BÁO CÁO THÍ NGHIỆM ĐIỀU KHIỂN SỐ.pdf

8/11/2019 BO CO TH NGHIM IU KHIN S.pdf

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BAI BO CO TH NGHIM H THNG IU KHIN S

H v tn : Lu Vn TunMSSV : 20102810

Lp : K-TDH1 K55S liu c giao Gz4(Giz5: FOH; Ttm=0.1e-3) Lz1,Lz2


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Muc Luc

A. M t bi thc hnh ............................................................................................................................ 3

Bi thc hnh s1 : Tm m hnh gin on ca CMC....................................................................... 4

1. Tm hm truyn t trn min nh z bng phng php hc thit k vng iu khin phnng 4

a. Dng phn ng .............................................................................................................................. 4

b. M hnh ng c mt chiu .......................................................................................................... 5

2. Sdng lnh c2d ca matlab tm hm truyn t trn min nh z theo cc phng phpZOH,FOH,TUSTIN ................................................................................................................................... 6

a. Dng phn ng .............................................................................................................................. 6

b. M hnh ng c mt chiu .......................................................................................................... 9

3.

M phng kho st .......................................................................................................................... 12

a. Dng phn ng ............................................................................................................................ 12

b. ng c in 1 chiu .................................................................................................................. 13

4. M hnh trng thi ca CMC trn min thi gian lin tc........................................................... 14

Bi thc hnh s2: Tng hp vng iu chnh dng phn ng ( iu khin momen quay)............ 18

1. Tm b iu khin Gri theo phng php Dead-beat ..................................................................... 18

1.1 Thit k b iu khin dng theo phng php Dead-Beat bc 1.......................................... 18

1.2 Thit k b iu khin dng theo phng php dead-beat bc 2 vi...................................... 23

2. Thit k b iu khin dng theo phng php cn bng m hnh................................................. 28

Bi thc hnh s 3: Tng hp vng iu chnh tc quay................................................................. 32

1. Tm hm truyn t trn min nh z ca i tng vng tc ..................................................... 32

2. S dng lnh c2d tm hm truyn t trn min nh z theo phng php foh........................... 33

3. Thit k b iu chnh PI cho tc ng c................................................................................. 36

a. Theo tiu chun tch phn bnh phng...................................................................................... 36

b. Theo phng php gn im cc ................................................................................................ 40

4. M phng kho st .......................................................................................................................... 42

Bi thc hnh 4: Tng hp b iu chnh tc quay trn KGTT ..................................................... 50

1. Tng hp b iu khin tc quay theo 2 phng php.............................................................. 50

a. Phng php PT1 ........................................................................................................................ 50

b. p ng hu hn (gn im cc ti gc ta trn min z)...................................................... 52

2. M phng kho st so snh 2 phng php .................................................................................... 55


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BO CO TH NGHIM IU KHIN S

A.M t bi thc hnh

i tng iu khin: ng c in mt chiu c m t nh sau

in p phn ng: A

A A A A A

diu e R i L

dt

Sc tng cm ng:A e

e k n

Tc quay: 1 ( )2

M T

dnm m

dt J

Momen quay:M M A

m k i

Hng sng c: 2e Mk k

Hng s thi gian phn ng 34 16.10250

A

a

A

LT

R

Cc tham s ca ng c- in trphn ng Ra=250 m- in cm phn ng La=4 mH

- Tthng danh nh r =0.04 Vs

-

M men qun tnh J=0.012 - Hng sng c ke=236.8 km=38.2M hnh ng c mt chiu theo cu trc cascade

i tng dng phn ng 0


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Bi thc hnh s1 : Tm m hnh gin on ca CMC

1.

Tm hm truyn t trn min nh z bng phng php hc thit kvng iu khin phn nga.

Dng phn ngi tng dng phn ng ca ng c l

11 . 1 . 11

Ta dng php bin i z tm

1 . 1 11 . 11 1 . 1 1 1

1 . 1 1 . .

1 . .

1 .

1 1 . . 1 1 . . 1

Vi cc thng sTt=100 s

Ra=250 mLa=4 mH

Ta=La/Ra=0.016 s

Thay svo ta c

4 640159 . 1 . 4159 . 1 Vi thi gian trch mu T=0.1 ms

0.009174327 0.00657738 1.361649 0.365587 Vi thi gian trch mu T=0.01 ms


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0.0001209 0.00011622 1.904212 0.904271

b. M hnh ng c mt chiu

Hm truyn t vng h

1 . 11 ... 12Thay s vo ta c

6.1120.001206 0.0754Hm truyn h kn

1 ..

Thay s vo ta c 6.1120.001206 0.0754 57.89Tnh Gk(z) bng php bin i z

1. 6.1120.001206 0.0754 57.890.10557

0.10557 31.25

31

216.820.0152. 216.82

31

216.82

Bin i z ta c }0.10557 1 0.10557

..cos216,82 2.216,82 . 0.0152..sin216,82 2.216,82 .

Hm truyn trn min nh z l1

0.10557 0.10557 1 .

.cos216,82 2.216,82 . 0.0152 1..sin216,82 2.216,82 .Vi chu k trch mu T=0.1 ms

1 2.5278 5 2.5226 5 1.9932911 0.9937649


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Vi chu k trch mu T=0.01 ms

2 2.5327 7 2.5322 7 1.9993703 0.99937512.

Sdng lnh c2dca matlab tm hm truyn t trn min nh z theocc phng php ZOH,FOH,TUSTINa. Dng phn ng

Lnh trn matlab

>> Tt=100e-6;Ra=250e-3;La=4e-3;Ta=La/Ra;T1=0.1e-3;T2=0.01e-3;

>> Gi=tf(1,[Tt 1])*(1/Ra)*tf(1,[Ta 1])

Gi =

4--------------------------

1.6e-06 s^2 + 0.0161 s + 1

Continuous-time transfer function.

Ta dng lnh c2d tnh cc m hnh gin on. Vi cc chu k trch muT1,T2 s tm c 6 m hnh gin on t Giz3 n Giz8

-

Vi chu k trch mu T1=0.1 ms

>> Giz1=tf([0.009174327 0.00657738],[1 -1.361649 0.365587],T1)

Giz1 =

0.009174 z + 0.006577

----------------------z^2 - 1.362 z + 0.3656

Sample time: 0.0001 seconds

Discrete-time transfer function.

>> Giz3=c2d(Gi,T1,'zoh')

Giz3 =


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0.009176 z + 0.006577----------------------

z^2 - 1.362 z + 0.3656

Sample time: 0.0001 secondsDiscrete-time transfer function.

>> Giz5=c2d(Gi,T1,'foh')

Giz5 =

0.003298 z^2 + 0.01046 z + 0.001998

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

z^2 - 1.362 z + 0.3656



>> Giz7=c2d(Gi,T1,'tustin')

Giz7 =

0.004154 z^2 + 0.008307 z + 0.004154

------------------------------------z^2 - 1.327 z + 0.3313



- Vi chu k trch mu l T2=0.01 ms

>> Giz2=tf([0.0001209 0.00011622],[1 -1.904212 0.904271],T2)

Giz2 =

0.0001209 z + 0.0001162-----------------------

z^2 - 1.904 z + 0.9043


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Sample time: 1e-05 seconds


>> Giz4=c2d(Gi,T2,'zoh')

Giz4 =

0.0001209 z + 0.0001169-----------------------

z^2 - 1.904 z + 0.9043

Sample time: 1e-05 secondsDiscrete-time transfer function.


Giz6 =

4.064e-05 z^2 + 0.0001585 z + 3.865e-05---------------------------------------

z^2 - 1.904 z + 0.9043



>> Giz8=c2d(Gi,T2,'tustin')

Giz8 =

5.951e-05 z^2 + 0.000119 z + 5.951e-05

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

z^2 - 1.904 z + 0.9042

Sample time: 1e-05 secondsDiscrete-time transfer function.


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b. M hnh ng c mt chiu

Lnh trn matlab

>> Ra=250e-3;La=4e-3;J=0.012;ke=236.8;km=38.2;phi=0.04;Ta=La/Ra;Tt=100e-6;T1=0.1e-3; T2=0.01e-3;

>>Gh=(1/Ra)*tf([1],[Ta 1])*km*phi*tf(1,[2*pi*J 0])

Gh =

6.112-----------------------

0.001206 s^2 + 0.0754 s

Continuous-time transfer function

>> Gk=feedback(Gh,ke*phi)

Gk =

6.112-------------------------------

0.001206 s^2 + 0.0754 s + 57.89


Ta sdng lnh cd2 tnh cc m hnh gin on ca hm truyn t hkn. Vichu k trch mu Ttm1 v Ttm2 ta stm c 6 m hnh gin on sau:

>> Gkz1=tf([0 2.5278e-5 2.5226e-5],[1 -1.9932911 0.9937649],T1)

Gkz1 =

2.528e-05 z + 2.523e-05

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

z^2 - 1.993 z + 0.9938



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1.263e-05 z^2 + 2.525e-05 z + 1.263e-05

---------------------------------------z^2 - 1.993 z + 0.9938


Discrete-time transfer function

- Vi chu k trch mu T2=0.01e-3

>> Gkz4=c2d(Gk,T2,'zoh')

Gkz4 =

2.533e-07 z + 2.532e-07

-----------------------z^2 - 1.999 z + 0.9994



>> Gkz6=c2d(Gk,T2,'foh')

Gkz6 =

8.443e-08 z^2 + 3.377e-07 z + 8.44e-08--------------------------------------

z^2 - 1.999 z + 0.9994



>> Gkz8=c2d(Gk,T2,'tustin')

Gkz8 =

1.266e-07 z^2 + 2.532e-07 z + 1.266e-07

---------------------------------------z^2 - 1.999 z + 0.9994



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3.M phng kho sta.

Dng phn ngTa dng cc lnh step v v lnh hold on gi cc th trn cng mt hnhLnh trong matlab

>> step(Gi)>> hold on

>> step(Giz1)>> step(Giz2)

>> step(Giz3)

>> step(Giz4)

>> step(Giz5)>> step(Giz6)

>> step(Giz7)

>> step(Giz8)

Kt qum phng

Nhn xt : p ng kt qutnh tay bm st gi trl thuyt nn c thkt lungi trtnh ton bng tay l chnh xc.

Vi dng phn ng ta s c 9 th


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- 1 th hm truyn lin tc Gi

- 2 th hm truyn gin on tnh tay l Gi1,Gi2- 6 th cn li Gi3 n Gi8 l th hm truyn gin on tnh ton theo

matlab

b.

ng c in 1 chiu>> step(Gk)

>> hold on>> step(Gkz1)

>> step(Gkz2)

>> step(Gkz3)

>> step(Gkz4)>> step(Gkz5)

>> step(Gkz6)

>> step(Gkz7)>> step(Gkz8)

Kt qu

Nhn xt: - p ng hm truyn gin on tnh bng lnh c2d bm vi png ca hm truyn trn min lin tc, cn 2 hm truyn tnh tay th c sailch i cht so vi p ng hm truyn lin tc.


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4. M hnh trng thi ca CMC trn min thi gian lin tc

Theo nh tnh ton trn ta c hm truyn h kn

2

6,112( )

0,001206 0,0754 57,89k

G ss s

M hnh trng thi trn min lin tc (tnh)

{ ( vi a,b,c,d l cc ma trn )

Chuyn sang min gin on{ 1 . . . .

Lnh trn matlab

>> [a,b,c,d]=tf2ss([6.112],[0.001206 0.0754 57.89])

a =

1.0e+04 *

-0.0063 -4.80020.0001 0


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b =

1

0

c =

1.0e+03 *

0 5.0680

d =

0

>> [Az,Bz]=c2d(a,b,0.1)

Az =

-0.0438 -2.92710.0001 -0.0399

Bz =

1.0e-04 *

0.6098

>> [Az1,Bz1]=c2d(a,b,0.01)

Az1 =

-0.4989 -133.8566

0.0028 -0.3245

Bz1 =


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0.00280.0000

>> H1=ss(Az,Bz,c,d,0.1)

H1 =

a =

x1 x2

x1 -0.04376 -2.927

x2 6.098e-05 -0.03995

b =

u1x1 6.098e-05x2 2.166e-05

c =x1 x2

y1 0 5068

d =

u1

y1 0

Sample time: 0.1 secondsDiscrete-time state-space model.

>> H2=ss(Az1,Bz1,c,d,0.01)

H2 =

a =x1 x2

x1 -0.4989 -133.9

x2 0.002789 -0.3245

b =u1


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x1 0.002789

x2 2.759e-05

c =

x1 x2

y1 0 5068

d =u1

y1 0


M phng p ng bc nhy

>> step(a,b,c,d)

>> hold on

>> step(H1)>> step(H2)

Kt qu


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Nhn xt :Vi chu k trch mu 0,1s, p ng bc nhy gn nh bqua qu trnhqu . Cn vi chu k trch mu 0,01s, p ng bm gn ging vi p ng cahlin tc.

Bi thc hnh s2: Tng hp vng iu chnh dng phn ng ( iu khinmomen quay)

Sliu c giao: Gz4(Giz5), Lz1,Lz2

1. Tm b iu khin Gri theo phng php Dead-beat

1.1Thit k b iu khin dng theo phng php Dead-Beatbc 1

Ta c

1

Ap dng cng thc iu khin Dead-Beat ta c . = . = Ta c 4 5T ta tm c Gri theo cng thc


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..Cc lnhtrong matlab

>> b0=0.003298;b1=0.01046;b2=0.001998;a0=1;a1=-1.362;a2=0.3656;>> l0=a0/((a0-a1)*(b0+b1+b2))

l0 =

26.8704

>> l1=-a1/((a0-a1)*(b0+b1+b2))

l1 =

36.5975

>> Lz1=filt([l0 l1],1,T1)

Lz1 =

26.87 + 36.6 z^-1


>> Ai=filt([a0 a1 a2],1,T1)

Ai =

1 - 1.362 z^-1 + 0.3656 z^-2



>> Bi=filt([b0 b1 b2],1,T1)

Bi =


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0.003298 + 0.01046 z^-1 + 0.001998 z^-2



>> Gri=(Lz1*Ai)/(1-Lz1*Bi)

Gri =

26.87 - 40.02 z^-2 + 13.38 z^-3

-------------------------------------------------0.9114 - 0.4018 z^-1 - 0.4365 z^-2 - 0.07312 z^-3


>> Gz4=filt([b0 b1 b2],[a0 a1 a2],T1)

Gz4 =

0.003298 + 0.01046 z^-1 + 0.001998 z^-2---------------------------------------

1 - 1.362 z^-1 + 0.3656 z^-2



>> Gk1=(Gri*Gz4)/(1+Gri*Gz4)

Gk1 =


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0.08077 + 0.1106 z^-1 - 0.4938 z^-2 - 0.0547 z^-3 + 0.7352 z^-4 - 0.289 z^-5

- 0.1604 z^-6

+ 0.05889 z^-7 + 0.01642 z^-8 - 0.003208 z^-9 - 0.0007147

z^-10

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

0.9114 - 2.884 z^-1 + 3.015 z^-2 - 0.8308 z^-3 - 0.4078 z^-4 + 0.1919 z^-5 +

0.01448 z^-6

- 0.009774 z^-7 + 4.668e-19 z^-8 - 5.791e-19 z^-9 - 9.275e-20z^-10


>> Gk2=feedback(Gri*Gz4,1)

Gk2 =

0.08862 + 0.2811 z^-1 - 0.07831 z^-2 - 0.3745 z^-3 + 0.05999 z^-4 + 0.02673

z^-5

--------------------------------------------------------------------------------1 - 1.362 z^-1 + 0.3656 z^-2 + 1.388e-17 z^-4 + 3.469e-18 z^-5



>> step(Gk1)

>> hold on>> step(Gk2)

Kt qu


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Nhn xt: T kt qu m phng trn Simulink ta thy u ra t gi tr xc lp sau3 chu k trch mu

1.2

Thit k b iu khin dng theo phng php dead-beat bc 2 vi2 01 11. 12Ap dng cng thc ca b iu khin dead-beat bc 2 ta c01 [ ] = 11 . [ ] =

12 .

[ ] =

Ta c 4 5T ta tm c Gri theo cng thc

..


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Lnh trong matlab

>> MSC=[a0*a0+a1*a1-a0*(a1+a2)]*(b0+b1+b2)

MSC =

0.0607

>> l01=(a0*a0)/MSC

l01 =

16.4790

>> l11=-(a0*a1)/MSC

l11 =

22.4444

>> l12=(a1*a1-a0*a2)/MSC

l12 =

24.5445

>> Lz2=filt([l01 l11 l12],1,T1)

Lz2 =

16.48 + 22.44 z^-1 + 24.54 z^-2



>> Gri1=(Lz2*Ai)/(1-Lz2*Bi)


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Gri1 =

16.48 + 3.553e-15 z^-1 - 8.882e-16 z^-2 - 25.22 z^-3 + 8.973 z^-4

-----------------------------------------------------------------0.9457 - 0.2464 z^-1 - 0.3486 z^-2 - 0.3016 z^-3 - 0.04904 z^-4



>> Gk3=(Gri1*Gz4)/(1+Gri1*Gz4)

Gk3 =

0.05139 + 0.07961 z^-1 - 0.2153 z^-2 - 0.06732 z^-3 - 0.05585 z^-4 + 0.4136z^-5 - 0.1353 z^-6

- 0.05655 z^-7 - 0.04227 z^-8 + 0.02335 z^-9 + 0.00651 z^-10 - 0.001559

z^-11

- 0.0003214 z^-12

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

0.9457 - 2.822 z^-1 + 2.768 z^-2 - 0.9309 z^-3 + 0.2426 z^-4 - 0.3321 z^-5 +0.1269 z^-6


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+ 0.008528 z^-7 - 0.006555 z^-8 - 7.606e-19 z^-9 + 1.914e-18 z^-10 +

9.802e

-20 z^-11 - 6.22e-20 z^-12



>> step(Gk3)

Kt qu

Nhn xt : Khi dng biu khin dead-beat bc 2 th u ra t gi trxcnh sau 4 chu k trch mu.T ta thy bdead-beat bc 2 c cht lngkhng bng bbc 1 do lu t ti gi trxc lp hn bbc 1.

M phngsimulink


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Kt qu

Nhn xt : Ta thy t kt qu m phng sau 4 chu k trch mu th u ra t gi trxc nh


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2. Thit k b iu khin dng theo phng php cn bng m hnh

(s liu c giao Gz4=Giz5 )

Gissau N chu k trch mu p ng u ra ca i tng bm vo gi trt,

nh vy hm truyn ca i tng c dng: . = Vi iu kin: { = 10 < < 1 Ta c .+. . =

Vi .

Trng hp N=2 ta c 1 . = 15 . 1

.51.5+ Chn

0.3;

0.7

Lnh trong matlab


>> Gi=tf(1,[Tt 1])*(1/Ra)*tf(1,[Ta 1])

Gi =

4

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

1.6e-06 s^2 + 0.0161 s + 1



Giz5 =


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0.003298 z^2 + 0.01046 z + 0.001998-----------------------------------

z^2 - 1.362 z + 0.3656


>> Gw1=filt([0 0.3 0.7],T1)

Gw1 =

0.3 z^-1 + 0.7 z^-2

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

0.0001

Sample time: unspecified


>> Gri=(1/Giz5)*(Gw1/(1-Gw1))

Gri =

3e-05 z^-1 + 2.915e-05 z^-2 - 8.435e-05 z^-3 + 2.559e-05 z^-4

----------------------------------------------------------------------------3.298e-11 - 9.882e-08 z^-1 - 5.446e-07 z^-2 - 7.92e-07 z^-3 - 1.399e-07 z^-4



>> Gk=feedback(Gri*Giz5,1)

Gk =

9.893e-08 z^-1 + 4.099e-07 z^-2 + 8.665e-08 z^-3 - 7.395e-07 z^-4 + 9.911e-08

z^-5

+ 5.113e-08 z^-6


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

3.298e-11 + 5.968e-11 z^-1 - 1.104e-10 z^-2 + 1.103e-11 z^-3 + 7.304e-12 z^-4 -

2.647e-23 z^

-5



Kim tra im cc ca hm truyn h kn Gk

>> pole(Gk)

ans =

0

-2.96720.9938

0.3679

-0.2042

0.0000

Ta thy c 1 im cc nm ngoi ng trn n v l -2.9672

+ Chn 0.4; 0.6>> Gw1=filt([0 0.4 0.6],T1)

Gw1 =

0.4 z^-1 + 0.6 z^-2


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

0.0001

Sample time: unspecified


>> Gri=(1/Giz5)*(Gw1/(1-Gw1))

Gri =

4e-05 z^-1 + 5.534e-06 z^-2 - 6.708e-05 z^-3 + 2.194e-05 z^-4

-----------------------------------------------------------------------------3.298e-11 - 1.318e-07 z^-1 - 6.162e-07 z^-2 - 7.074e-07 z^-3 - 1.199e-07 z^-4


Discrete-time transfer function.>> Gk=feedback(Gri*Giz5,1)

Gk =

1.319e-07 z^-1 + 4.366e-07 z^-2 - 8.339e-08 z^-3 - 6.181e-07 z^-4 + 9.539e-08

z^-5

+ 4.383e-08 z^-6

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

3.298e-11 + 5.968e-11 z^-1 - 1.104e-10 z^-2 + 1.103e-11 z^-3 + 7.304e-12 z^-4

+ 2.647e-23 z^

-5 + 6.617e-24 z^-6


Kim tra im cc ca hm truyn h kn

>> pole(Gk)


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ans =

-2.9672 + 0.0000i

0.9938 + 0.0000i

0.3679 + 0.0000i

-0.2042 + 0.0000i-0.0000 + 0.0000i

-0.0000 - 0.0000i

Ta thy c 1 im cc nm ngoi ng trn n v -2.9672

T 2 cch chn trn ta thy hm truyn h kn lun c c 1 im cc nm

ngoi ng trn n v. iu ny chng t h knkhng n nh.Vy biu chnh ny khng iu khin c.

Bi thc hnh s 3: Tng hp vng iu chnh tc quay

1. Tm hm truyn t trn min nh z ca i tng vng tc

Ta c cng thc tnh gn ng ca hm truyn h kn

112 .Vi Tt=100e-6 l hng s thi gian ca b chnh luHm truyn i tng vng tc

. . . 12.. .. 2.. . 1. 12 ..

2.. . 1

2

1 2.

Ta c . 2.. . 11 21 2. . 2.. 1 2 4

1 2.

}. 2.. . . 1 2. 1 2.


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Vy1 .

2.. . ( 2 1) 2 1 .

1

Vi T=0.1e-3 ta c4 4.3178 4. 3.656 4 1.6065 0.6065

2. S dng lnh c2d tm hm truyn t trn min nh z theo phng phpfoh

Lnh trn matlab


>> Km=38.2;phi=0.04;J=0.012;>> Gk=tf(1,[2*Tt 1])

Gk =

1

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

0.0002 s + 1


>> Gn=Gk*Km*phi*tf(1,[2*pi*J 0])


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Gn =

1.528

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

1.508e-05 s^2 + 0.0754 s


>> Gnz=c2d(Gn,T1,'foh')

Gnz =

0.0001497 z^2 + 0.000531 z + 0.0001166

--------------------------------------z^2 - 1.607 z + 0.6065



so snh 2 m hnh trn ta dng lnh step v v hold on gi cc thtrn cng 1 hnh>> Gn4=tf([4.3178e-4 3.656e-4],[1 -1.6065 0.6065],T1)

Gn4 =

0.0004318 z + 0.0003656-----------------------

z^2 - 1.607 z + 0.6065



>> step(Gn4)>> hold on

>> step(Gnz2)

Kt qu


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Nhn xt : ta thy hm truyn tnh bng tay v bng matlab c th gn stnhau v lun tng

Nu s dng b iu khin P ta s c>> Gkn=feedback(Gnz*4,1)

Gkn =

0.0008636 z^2 + 0.001595 z + 0.0007312--------------------------------------

1.001 z^2 - 1.605 z + 0.6073


>> step(Gkn)

Kt qu


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Nhn xt :t trn ta thy khi dng b iu khin P s a h kn v n nh

3. Thit k b iu chnh PI cho tc ng ca.

Theo tiu chun tch phn bnh phng

Biu chnh PI sc dng:1 1

1 0 1

1 1

1

( )( )

1 ( )Rn

r r z R zG z

p z P z

chn1

1p

Ta c:

1 1 2

0 1 0 1 2

1 1 2

1 2

1( ) W( )

1 .1 1

E z zr r z b b z b z

z a z a z

1 2 3

0 0 1 0 1 1 0 2 1 0 2 1 1 1 2 2

1 2 3

1 2 1 2

( ) (1 ) ( 1 ) ( ) ( )

W( ). 1 ( 1) ( )

E z r b a r b r b z a a r b r b z r b a z

z a z a a z a z

Suy ra sai lch iu chnh vit di dng sai phn:0 0 1 1 2 2 1 3 2

1 1 0 1 1 0 2 2 1 0 2 1 1 3 1 2 2

.(1 ) w ( 1) ( ) ( )

( 1 ) ( ) ( )

k k k k k

k k k

e r b w a w a a w a

e a r b r b e a a r b r b e r b a

Trong w 1kk


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37

0

0 0

1 0 0 0 1 1 01

0 0

2 1 0 2 1 1 0 1 1 0 1 0 1 1 0

3 2 1 0 1 1 0 1 2 1 0 2 1 1 1 2 2

4 3 1 0 1 1 0 2 2 1 0 2 1 1 1

10

1

11

1

2 (1 ).( 1 )

3 ( 1 ) ( ) ( )

4 ( 1 ) ( )

k er b

a r b r b r bk e

r b

k e a r b r b r b r b a r b r b

k e e a r b r b e a a r b r b r b a

k e e a r b r b e a a r b r b e

1 2 2( )r b a

Tiu chun tch phn bnh phng:

2

0

42

0

( ) min

minQ kk

J e t dt

I e

Tm 0 1,r r QI min bng cng cOptimization toolbox ca matlab.To mt m-file c tn function1.m c ni dung:

%function1.m

functionF = function1(r)b0=0.0001497;b1=0.000531;b2=0.0001166;b3=0;

a0=1;a1=-1.6065;a2=0.6065;F=1+(1-r(1)*b1)^2+(1+(a1*b1-2*b1-b2)*r(1)+b1^2*r(1)^2-b1*r(2))^2+(-(a1-

1+r(1)*b1)*(1+(a1*b1-2*b1-b2)*r(1)+b1^2*r(1)^2-b1*r(2))-(a2-

a1+r(1)*b2+r(2)*b1)*(1-r(1)*b1)-(r(2)*b2-a2))^2+((-(a1-1+r(1)*b1)*(1+(a1*b1-2*b1-b2)*r(1)+b1^2*r(1)^2-b1*r(2))-(a2-a1+r(1)*b2+r(2)*b1)*(1-r(1)*b1)-(r(2)*b2-a2))*(a1-1+r(1)*b1)-(1+(a1*b1-2*b1*b2)*r(1)+b1^2*r(1) 2-

b1*r(2))*(a2-a1+r(1)*b2+r(2)*b1)-(1-r(1)*b1)*(r(2)*b2-a2)-r(2)*b3)^2;

Trn ca sComand Window g cc lnh:>> options=optimset('fminunc');>> options=optimset(options,'Display','iter','LargeScale','off');

>> r0=[-10 20];

>> [r,fval]=fminunc('function1',r0,options)

First-order

Iteration Func-count f(x) Step-size optimality

0 3 22.0298 0.1381 15 8.59576 820 0.0694

2 18 2.69566 1 0.0187


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Grz =

904.6 - 896.7 z^-1

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

1 - z^-1



>> Gkn=(Grn*Grz)/(1+Grn*Grz)

Gkn =

0.1354 - 0.006859 z^-1 - 0.9731 z^-2 + 1.545 z^-3 - 0.7577 z^-4 - 0.00657 z^-5 +0.06341 z^-6

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

1.135 - 5.22 z^-1 + 10.25 z^-2 - 11.2 z^-3 + 7.301 z^-4 - 2.691 z^-5 + 0.4313

z^-6


>> pole(Gkn)

ans =

0.4998 + 0.6181i

0.4998 - 0.6181i1.0000 + 0.0000i

1.0000 + 0.0000i

0.9912 + 0.0000i0.6065 + 0.0000i

Ta thy rng tt c nghim ca h kn nm trong vng trn n v


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b. Theo phng php gn im cc

a thc c tnh ca hm truyn cho:

2 2

1 2 0 1 0 1 2

3 2

0 0 1 1 0 0 1 2 1 1 1 2 0 2 2 1

( ) ( ). ( ) ( ). ( )

( 1)( ) ( )( )

(1 ) (1 ) ( ) ( )

N z P z A z R z B z

z z a z a r z r b z b z b

r b z a b r b r z a a b r b r z a b r

Chn im cc ca i tng l1 2 3

, ,z z z th a thc c tnh l:

1 2 3

3 2

1 2 3 1 2 2 3 3 1 1 2 3

( ) ( ).( ).( )

( ) ( )

N z z z z z z z

z z z z z z z z z z z z z z z

Cn bng h s ta c

1 1 0 0 1

1 2 3

0 0

2 1 1 1 2 0

1 2 2 3 3 1

0 0

2 2 1

1 2 3

0 0

1

1

1

1

a b r b r z z z

b r

a a b r b r z z z z z z

b r

a b rz z z

b r

Chn cp im nghim phc , 0.9 0.1Gii h phng trnh 3 n

2 21 0 1 2 0 0 1 1 1 21 2 1 2

1 2 1 22 0 1 2 0 1 2 1 1 2 2 2 1

1 2 1 2

2 2 13

0 0 1 2

( ) . . 1 ( )

( ). .

(1 )

b ab b z z r b r a z z

z z z z

z z z zb b z z r b b r z z a a a

z z z z

a b rz

b r z z

Gii ra ta c 0 84.261 77.73 0.741 Kim tra li kt qu

>> Grz=filt([84.26 -77.7],[1 -1],0.1e-3)


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41

Grz =

84.26 - 77.7 z^-1

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

1 - z^-1


>> Grn=filt([0.0001497 0.000531 0.0001166],[1 -1.6065 0.6065],0.1e-3)

Grn =

0.0001497 + 0.000531 z^-1 + 0.0001166 z^-2

------------------------------------------1 - 1.607 z^-1 + 0.6065 z^-2



>> Gkn=(Grn*Grz)/(1+Grn*Grz)

Gkn =

0.01261 + 0.0002327 z^-1 - 0.08982 z^-2 + 0.1385 z^-3 - 0.06603 z^-4 -

0.0009847 z^-5

+ 0.005495 z^-6

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

1.013 - 5.213 z^-1 + 11.13 z^-2 - 12.61 z^-3 + 7.993 z^-4 - 2.685 z^-5 + 0.3733

z^-6


>> pole(Gkn)


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43

Ta thy qu iu chnh ln hn 20% nn cn hiu chnh li s liu ca biu chnh PI

Chn r0=283.2 r1=-283.7 ta c s

Kt qu


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44

Nhn xt : Sau khi hiu chnh ta thy qu iu chnh nh hn 20% tha mnyu cu.

Bnh phng sai lnh tnh


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45

Nhn xt: ta thy bnh phng sai lch tnh tin dn n 0

Khi c nhiu u vo dng bc nhy sau thi im 0.005s


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46

Kt qu

Nhn xt: khi c nhiu u vo b iu khin vn a h thng v gi tr xc lpmi

Khi c nhiu u ra ngoi vng iu khin phn hi

Kt qu


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47

Nhn xt : khi c nhiu u ra nm ngoi vng phn hi th h thng t ngay tigi tr xc lp mi

M hnh khi c nhiu u ra nm trong vng iu khin phn hi


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Kt qu

Nhn xt :khi c nhiu u ra th h thng nhanh chng a v trng thi xc lpsau mt vi chu k

+ M phng vi kt qu b iu chnh tnh theo phng php gn im cc

Kt qu


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49

Nhn xt :ta thy qu iu chnh ln hn 20% nn cn hiu chnh li s liu

Ta hiu chnh li s liu.Chn r=[84.24 -80.7]


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50

Kt qu

Nhn xt: ta thy qu iu chnh =20%tha mn iu kin

Bi thc hnh 4: Tng hp b iu chnh tc quay trn KGTT1. Tng hp b iu khin tc quay theo 2 phng phpa.

Phng php PT1Chn im cc thc dng

>> p1=[0.5 0.5]

p1 =

0.5000 0.5000

>> K1=acker(Az,Bz,p1)

K1 =

1.0e+04 *

-0.4645 -3.6948

Vi chu k trch mu T=0.1 s


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>> G1=ss(Az-Bz*K1,Bz,c,d,T1)

G1 =

a =

x1 x2x1 0.2395 -0.674

x2 0.1007 0.7605

b =

u1

x1 6.098e-05x2 2.166e-05

c =x1 x2

y1 0 5068

d =u1

y1 0


Discrete-time state-space model.

>> step(G1)

>> K2=acker(Az1,Bz1,p1)

K2 =

1.0e+04 *

-0.0229 -4.2914

Vi chu k trch mu T2=0.01 s

>> G2=ss(Az1-Bz1*K2,Bz1,c,d,T2)

G2 =


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a =

x1 x2x1 0.1404 -14.19

x2 0.009114 0.8596

b =u1

x1 0.002789x2 2.759e-05

c =

x1 x2y1 0 5068

d =u1

y1 0


>> hold on>> step(G2)

b.

p ng hu hn (gn im cc ti gc ta trn min z)

Chn im cc p2=[0 0]>> p2=[0 0]

p2 =

0 0

>> K3=acker(Az,Bz,p2)

K3 =

1.0e+03 *

-0.0275 -3.7862


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Vi chu k trch mu T1=0.1 s>> G3=ss(Az-Bz*K3,Bz,c,d,T1)

G3 =

a =x1 x2

x1 -0.04208 -2.696x2 0.0006568 0.04208

b =

u1x1 6.098e-05

x2 2.166e-05

c =x1 x2

y1 0 5068

d =

u1

y1 0


Discrete-time state-space model

>> K4=acker(Az1,Bz1,p2)

K4 =

1.0e+04 *

-0.0022 -2.7649

Vi chu k trch mu T2>> G4=ss(Az1-Bz1*K4,Bz1,c,d,T2)

G4 =

a =

x1 x2


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x1 -0.4384 -56.75

x2 0.003387 0.4384

b =

u1

x1 0.002789x2 2.759e-05

c =

x1 x2

y1 0 5068

d =

u1

y1 0


Discrete-time state-space model.

>> step(G3)>> step(G4)


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2. M phng kho st so snh 2 phng php

Ta dng cc lnh step v th v lnh hold on gi th trn cng 1 hnh

Kt qu

Nhn xt:

Tng hp biu khin tc quay theo phng php phn hi trng thisao cho p ng c dng PT1 th sau nhiu chu ktrch mu u ra mi xclp. Nhng gi trxc lp tin ti 1, sai lch tnh tin ti 0, t yu cu iukhin.

Tng hp biu khin tc quay theo phng php p ng hu hn thsau 2 chu ktrch mu u ra t gi trxc lp do 2 im cc c gn unm gc ta , tuy nhin tn ti sai lch tnh rt ln.


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