BO CO TH NGHIM

BO CO TH NGHIM

Bi 1: Tm m hnh gin on ca CMCCc tham s ca ng c: in tr phn ng RA=250m - M men qun tnh J=0,012 kgm2 in cm phn ng LA=4mH - Hng s ng c ke=236,8; kM=38,2 T thng danh nh

Hinh 1.1. S cu trc CMC kch thch c lp

Hinh 1.2. S h thng iu khin CMC theo cu trc Casecade1. Xc nh hm truyn t trn min nh z thch hp thit k vng trong cng K dng phn ngHm truyn ca i tng : Hm truyn trn min Z: Trong :

Do :

Trong : Thay s vo ta c:Vi Ttm1=0.1ms

Vi Ttm2=0.01ms 2.S dng lnh c2d ca matlab tm hm truyn t trn min nh z theo phng php ZOH, FOH v TustinLnh 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;Tm1=0.1e-3; Tm2=0.01e-3;>> Gi=tf([1],[Tt 1])*(1/Ra)*tf([1],[Ta 1])Hm truyn trn min Laplace:

>> step(Gi)

S dng lnh c2d vi cc chu k trch mu T1 v T2, ta s thu c 6 m hnh gin on ca Gi(s), v 6 m hnh gin on ca Gk(s):>> Giz3=c2d(Gi,Ttm1,'zoh') >> Giz4=c2d(Gi,Ttm1,'foh') >> Giz5=c2d(Gi,Ttm1,'tustin') >> Giz6=c2d(Gi,Ttm2,'zoh') >> Giz7=c2d(Gi,Ttm2,'foh') >> Giz8=c2d(Gi,Ttm2,'tustin')

3. M phng v kho st>> step(Gi); hold on>> step(Gzi1)>> step(Gzi2)>> step(Gzi3)>> step(Gzi4)>> step(Gzi5)>> step(Gzi6)>> step(Gzi7)>> step(Gzi8)

Nhn xt: p ng bc nhy ca hai hm truyn tnh bng tay v 6 hm truyn gin on bng lnh c2d gn nh trng vi p ng ca hm truyn trn min lin tc

4.Xy dng m hnh trng thi CMC trn min thi gian lin tc.Hm truyn ng c:

Chuyn v khng trng thi ta dng lnh:>> [a,b,c,d]=tf2ss(81.06,[0.016 1 767.8])

a = 1.0e+004 * -0.0063 -4.7987 0.0001 0

b = 1 0

c = 1.0e+003 * 0 5.0663d = 0Gin on ha m hnh:Chu k trch mu T = 0.01s

>> [Az1,Bz1] = c2dm(a,b,c,d,0.01)

Az1 =

-0.4987 -133.8787 0.0028 -0.3243

Bz1 =

0.0028 0.0000>> K1 = ss(Az1,Bz1,c,d,0.01) a = x1 x2 x1 -0.4987 -133.9 x2 0.00279 -0.3243

b = u1 x1 0.00279 x2 2.76e-005 c = x1 x2 y1 0 5066 d = u1 y1 0 Sampling time: 0.01Discrete-time model.

Chu k trch mu T = 0.1s>> [Az2,Bz2] = c2dm(a,b,c,d,0.1)

Az2 =

-0.0438 -2.9585 0.0001 -0.0399

Bz2 =

1.0e-004 *

0.6165 0.2167

>> K2 = ss(Az2,Bz2,c,d,0.1) a = x1 x2 x1 -0.04378 -2.959 x2 6.165e-005 -0.03993 b = u1 x1 6.165e-005 x2 2.167e-005 c = x1 x2 y1 0 5066 d = u1 y1 0 Sampling time: 0.1Discrete-time model. th thu c ca hm truyn>> step(K1); hold on>> step(K2)

Nhn xt: vi chu k trch mu 0,1s, p ng bc nhy gn nh b qua qu trnh qu . Cn vi chu k trch mu 0,01s, p ng bm gn ging vi p ng ca h lin tc.

Bi 2: Tng hp vng iu chnh dng phn ng (iu khin mmen quay)Trong bi 1 ta tm c hm truyn phn ng trn min nh z bng phng php ZOH vi chu k trch mu Ts1=0.1ms l:

Giz3 = filt([0 ],[1 -1.362 0.3656],0.1e-3)

Giz3 = =

2.1Thit k b iu khin dng theo phng php Dead-Beat

Vi a thc l bc 2 c dng: >> a0=1;a1=-1.362;a2=0.3656;>> b0=00;b1=0.009176;b2=0.006577;>> l0=a0/((a0 a1).(b0+b1+b2))>> l1=- a1/((a0 a1).(b0+b1+b2))

a thc : >> Lz1=filt([l0 l1],1,0.1e-3)>> Bz=filt([0 0.009176 0.006577],[1],0.1e-3)>> Az=filt([1 -1.362 0.3656],[1],0.1e-3)Hm truyn ca b iu chnh dng theo phng php dead-beat:>> GRi=Lz1*Az/(1-Lz1*Bz)

GRi(z) =

Hinh 2.1. S SimulinkKt qu m phng:

Nhn xt : t th ta thy sau 4 bc i tng iu khin ui kp gi tr t ca i lng ch o.Hm truyn h kn tnh bng lnh: Gk=GRi*Giz3/(1+ GRi*Giz3)Kt qu im cc ca hm truyn h kn c xc nh bng lnh:>> pole(Gk)c cc im cc l:0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.3767 + 0.3144i -0.3767 - 0.3144i 1.0000 + 0.0000i 0.9943 + 0.0000i 0.9943 + 0.0000i 0.3677 + 0.0000i 0.3677 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i 2.2 Thit k b iu chnh dng theo phng php cn bng m hnh

Gi s sau 3 chu k trch mu p ng ca i tng bm vo gi tr t, nh vy hm truyn ca i tng c dng:

Vi iu kin: Chn x1= 0.3; x2= 0.3; x3= 0.4Hm truyn ca i tng tm bng lnh:>> Gw3=filt([0 0.3 0.3 0.4],[1],0.1e-3)Hm truyn ca b iu chnh theo phng php cn bng m hnh tnh nh sau:

Tnh trn matlab:GRi(z-1) =

Kt qu m phng:

Nhn xt : t th ta thy sau 4 bc i tng iu khin ui kp gi tr t ca i lng ch o.Sau chu k u tin t ti gi tr x1 ,n chu k th 4 t gi tr x1 +x2 +x3 =1.Hm truyn h kn xc nh bi: >> Gk=GRi*Giz3/(1+ GRi*Giz3)Cc im cc ca hm truyn h kn:ans =

0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.3767 + 0.3144i -0.3767 - 0.3144i 1.0000 + 0.0000i 0.9943 + 0.0000i 0.9943 + 0.0000i 0.3677 + 0.0000i 0.3677 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i

Bi tp thc hnh s 3 Tng hp vng iu chnh tc quay3.1Tm hm truyn t trn min z ca i tng vng tc Hm truyn kn ca bi 2 xp x thnh khu qun tnh bc nht:

trong l hng s thi gian ca b chnh lu.Hm truyn i tng ca vng iu chnh tc l:

Suy ra: Tm hm truyn trn min z theo ZOH, chu k trch mu T1=0,1ms:Lnh: Gnz=c2d(Gn,T1,'ZOH')Gnz(z) = Chuyn sang m m:Gnz(z-1) = = b0 =0; b1=; b2 = ; a0 =1;a1= -1.607;a2 = 0.6065;3.2.Thit k b iu chnh PI cho tc ng cTheo tiu chun tch phn bnh phng

B iu chnh PI s c dng: chn Ta c:

Sai lch iu chnh vit di dng sai phn:

Trong

To hm function trong mfile :%function1.mfunction F = function1(r)b0 =0; b1=; b2 = ; a0 =1;a1= -1.607;a2 = 0.6065;F=(1/(1+r(1)*b0))^2+((a1-(1/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0))/(1+r(1)*b0))^2+((a2-((a1-(1/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0))/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0)-(1/(1+r(1)*b0))*(a2-a1+r(1)*b2+r(2)*b1))/(1+r(1)*b0))^2+((-((a2-((a1-(1/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0))/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0)-(1/(1+r(1)*b0))*(a2-a1+r(1)*b2+r(2)*b1))/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0)-((a1-(1/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0))/(1+r(1)*b0))*(a2-a1+r(1)*b2+r(2)*b1)-(1/(1+r(1)*b0))*(r(2)*b2-a2))/(1+r(1)*b0))^2+((-((-((a2-((a1-(1/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0))/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0)-(1/(1+r(1)*b0))*(a2-a1+r(1)*b2+r(2)*b1))/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0)-((a1-(1/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0))/(1+r(1)*b0))*(a2-a1+r(1)*b2+r(2)*b1)-(1/(1+r(1)*b0))*(r(2)*b2-a2))/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0)-((a2-((a1-(1/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0))/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0)-(1/(1+r(1)*b0))*(a2-a1+r(1)*b2+r(2)*b1))/(1+r(1)*b0))*(a2-a1+r(1)*b2+r(2)*b1)-((a1-(1/(1+r(1)*b0))*(a1-1+r(1)*b1+r(2)*b0))/(1+r(1)*b0))*(r(2)*b2-a2))/(1+r(1)*b0))^2;endLnh trong matlab:>> options = optimset('fminunc');>> options = optimset(options, 'Display','iter', 'LargeScale','off');>> rn = [-1 1];>> [r, fval]=fminunc('function1',rn,options)Ta thu c kt qu :r =

1.0e+03 *

0.8856 -1.2213

fval =

1.4677Chn kt qu:Chn r0 = 8856 ; r1 = -12213GRn(z-1) = u ra khng n nh:Ta chn li : r0 = 145 ; r1= -144 ;Ta c s Simulink:

u ra :

Sai lch ek

Nhn xt :u ra b iu khin tin ti xc lp sau khong thi gian kh di,tuy nhin vn khng thc s t gi tr mong mun.p ng u ra khi c nhiu : Nhiu gi tr t :t thm tn hiu bc nhy vo h thng sau khong thi gian 0.01sS Simulink

Kt qu m phng:Nhn xt: Khi c tc ng ca nhiu u vo b iu khin a h thng v gi tr xc lp mi. Nhiu ph ti: t thm tn hiu bc nhy vo h thng sau khong thi gian 0.01sS Simulink

Kt qu m phng:

Nhn xt: Khi c tc ng ca nhiu u ra b iu khin dao ng mnh,sau a h thng v gi tr cn bng nhanh chng.Theo phng php gn im cca thc c tnh ca hm truyn ch o:

Chn im cc ca i tng l th a thc c tnh l:

Cn bng h s, ta c:

Chn cp im cc phc Gii h phng trnh 3 n r0, r1, z3:

Thay s vo h phng trnh ta gii c: S Simulink

Tn hiu ra :

Sai lch:

p ng u ra khi c nhiu: Nhiu gi tr t :t thm tn hiu bc nhy vo h thng sau khong thi gian 0.01sS Simulink

Kt qu m phng:

Nhiu ph ti: t thm tn hiu bc nhy vo h thng sau khong thi gian 0.01sS Simulink:

Kt qu m phng:

Bi tp thc hnh s 4tng hp b iu chnh tc quay trn khng gian trng thi

Hm truyn t kn tm c trong bi 1:

Tm ma trn trn khng gian trng thi bng lnh:>> [A,B,C,D]=tf2ss([81.06],[0.016 1 767.8])Ma trn trn min gin on:>>[Az1,Bz1]=c2d(A,B,0.1)>>[Az2,Bz2]=c2d(A,B,0.01)4.1.Phng php phn hi trng thi sao cho p ng c dng PT1>>p1=[0.54 0.46]>>K1=acker(Az1,Bz1,p1)>>G1=ss(Az1-Bz1*K1,Bz1,C,D,0.1)>>step(G1)

.>> p2=[0.61 0.36]>> K2=acker(Az2,Bz2,p2)>> G2=ss(Az2-Bz2*K2,Bz2,C,D,0.01)>>step(G2)

4.2.Phng php p ng hu hn (Deat-beat-gn im cc ti gc ta trn min nh z)>> p3=[0 0]>> K3=acker(Az1,Bz1,p3)>> G3=ss(Az1-Bz1*K3,Bz1,C,D,0.1)>> step(G3)

..>>p4=[0 0]>>K4=acker(Az2,Bz2,p4)>>G4=ss(Az2-Bz2*K4,Bz2,C,D,0.01)>>step(G4)

Nhn xt : Tng hp b iu khin tc quay theo phng php phn hi trng thi sao cho p ng c dng PT1 th sau nhiu chu k trch mu u ra mi xc lp. Nhng gi tr xc lp tin ti 1, sai lch tnh tin ti 0, t yu cu iu khin. Tng hp b iu khin tc quay theo phng php p ng hu hn th sau 2 chu k trch mu u ra t gi tr xc lp do 2 im cc c gn u nm gc ta , tuy nhin tn ti sai lch tnh rt ln.4.3.Kim tra tnh iu khin c v quan st cTnh quan st cMa trn quan st:>> Q1=obsv(Az1,C)

>> Q2=obsv(Az2,C)

Kim tra hng ca 2 ma trn quan st:>> rank(Q1)ans=2>> rank(Q2)ans=2Vy h l quan st c vi hai tn s trch mu T1 v T2Tnh iu khin cMa trn iu khin:>> Ct1=ctrb(Az1,B)

>> Ct2=ctrb(Az2,B)

Kim tra hng ca hai ma trn iu khin:>> rank(Ct1)ans=2>> rank(Ct2)ans=2Vy h l iu khin c vi hai tn s trch mu T1 v T2

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