dktd-buoi2(nhom n)

8/14/2019 dktd-buoi2(nhom n)

1/22

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)


2/22

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=


3/22

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


4/22

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 =

+ =

+ + +


5/22

( ) ( ) ( )

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


6/22

+ 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.


7/22

+ 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


8/22

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 (


9/22

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 :


10/22

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:


11/22

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)


12/22

+ 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:


13/22

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 :


14/22

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


15/22

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


16/22

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 :


17/22

-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)


18/22

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)


19/22

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


20/22

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::


21/22

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:


22/22

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

dktd-buoi2(nhom n)

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