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8/14/2019 dktd-buoi2(nhom n)
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G(s)Gc(S)
BI TP: MN THC HNH LTKT
GV: HUNH MINH NGC
LP HT-3A
NHM THC HNH 1 ( BUI CHIU TH 3 )
TRN NGC CA 07705741
TRN DANH CU 07707361
BI VN HI 07709981
BI 1: Thit k khu hiu chnh sm pha dng phng php qu o nghim s, c hthng iu khin nh hnh v: vi G(s)=
20
( 1)( 2) s s s+ +
R(s)-C(p)
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Hm truyn ca khu hiu chnh sm pha Gc(s) c dng Gc(s)= Kc(1/ )
(1 )
s T
s T
++ +
Ta cn xc nh cc h s ca phng trnh trn. Ta tin hnh theo cc bc sau:Bc 1: xc nh cp cc quyt nh.
Theo yu cu thit k vt l POT < 20% v thi gian xc lp
xlt
< 8s ta c:
POT=exp
21
< 0.2
2
2 2
ln 0.2 1.61
1.95 1 4.8 1 0.45
< =
> > >
Chn
= 0.707
xlt
=4
8n
0.707n >
Chn
n
= 1
Vy cp cc quyt nh l:* 2 2
1.2 1 0.707 1 1 1 0.707n n s j j = =
*
1.2 0.707 0.707s j=
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Bc 2: xc nh gc pha cn b
* 0
1 2 3180 ( ) = + + +
0 0 0 0 0180 (135 67.5 28.7 ) 51.2= + + + =
Bc 3 : xc nh cc v zero ca khu hiu chnh sm pha bng phng php ngphn gic.
V PA l phn gic ca gc OPx
V PB, PC sao cho gc APB =*
2
v gc APC =*
2
im B chnh l v tr cc v im C chnh l v tr zero ca khu hiu chnh
1
T
= OB v1
T
= OC
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p dng h thc lng trong tam gic ta c:
OB = OP
*
*
2 2
2 2
O PxSin
O PxSin
+
=0 0
0 0
135 51.2
2 2
135 51.2
2 2
Sin
Sin
+
= 1.5
OC = OP
*
*
2 2
2 2
O PxSin
O PxSin
+
=0 0
0 0
135 51.2
2 2
135 51.2
2 2
Sin
Sin
+
= 0.67
Gc(s)= Kc
1.5
0.67
s
s
++
Bc4: tnh Kc
*( ). ( ) 1C s sG s G s = =
0.707 0.707
1.5 201
0.67 ( 1)( 2)C
s j
sK
s s s s =
+ =
+ + +
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( ) ( ) ( )
0.707 0.707 1.5 2010.707 0.707 0.67 0.707 0.707 0.707 0.707 1 0.707 0.707 2
C
jK j j j j
+ + = + + + + + + +
1.33 20 1CK =
CK
= 0.04
Vy hm truyn ca khu hiu chnh sm pha cn tm l:Gc(s)= 0.04
1.5
0.67
s
s
++
a) E
B. Khai bo hm truyn Gs=20ss+1(s+2)
H(s) =1
S dng sisotool
Khai bo:
>> num=20
>> den=[1 3 2 0]
>> g=tf(num,den)
>> h=tf(1)>> sisotool
+u tin ta thit lp cc hm truyn: file/importLc ny ca s import system data xut hin ta thit lp hm
truyn. thit lp xong chn Ok
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+ by gi ta xem hm khi cha hiu chnh: vo menu chn analysis/otherloop pesponses chn cc thit lp tng ng ta c hnh sau:
0 10 20 30 40 50-270
-180
-90
P.M.: -28.1deg
Freq: 2.43rad/sec
Frequency (rad/sec)
-100
-50
0
50
G.M.: -10.5dB
Freq: 1.41rad/sec
Unstableloop
Open-LoopBodeEditor (C)
-6 -4 -2 0 2-4
-3
-2
-1
0
1
2
3
4Root Locus Editor (C)
Real Axis
StepResponse
Time(sec)
Amplitude
0 1 2 3 4 5 6-10
-8
-6
-4
-2
0
2
4
6
8
+ kch chut phi vo vng QNS, menu xut hin: ta chn add pole/zero lead (hiu chnh sm pha)+ dng chut xc nh im cc v zero cn thit c hiu chnh nh mongmun.
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+ nhng thng nh vy s rt mt thi gian v sai s ln n c khonghiu chnh ti u, nn ta da vo tnh ton l thuyt ri sau hiu chnh trongkhong no th tt hn.Sau khi c b hiu chnh C(s) nh mong mun ta xem kt qu: bng cch chnanalysis/other loop pesponses chn cc thit lp tng ng ta c hnhsau khi hiu chnh:
0 10 20 30 40-270
-180
-90
P.M.: 22.8deg
Freq: 0.594rad/sec
Frequency(rad/sec)
-100
-50
0
50
G.M.: 7.04dB
Freq: 0.925rad/sec
Stableloop
Open-LoopBodeEditor (C)
-6 -4 -2 0 2-4
-3
-2
-1
0
1
2
3
4Root LocusEditor (C)
Real Axis
StepResponse
Time(sec)
Amplitude
0 1 2 3 4 5 6 7 80
0.2
0.4
0.6
0.8
1
1.2
1.4
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Bi 2 :Hy thit k khu hiu chnh Gc(s) sao cho h thng c s khi di y saukhi hiu chnh c sai s i vi tn hiu vo l hm dc l 0.02 v p ng qu thayi khng ng k.
R(s)
Tnh ton l thuyt:
H s vn tc ca h thng trc khi hiu chnh:
Kv = lims0sGs=lims010ss+3s+4=0.83
Sai s xc lp ca h thng trc khi hiu chnh:
exl = 1Kv = 10.83=0.1
do y l bi ton thit k hiu chnh tr pha nn:
Gc(s)=Kcs+1Ts+1T (
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Gc(s)=Kcs+1Ts+1T= Kc-1+j+1T-1+j+1T vi 1T Re(s1,2*)hay 1T1
Khi 1 + G(s)Gc(s)s = s1,2*= 0 GC(s)G(s)G(s)Gc(s)s = s1,2* ==1-1800
Ta xt pha : G(s)Gc(s)s = s1,2*= -1800 Gc(s)s = s1,2* + G(s)s = s1,2*= -1800
Gc(s)s = s1,2*= -1800 - G(s)s = s1,2*
-1800 - G(s)s=s1,2 = -1800+1800 = 00
Bi vy khi thit k ta chn sao cho Gc(s)s = s1,2* cng v 00 cng tt, thngth ngi ta chn sao cho -50 < Gc(s)s = s1,2* < 00 .
Vy ta chn Gc(s)s = s1,2*= - 40 ; tg(-40) 0.07 (1)
Mt khc Gc(s)=Kcs+1Ts+1T ; t a= 1T do a1(*)
Vy Gc(s)=Kcs+as+a = Kc-1+j +a-1+j+a
= Kc-1 +a-1+a+1-1+a2 +1+j-1+a--1 +a-1+a2+1
M Gc(s)s = s1,2* = arctg -1+a-(-1+a)-1 +a-1+a+1 = arctga(-1)a2+ a1++2 (2)
T (1),(2) ta c:
a(-1)a2+ a1++2=0.07a=0.13a=14.9 ta chn a = 0.13tha k (*)
Vy sau khi khi hiu chnh th: Gc(s)= Kcs+0.13s+0.00221 ; by gi ta ch cn chngminh Kc sau hiu chnh 1 th xem nh hon thnh.
Tnh Kc sau khi hiu chnh:
G(s)Gc(s)s = s1,2* =1 Kcs+0.13s+0.00221*10ss+3(s+4)= 1
Kc-1+j+0.13-1+j+0.00221*10-1+j-1+j+3(-1+j+4) =1
Kc =1.0657 1 (pcm)
Vy sau khi hiu chnh tr pha :
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Gc(s)= s+0.13s+0.00221
M phng bng matlab dng cng c sisotool:
Khai bo hm truyn:
Gs=10ss+3(s+4) Hs=1
Ta s khai bo trong matlab nh sau:>> s=tf('s')>> g=10/(s*(s+3)*(s+4))>>h=tf(1)>>sisotoolCa s sisotool xut hin:+ u tin ta thit lp cc hm truyn: file/import
Lc ny ca s import system data xut hin ta thit lp hmtruyn. thit lp xong chn Ok+ by gi ta xem hm khi cha hiu chnh: vo menu chn menutool/draw simulik.Ca s xut hin nh sau:
Ta chn ng vo l hm dc ( ramp ) nh sau:
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Hm truyn cha hiu chnh c dng nh sau:
Tip theo ta hiu chnh tr pha bng cch:
+ kch chut phi vo vng QNS, menu xut hin: ta chn add pole/zero lag (hiu chnh tr pha)
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+ dng chut xc nh im cc v zero cn thit c hiu chnh nh mongmun.+ nhng thng nh vy s rt mt thi gian v sai s ln n c khonghiu chnh ti u, nn ta da vo tnh ton l thuyt ri sau hiu chnh trongkhong no th tt hn.Sau khi c b hiu chnh C(s) nh mong mun ta xem kt qu tng t nh trnta c:
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Bi 3: Cho h thng hi tip m n v. C hm truyn h h l G(s) = 4s(s+0.5)
Thit k b hiu chnh sm tr pha h thng c = 0.5 ,n = 5 (rad/s) , v hs vn tc Kv= 80.
Bi gii.a) Tnh ton l thuyt.
H cha hiu chnh c = 0.125 , ,n =2 (rad/s) ,Kv = 8 ; cc cc l p1 = 0, p2 =-0.5 . Gi Gc(s) l khu hiu chnh sm tr pha : Gc(s) = Gc1(s).Gc2(s)
Bc 1: thit k khu hiu chnh sm pha Gc1(s).
Gc1s=Kc1 1+T1.s1+T1.s vi >1
Cp cc quyt nh sau khi hiu chnh l :S1,2 = - n j n1- 2 = -(0.5)(5) j(5) 1-0.52 S1,2 = -2.5 j4.33
Gc pha cn b:
=-1800+(1200+1150) = 550
Chn zero ca khu hiu chnh l -0.5 trng vi cc p = -0.5 ca G(s) h bc hthng sau khi hiu chnh. Ta c:
1T1=0.5=OA
T cc S1 v hai na ng thng to vi nhau mt gc l . Cc ca khu sm pha tiim B .1T1=OB
Ta c : OB = OA + AB vi OA = 0.5 , AB = PAsinAPBsinPBA trong P l im tinghim S c phn thc m.
Ta c : PA = 22+4.332 = 4.76
Gc APB = = 550 ; PBA = 1150-550= 600 AB = 4.76sin55sin60
1T1=OB=0.5+4.5=5
Vy Gc1s=Kc1 0.5+s5+s
Tm Kc1 :
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Gc1s.G(s)s=s1=1 Kc1.s+0.5s+5.4s(s+0.5)s=-2.5+j4.33=1
Kc1 = 6.25
Vy : Gc1s=6.25 0.5+s5+s = 0.6251+2s1+0.2s
Hm truyn h h sau khi hiu chnh sm pha l :
G1(s) = Gc1(s).G(s) = 6.25 0.5+s5+s4s(s+0.5) G1(s) = 25s(s+5)
Bc 2: Thit k khu hiu chnh tr pha Gc2(s).
Gc2s=Kc2 1+T2.s1+T2.s vi
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a) Thc hin bng Sisotool.
Bc 1: thit k khu hiu chnh sm pha Gc1(s). chnh l C(s) trong matlap.
Khai bo hm truyn G(s),H(s),C = 1,F =1.
G=tf(4,[1 0.5 0])
H=tf(1)
sisotool
T ca s sisotool vo file import- nhp hm
Thit k C(s).
T yu cu bi ton cp cc quyt nh sau hiu chnh c = 0.5 ,n = 5 (rad/s),nn ta c:
vt l cn thit k l : POT = e-(1-2)= e-(0.51-0.52)= 0.163 , chn vt lthit k < 17%
Thi gian qu ( theo tiu chun 2%) : tqd = 4n =45.0,5 = 1.6 ,chn thi gian qu thit k < 1.7s
Vo menu chn menu tool/draw simulik v p ng vi u vo hm dc v qu onghim s trc khi hiu chnh v lu lai:
-0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0-2
-1.5
-1
-0.5
0
0.5
1
1.5
2Root LocusEditor(C)
Real Axis
ImagAxis
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Click chut phi vo QDNS add pole/zero lead thm khu hiu chnh sm pha voh thng. Click chut phi vo QDNS chn Design constraints new ci vt l vthi gian xc lp theo thit k.
By gi di chuyn cc cc v zero ca b hiu chnh C(s) trn trc thc sao cho nhanhQDNS ko vo vng tha mn thit k .hoc ta c th nhp trc tip cc v zero ca C(s),theo phng php kh cc. so snh vi cu a ta nhp cc v zero ca C(s) nh tnh. Ta c QDNS sau hiu chnh sm pha v p ng vi ng vo hm dc nh hnh v :
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-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0-5
-4
-3
-2
-1
0
1
2
3
4
5Root LocusEditor(C)
Real Axis
ImagAxis
Bc 2: Thit k khu hiu chnh tr pha Gc2(s)
By gi ta phi nhp li hm truyn vi G(s) by gi l G1(s)
G1(s) = 25s(s+5).
G1(s)=tf(25,[1 5 0])
H=tf(1)
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sisotool
Thit k Gc2(s) ,cng l C(s) trong matlap.
Tng t nh bc 1.
Click chut phi vo QDNS add pole/zero lag thm khu hiu chnh sm pha voh thng. By gi di chuyn cc cc v zero ca b hiu chnh C(s) trn trc thc sao chonhanh QDNS ko vo vng tha mn thit k
Sau khi hiu chnh sm tr pha vi ng vo hm dc ta c biu p ng ca h thngv QDNS nh sau:
BI 1 TRANG 175: cho h thng hm truyn nh hnh v:
R(s)C(s) G(s)
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Gs=20ss+1(s+2)
Thit k b hiu chnh sm fa c vt l POT nh hn 20% v thi gian xclp nh hn 8s
Trnh by:Do hiu chnh tr pha : Gc(s)=Kcs+1Ts+1T
POT=exp (-1-2) 1-2 4,82 > 1 =0.45
Chn = 0.707
tqd =4Wn < 8Wn =0.707 vy chon Wn=0.707
vy cp cc quyt nh l:
s*1,2 - Wn jWn1-2= -0.707*0.707j0.7071-0.7072
s*1,2 = -0.5j0.5
* = -1800 + {arg[(-0.5+j0.5) 0] + arg[(-0.5+j0.5) ( -1 )] + arg[(-0.5+j0.5) ( -2 )] }
= -1800 + {arctan(0.5-0.5) + arctan(0.50.5) + arctan(0.51.5) }
= -1800 + (135 + 45 +18.4)
* =18.40
V PA l phn gic ca gc OPx
V PB v PC sao cho gc APB = *2, APC = *2
im B chnh l v tr cc v C l v tr zero ca khu hiu chnh.
1T=OB 1T=OC
p dng cc tnh cht trong tam gic:
OB = 0.6, OC = 0.8
Gc(s)= Kcs+0.8s+0.6
Tnh Kc:
G(s)Gc(s)s = s1,2* =1 Kcs+0.8s+0.6*20ss+1(s+2) = 1
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Kc0.3+j0.50.1+j0.5*20-0.5+j0.50.5+j0.5(1.5+j0.5) =1
Kc =0.54 vy hm truyn hiu chnh sm fa l:
Gc(s)= 0.54 s+0.8s+0.6
M phng:
Khai bo hm truynGs=20ss+1(s+2)
H(s) =1
S dng sisotool
Khai bo:
>> num=20
>> den=[1 3 2 0]
>> g=tf(num,den)
>> h=tf(1)
>> sisotool
+u tin ta thit lp cc hm truyn: file/import
Lc ny ca s import system data xut hin ta thit lp hmtruyn. thit lp xong chn Ok+ by gi ta xem hm khi cha hiu chnh: vo menu chn analysis/otherloop pesponses chn cc thit lp tng ng ta c hnh sau::
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Step Response
Time (sec)
Amplitude
0 1 2 3 4 5 6-10
-8
-6
-4
-2
0
2
4
6
8
+ kch chut phi vo vng QNS, menu xut hin: ta chn add pole/zero lead (hiu chnh sm pha)+ dng chut xc nh im cc v zero cn thit c hiu chnh nh mongmun.+ nhng thng nh vy s rt mt thi gian v sai s ln n c khonghiu chnh ti u, nn ta da vo tnh ton l thuyt ri sau hiu chnh trongkhong no th tt hn.Sau khi c b hiu chnh C(s) nh mong mun ta xem kt qu: bng cch chnanalysis/other loop pesponses chn cc thit lp tng ng ta c hnhsau khi hiu chnh:
Sau khi hiu chnh:
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Step Response
Time (sec)
Amplitude
0 2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
1.2
1.4