Tn: H ng DngMSSV:20112560Lp: K &TH1
BI THC HNH S 3TNG HP VNG IU CHNH TC QUAY1. Xc nh hm truyn t trn
min nh z ca i tng ca khu iu chnh tc quay.
i tng tc bi ny c tnh bng :Gn= Gk(b2)kM Vi Gkn(bi 2) c sp x mt
khu tch phn qun tnh bc nht Gk(b2)= , Vi Tt = 100e-6 S dng matlab
tnh ton:>> Ttm1=0.1e-3; phi=0.04; J=0.012; Km=38.2;Ke=236.8;
Ta=La/Ra;Tt=100e-6;>>Gn=tf(1, [2*Tt 1])*Km*phi*tf(1, [2*pi*J
0])
Gn =- Chuyn sang min nh z vi chu k trch mu Ttm1, phng php gi mu
ZOH >>Gnz=c2d(Gn,Ttm1,'zoh') Gnz = Chuyn i sang Gn(>>
b0=0;b1=0.0004318;b2=0.0003656;>>
a0=1;a1=-1.607;a2=0.6065;>> Bz=filt([b0 b1 b2],1,Ttm1) Bz =
0.0004318 z-1 + 0.0003656 z-2>> Az=filt([a0 a1 a2],1,Ttm1) Az
= 1 - 1.607 z-1 + 0.6065 z-2>>Gnz1=Bz/Az Gnz1
=>>step(Gnz)
- Nhn xt: T th l mt khu tch phn. Ti thiu ta cn 1 khu t l - Ta x
kim chng li nhn xt
trn.>>Kp=1;>>Gk=feedback(Kp*Gnz,1);>>step(Gk)
2. Tng hp (thit k) b iu chnh PI cho tc ng c theo hai phng php:a)
Theo phng php gn im cc - Vit li hm truyn trn di dng nh sau:
- Hm truyn ca h kn l:
Ta cho p=-1 ta s c :
B iu khin c dng nh sau:
a thc c tnh ca hm truyn ch o:N(z)=P(z).A(z)+R(z)B(z) (a0=1)
Gi s im cc ca i tng ch o l th ta c:
Vi Gii h phng trnh 3 n r0 ; r1 ; z3 t n >>
z2=0.8;z3=0.8;p=-1;>> k1=z2+z3;k2=z2*z3;>> A=[b1 0 1;b2
b1 -k1;0 -b2 -k2]A =
0.0004 0 1.0000 0.0004 0.0004 -1.6000 0 -0.0004 -0.6400>>
B=[-k1-a1+1;k2+a1-a2;-a2]B =
1.0070 -1.5735 -0.6065 >> X=inv(A)*BX = 59.6998 -58.7578
0.9812>> r0=59.6998;r1=-58.7578;>>Rz=filt([r0
r1],1,Ttm1) Rz = 59.7 - 58.76 z-1>>Pz=filt([1 -1],1,Ttm1) Pz
=1 - z-1>>Grn=Rz/Pz Grn =
th p ng vi b iu khin thit k bng phng php gn im ccNhn xt th p ng
vi b iu khin thit k bng phng php gn im cc qu iu chnh >b0=0;b1=
0.0004318; b2=0.0003656;>>a0=1;a1= - 1.607;a2= 0.6065;-Ta c
sai lch iu chnh :E(z)=W(z).-Vit sai lch iu chnh di dng sai phn : ek
= (wk + wk-1(a1-1) +wk-2(a2-a1) wk-3(a2) ek-1(r0.b1+r1.b0+a1-1)
ek-2(r0.b2+r1.b1+a2-a1) ek-3(r1.b2-a2))/(1+r0.b0)- Vi wk = vi mi k
e0= (1/(1+r0*b0)) e1= (1+(a1-1)-e0*(r0*b1+r1*b0+a1-1))/(1+r0*b0)
e2=(1+(a1-1)+(a2-a1)-e1*(r0*b1+r1*b0+a1-1)-e0*(r0*b2+r1*b1+a2-
a1))/(1+r0*b0)
e3=(1+(a1-1)+(a2-a1)-a2-e2*(r0*b1+r1*b0+a1-1)-e1*(r0*b2+r1*b1+a2
-a1)-e0*(r1*b2-a2))/(1+r0*b0)
- Hm Jz == +++- Ta s khai bo hm J= trong m file:function J=
bai3(x)b0 = 0;b1 = 0.0004318;b2=0.0003656;a0 = 1;a1 = - 1.607;a2 =
0.6065;e0 = 1/(1+x(1)*b0);e1 =
(1+(a1-1)-e0*(x(1)*b1+x(2)*b0+a1-1))/(1+x(1)*b0);e2=(1+(a1-1)+(a2-a1)-e1*(x(1)*b1+x(2)*b0+a1-1)-e0*(x(1)*b2+x(2)*b1+a2-
a1))/(1+x(1)*b0); e3 =
(1+(a1-1)+(a2-a1)-a2-e2*(x(1)*b1+x(2)*b0+a1-1)-e1*(x(1)*b2+x(2)*b1+a2
-a1)-e0*(x(2)*b2-a2))/(1+x(1)*b0) ; J= e0^2+e1^1+e2^2+e3^2;s
Lnh tm ti u cc tiu command windown:>>options =
optimset('fminunc');>>options =
optimset(options,'Display','iter','LargeScale','off');>>r =
60 60];>>[r,fval]=fminunc('bai3',r,options)Ta thu c cp im cc
tiu l [r0 r1] = [ 1328 -2185] fval =15.129B iu khin Grz:>>
Grz= filt([1.3275e3 -2.1849e3],[1 -1],Ttm1)>>
Gk=feedback(Gnz*Grz,1)
Gk =
Kim Tra im cc:>>Pole(Gk)Ans= 1.4886 0.2724 + 0.9327i
0.2724 - 0.9327i >>step(Gk)
Nhn xt: H khng n nh. Cn chn li tham s b iu khinChn li tham s r0
= 57, r1 = -57p ng:
Sai lch e2
Tc ng Nhiu u Vo Tstep=0.04
u ra:
Sai lch e^2:Nhn xt: khi tc ng nhiu u vo th h n nh t trng thi xc
lp mi
Tc ng nhiu u ra:
u ra:Sai lch :
Nhn xt: Khi tc ng nhiu u ra h n nh th u ra tr v trng thi xc lpBI
THC HNH S 4TNG HP B IU CHNH TC QUAY TRN KGTTTheo bi 1 cu 4 ta
c:
>>[Ak1,Bk1]=c2d(A,B,Ttm3)
Ak1 = -0.0438 -2.95490.0001 -0.0399Bk1 = 1.0e-004 * 0.6157
0.2167-------------------------->>[Ak2,Bk2]=c2d(A,B,Ttm4)
Ak2 = -0.4987 -133.8774 0.0028
-0.3244--------------------------Bk2 = 0.0028
0.0000------------------------->> H1=ss(Ak1,Bk1,C,D,Ttm3)
a = x1 x2x1 -0.04378 -2.955x2 6.157e-005
-0.03994-----------------------------------b = u1x1 6.157e-005x2
2.167e-005-----------------------------------c = x1 x2 y1 0 5066
----------------------------------d = u1 y1 0
--------------------------------Sampling time:
0.1>>H2=ss(Ak2,Bk2,C,D,Ttm3)a = x1 x2x1 -0.4987 -133.9x2
0.00279 -0.3244--------------------------------
b = u1x1 0.00279x2 0--------------------------------c = x1 x2 y1
0 5066 -------------------------------d = u1 y1 0 Sampling time:
0.011. Phn hi trng thi sao cho p ng c dng PT1 Vi Ttm3=0.1ms>>
p1=[0.59 0.72]>> K1=acker(Ak1,Bk1,p1)K1 = 1.0e+004 * -0.7450
-4.2686 Vi Ttm4=0.01s>> p2=[0.5 0.5]>>
K2=acker(Ak2,Bk2,p2)K2 = 1.0e+004 * -0.0229 -4.29022. p ng hu hn
Dead-Beat Ta thc hin tnh ton trn Matlab nh sau:>> p3 =[0
0]>> K3=acker(Ak1,Bk1,p3)K3 = 1.0e+003 * -0.0272
-3.7860>> K4=acker(Ak2,Bk2,p3)K4 = 1.0e+004 * -0.0022
-2.76413. M phng kho st, so snh hai phng php iu khin Ta thc hin tnh
ton trn Matlab nh sau:>>G1=ss(Ak1-Bk1*K1,Bk1,C,D,Ttm3) G1 = a
= x1 x2 x1 0.4149 -0.3267 x2 0.1615 0.8851 b = u1 x1 6.157e-05 x2
2.167e-05 c = x1 x2 y1 0 5066 d = u1 y1 0 Sample time: 0.1
secondsDiscrete-time state-space model.>>
G2=ss(Ak2-Bk2*K2,Bk2,C,D,Ttm4) a = x1 x2 x1 0.1404 -14.19 x2
0.009112 0.8596
b = u1 x1 0.00279 x2 2.76e-005
c = x1 x2 y1 0 5066
d = u1 y1 0
Sampling time (seconds): 0.01Discrete-time model.
>>G3=ss(Ak1-Bk1*K3,Bk1,C,D,Ttm3) a = x1 x2 x1 -0.04211
-2.722 x2 0.0006514 0.04211
b = u1 x1 6.157e-005 x2 2.167e-005
c = x1 x2 y1 0 5066
d = u1 y1 0
Sampling time (seconds): 0.1Discrete-time model.>>
G4=ss(Ak2-Bk2*K4,Bk2,C,D,Ttm4) a = x1 x2 x1 -0.4384 -56.77 x2
0.003386 0.4384
b = u1 x1 0.00279 x2 2.76e-005
c = x1 x2 y1 0 5066
d = u1 y1 0
Sampling time (seconds): 0.01Discrete-time model. M phng kho st,
so snh hai phng php iu khin:>> hold
on>>step(G1)>>step(G2)>>step(G3)>>step(G4)
Nhn xt: Nhn xt: Phng php phn hi trng thi sao cho p ng c dng PT1:
Sau nhiu chu k trch mu, u ra mi t trng thi xc lp. Phng php p ng hu
hn: Sau 2 chu k trch mu u ra t gi tr xc lp do 2 im cc c gn u nm gc
ta .
