tng vt l xy ra, vt l ny khng ln nn ta c th chp nhn c. b. Thc hin kho st h thng vi b iu khin PI (Kp=2, KD=0) ta c bng sau:

KI POT exl txl

0,1 0.5 Khng c Khng c 0 0 110 20

0,8 0.36% 0 10

1 2,5% 0 7

2 12,6% 0 6

Nhn xt: Khi tng KI thi gian xc lp gim nhng vt l tng, dn n cht lng ca h thng cng gim xung. c. Thc hin kho st h thng vi b iu khin PID (Kp = KI = 2). Ta c bng sau KD POT exl txl 0,1 11,2% 0 8 0,2 10,57% 0 7 0,5 10,4% 0 6.5 1 16,33% 0 8 2 25,2% 0 15

Nhn xt: Khi tng KD (KD < 1) cht lng h thng c nng cao v c vt l v thi gian xc lp gim xung nhng nu KD > 1 th ngc li d. Nhn xt nh hng ca cc khu P,I,D ln cht lng ca h thng +, i vi khu P - Thi gian xc lp khng ph thuc vo Kp - Khi Kp tng th sai s xc lp gim cn vt l tng khng ng k - Kp nh th khng c hin tng vt l +, i vi khu I - Khi KI nh th khng c hin tng vt l - KI tng th vt l tng cn thi gian xc lp gim - Sai s xc lp nh +, i vi khu D - vt l v thi gian xc lp t l nghch vi KD khi KD < 1, t l thun khi KD > 1

III.2.b. Kho st m hnh iu khin v tr ng c DC - Muc ich: Trong phn nay, chung ta se xy dng m hinh iu khin vi tri ng c DC dung b iu khin PID co tinh n s bao hoa cua b iu khin. Khao sat anh hng cua b iu khin PID n ap ng ngo ra vi tin hiu u vao la ham dc.

- Thi nghim: Xy dng m hinh h thng iu khin PID vi tri ng c DC nh sau:

Trong o: - Tin hiu t u vao ham dc co bin = 10, tn s 0,1Hz - Khu bao hoa Saturation co gii han la +30/-30 - Cac Transfer Fcn th hin m hinh vi tri ng c DC a. Chinh thi gian m phong Stop time = 50s. Thc hin khao sat vi b iu khin P (KI = KD = 0) ta co bang sau: Kp POT exl txl 1 10 20 50 100