bài 1 tiep theo - thí nghiệm Điều khiển tự Động

8/2/2019 Bi 1 tiep theo - Th Nghim iu Khin T ng

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BI 1. PHN TCH H THNG IU KHIN TNG

(tip theo)

Sinh Vin Thc Hin: (Nhm 1Sng tht)

Nguyn nh Dng 09090421

Hunh Gia An - 09206461

Cao Trng Duy Dng - 09216381

3. Kho st h thng dng biu Nyquist

Hm truyn h:

()

( )( )

a/ Khi K= 10, thc hin v biu Nyquist trn MatLAB nh sau:

>> TS=10;MS=conv([1 0.2],[1 8 20]);

>> G=tf(TS,MS)

Transfer function:

10

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

s^3 + 8.2 s^2 + 21.6 s + 4

>> nyquist(G)


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b/Xc nh tn s ct pha, tn s ct bin, trpha, tr bin:

Do matlab cha h trxc nh trc tip tn s ct pha, tn s ct bin, trpha, tr

bin trn ca s biu Nyquist, nn ta sxc nh bng phng php th cng:

Trc tin ta s v biu Nyquist nh bc 1

Sau nhp lnh sau vng trn n v:

>> hold on

>> tron = linspace(0, 2*pi, 360);

x = cos(tron);

y = sin(tron);

plot(x,y,'m')

axis('equal')

grid on


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a l khong cch tim m pha bng 180on im -1

tr bin:

GM = 20*log10(a) [dB]

Kt qu ca cch tnh ny chmang tnh tng i v gn ging vi cch tnh biu bode, v mt sthng srt kh xc nh.

nhn c kt qu chnh xc ta thc hin lnh sau:

>> [Gm,Pm,wcp,wcg]=margin(G)

Gm = 17.3123 dB

Pm = 103.3350

wcp = 4.6476 rad/s


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wcg = 0.4546 rad/s

c/ Tiu chun n nh biu nyquist:

trng hp ny, dng lnh sau xc nh cc ca hm h:

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

cuc =

-4.0000 + 2.0000i

-4.0000 - 2.0000i

-0.2000

zero =

Empty matrix: 0-by-1

Nh vy m=3(Nu nh th sbao im -1+0j s vng l 1.5 vng)


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Tht vy, t biu nyquist ta thy ng cong nyquist bao im -1+j0 ng 1.5 vngtheo chiu dng.

Vy h thng n nh theo tiu chun Nyquist v ging nh tiu chun Bode

d/ khi K=400:

Ta thc hin tng t:

Lnh thc hin:

>> TS=400;MS=conv([1 0.2],[1 8 20]);G=tf(TS,MS)

Transfer function:

400

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

s^3 + 8.2 s^2 + 21.6 s + 4


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>> nyquist(G)

>> grid on

>> [Gm,Pm,wcp,wcg]=margin(G)%Xc nh chnh xc cc tn s ct v d tr

Warning: The closed-loop system is unstable.

In warning at 26

In DynamicSystem.margin at 60

Gm = 0.4328

Pm = -23.4305

wcp = 4.6476

wcg = 6.7265

Nhn xt: ta thy sau lnh trn nhn c dng cnh bo sau: The closed-loop system isunstable [tm dch l h kn khng n nh] v theo tiu chun bode th l gii vic ny ln gin v Pm[ trpha] < 0.

Tht vy khi xt theo tiu chun Nyquist (lu l nn gii hn biu nyquist bng cchduoble click vo biu , ca s Properties hin ln hy gii hn X thuc [-3,2] v Ythuc [-2,2]) nh vy ta s dxc nh svng cng nh chiu bao im -1+j0 hn.


cuc =

-4.0000 + 2.0000i

-4.0000 - 2.0000i

-0.2000

zero =


Suy ra m=3


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Nhn trn biu ta thy ng Nyquist bao im -1+j0 theo chiu m.

Vy h kn khng n nh

3.1 [Lm thm ] Dng tiu chun Nyquist kho st h thng:

()

( )( )

Nh bi 3.

a & b/ Khi k=10

>> TS=10;MS=conv([1 1],[1 1 4]);G=tf(TS,MS)

Transfer function:

10

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


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s^3 + 2 s^2 + 5 s + 4

>> nyquist(G)



> In warning at 26


Gm = 0.6000

Pm = -23.8089

wcp = 2.2361

wcg = 2.5641

Nh vy ta cng nhn c cng bo l h thng kn khng n nhnh bi 3. L giitheo bode th ta thy do Pm = -23.8089 < 0 nn h kn skhng n nh.

c/ Xt theo tiu chun Nyquist


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Tm s cc:


cuc =

-0.5000 + 1.9365i

-0.5000 - 1.9365i

-1.0000

zero =


Suy ra m=3(nu h thng kn n n th ng cong Nyquist se bao im -1+0j 1,5 vngtheo chiu dng.

Nh vi h thng ny th khng phi vy: ng cong Nyquist bao im -1+j0 theo chiudng.

d/ Lm li vi K=400


Transfer function:

400

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

s^3 + 2 s^2 + 5 s + 4

>> nyquist(G)

>> grid on


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Xc nh tn s cc v tr bin-pha:



> In warning at 26


Gm = 0.0150

Pm = -74.2451

wcp = 2.2361

wcg = 7.5037

Ta cng nhn c cnh bo: H kn khng n nh : Pm = -74.2451


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Xt c th theo tiu chun n nh Nyquist:

Ta cn phng to hn vi gii hn chiu X l [-2;2] v chiu Y l [-3;3].


cuc =

-0.5000 + 1.9365i

-0.5000 - 1.9365i

-1.0000

zero =


Suy ra m=3(nu h thng kn n n th ng cong Nyquist se bao im -1+0j 1,5 vngtheo chiu dng.


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()

( )

a/Khi K=10

Tin hnh nhp hm truyn h:

>> TS=10;MS=conv([2 1],conv([2 1],[2 1]));G=tf(TS,MS)

Transfer function:

10

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

8 s^3 + 12 s^2 + 6 s + 1

>> nyquist(G)

>> grid on


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b/ Tm tn s ct v tr bin



> In warning at 26


Gm = 0.8001

Pm = -7.0310

wcp = 0.8661

wcg = 0.9541

Vi cnh bo sau khi thc hin lnh, ta bit rng h thng khng n nh Pm = -7.0310



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Zoom theo gii hn chiu X l [-2;1.5] v chiu Y l [-2;2]

Tip tc thc hin lnh tm cc


cuc =

-0.5000

-0.5000 + 0.0000i

-0.5000 - 0.0000i

zero =



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Theo m=3(nu h thng kn n n th ng cong Nyquist se bao im -1+0j 1,5vng theo chiu dng.


d/ Khi K=400

Ta nhp li TS=400

>> nyquist(G)

>> grid on

Tm tn s ct v tr bin:




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> In warning at 26


Gm = 0.0200

Pm = -66.5991

wcp = 0.8661

wcg = 3.6499

Nh vy h kn skhng n nh do c cnh bo v theo bode th do Pm < 0.

Xt theo tiu chun Nyquist:

Zoom theo gii hn chiu X l [-2;2] v Y l [-2;2]

Tm s cc:


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cuc =

-0.5000

-0.5000 + 0.0000i

-0.5000 - 0.0000i

zero =


Theo m=3(nu h thng kn n n th ng cong Nyquist sbao im -1+0j 1,5vng theo chiu dng.

Nh vi h thng ny th khng phi vy: ng cong Nyquistbao im -1+j0 theo chiudng.


() ( )

( )( )

a/Khi K=10

Tin hnh nhp hm truyn h:

>> TS=conv(10,[1 1]);MS=conv([1 0],conv([1 3],[1 8 20]));G=tf(TS,MS)

Transfer function:

10 s + 10

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

s^3 + 11 s^2 + 44 s + 60

>> nyquist(G)

>> grid on


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b/ Tm tn s ct, tr bin:>> [Gm,Pm,wcp,wcg]=margin(G)

Gm = 32.2178

Pm = 92.4899

wcp = 5.8945

wcg = 0.1686

Nh vy khng c cnh bo no sau khi thc hin lnh v cng theo tiu chun bode thh kn lun n nh.



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Zoom theo gii hn chiu X l [-0.1;0.1] v Y l [-0.1;0.1]

Tm s cc ca h thng:


cuc =

0

-4.0000 + 2.0000i

-4.0000 - 2.0000i

-3.0000

zero =

-1


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Theo m=4 (nu h kn n nh th ng cong nyquist s bao theo chiu dng im -1 + 0j 2 vng).

Tht vy, t biu nyquist ta thy ng cong nyquist bao im -1+j0 ng 2 vngtheo chiu dng.

Vy h thng n nh theo tiu chun Nyquist v ging nh tiu chun Bode

d/ Khi K=400

Ta nhp li TS=400(s+1)

>> TS=conv(400,[1 1]);MS=conv([1 0],conv([1 3],[1 8 20]));G=tf(TS,MS)

Transfer function:

400 s + 400

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

s^4 + 11 s^3 + 44 s^2 + 60 s

>> nyquist(G)

>> grid on


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Xc nh tn s ct, tr bin



> In warning at 26


Gm = 0.8054

Pm = -7.1198

wcp = 5.8945

wcg = 6.4985

Xut hin cnh bo tc h thng btn nh v cnh bo cng ng theo tiu chun nnh Bode.


22/32

Xt theo tiu chun Nyquist:

Tm s cc ca h thng:


cuc =

0

-4.0000 + 2.0000i

-4.0000 - 2.0000i

-3.0000

zero =

-1


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Theo m=4(nu h thng kn n n th ng cong Nyquist sbao im -1+0j 2 vngtheo chiu dng.)


4. Kho st h thng dng phng php QNS:

Kho st h thng phn hi m n v c hm truyn vng h:

()

( )( )

a/ Tin hnh nhp hm truyn h(lu khng nhp K t s=1)

Th tc nh sau:


Transfer function:

1

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

s^3 + 11 s^2 + 44 s + 60

Sau vQNS bng hm rlocus()

+ Kgh chnh in giao gia hm truyn v trc o.


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Vy Kgh=426

b/Tm K h thng tn sdao ng t nhin wn = 4.

Ta tm trn QNS ni c gi trFrequency(rad/s) = 4[lu ch cn double click voQNS l thng s s hin ln]. T suy ra gi tr K.


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Vy K=51.4

c/ Tm K h thng c h s tt = 0.7.

Tng tta tm ni c Dampling=0.7


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Nh vy K=20

d/ Tm K h thng c vt l POT = 25%.

Tm ni c Overshoot(%)=25%. T suy ra K


27/32

Vy K=77

e/ Tm K h thng c thi gian xc lp txl = 4s.

Ta bit thi gian xc lp(chn chn s tiu chun 2%)

Vy =1

Trn QHS ta tm im c tch trn bng 1: tng tnh cp s 5*0.2=1:

Nh trn hnh ta xc nh c im c v

Th li ta c

(Con s ny l chp nhn c)


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Tim ny ta c K=171

5. nh gi cht lng ca h thng:

Kho st h thng phn hi m n v c hm truyn vng h:

()

( )( )

a/Tcu trn ta tm c Kgh=426:

vp ng qu ta tm hm truyn kn ca h thng t cng thc sau:

() ()

()

Th tc vi Matlab nh sau:


29/32


Transfer function:

426

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

s^3 + 11 s^2 + 44 s + 60

>> Gk=feedback(G,1)

Transfer function:

426

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

s^3 + 11 s^2 + 44 s + 486

>>step(Gk)


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p ng ng ra dao ng

b/Tcu 4d ta tm c K=77:

Thc hin tng t ta c:

>> TS=77;MS=conv([1 3],[1 8 20]);G=tf(TS,MS);Gk=feedback(G,1);step(Gk)

Lu tm vot l chnh xc nht th th tc nh sau:

T ca sp ng qu : Chut phi => Characteristics =>Peak Response, sau pchut vo nh vt l s hin ln.

Nh vy vt ll 20.9% so vi 25% cu 4

c/ Tm c K =171

TS=171;MS=conv([1 3],[1 8 20]);G=tf(TS,MS);Gk=feedback(G,1);step(Gk)


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T ca sp ng qu : Chut phi => Characteristics => Settling Time, sau pchut vo txl s hin ln.

Nh vy txl = 3.47s so vi txl =4s cu 4, iu ny chng t c sai strong lc xc nhtxl.

d/Th tc nh sau:


>> hold on



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