BÁO CÁO THÍ NGHIỆM ĐIỀU KHIỂN SỐ.pdf
Transcript of BÁO CÁO THÍ NGHIỆM ĐIỀU KHIỂN SỐ.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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> Giz7=c2d(Gi,T1,'tustin')
Giz7 =
0.004154 z^2 + 0.008307 z + 0.004154
------------------------------------z^2 - 1.327 z + 0.3313
Sample time: 0.0001 seconds
Discrete-time transfer function.
- 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
Discrete-time transfer function.
>> 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=c2d(Gi,T2,'foh')
Giz6 =
4.064e-05 z^2 + 0.0001585 z + 3.865e-05---------------------------------------
z^2 - 1.904 z + 0.9043
Sample time: 1e-05 seconds
Discrete-time transfer function.
>> 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
Continuous-time transfer function.
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
Sample time: 0.0001 secondsDiscrete-time transfer function.
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1.263e-05 z^2 + 2.525e-05 z + 1.263e-05
---------------------------------------z^2 - 1.993 z + 0.9938
Sample time: 0.0001 seconds
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
Sample time: 1e-05 seconds
Discrete-time transfer function.
>> 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
Sample time: 1e-05 seconds
Discrete-time transfer function.
>> 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
Sample time: 1e-05 seconds
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Discrete-time transfer function.
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
Sample time: 0.01 secondsDiscrete-time state-space model.
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
Sample time: 0.0001 secondsDiscrete-time transfer function.
>> Ai=filt([a0 a1 a2],1,T1)
Ai =
1 - 1.362 z^-1 + 0.3656 z^-2
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> Bi=filt([b0 b1 b2],1,T1)
Bi =
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0.003298 + 0.01046 z^-1 + 0.001998 z^-2
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
Sample time: 0.0001 secondsDiscrete-time transfer function.
>> 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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
Sample time: 0.0001 secondsDiscrete-time transfer function.
>> 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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
>> 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.
>> Giz5=c2d(Gi,T1,'foh')
Giz5 =
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0.003298 z^2 + 0.01046 z + 0.001998-----------------------------------
z^2 - 1.362 z + 0.3656
Sample time: 0.0001 secondsDiscrete-time transfer function.
>> Gw1=filt([0 0.3 0.7],T1)
Gw1 =
0.3 z^-1 + 0.7 z^-2
-------------------
0.0001
Sample time: unspecified
Discrete-time transfer function.
>> 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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
Sample time: 0.0001 seconds
Discrete-time transfer function.
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
Discrete-time transfer function.
>> 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
Sample time: 0.0001 seconds
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
Sample time: 0.0001 secondsDiscrete-time transfer function.
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
>> Tt=100e-6;Ra=250e-3;La=4e-3;Ta=La/Ra;T1=0.1e-3;T2=0.01e-3;
>> Km=38.2;phi=0.04;J=0.012;>> Gk=tf(1,[2*Tt 1])
Gk =
1
------------
0.0002 s + 1
Continuous-time transfer function.
>> 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
Continuous-time transfer function.
>> Gnz=c2d(Gn,T1,'foh')
Gnz =
0.0001497 z^2 + 0.000531 z + 0.0001166
--------------------------------------z^2 - 1.607 z + 0.6065
Sample time: 0.0001 seconds
Discrete-time transfer function.
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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
Sample time: 0.0001 secondsDiscrete-time transfer function.
>> 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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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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
Sample time: 0.0001 secondsDiscrete-time transfer function.
>> 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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40
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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Grz =
84.26 - 77.7 z^-1
-----------------
1 - z^-1
Sample time: 0.0001 secondsDiscrete-time transfer function.
>> 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
Sample time: 0.0001 seconds
Discrete-time transfer function.
>> 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
Sample time: 0.0001 secondsDiscrete-time transfer function.
>> pole(Gkn)
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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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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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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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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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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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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
Sample time: 0.1 seconds
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
Sample time: 0.01 secondsDiscrete-time state-space model.
>> 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
Sample time: 0.1 seconds
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
Sample time: 0.01 seconds
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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