Mô Hình Hệ Thống Điều Khiển Tự Động

M hnh h thng iu khint ng

Bi:

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M HNH H THNG IU KHIN T NG

MC TIU

Trong bi th nghim ny chng ta s tm hiu phng php m hnh ha mt h iukhin t ng, bao gm:

Hm truyn v phng trnh trng thi ca h thng p ng vng h v p ng vng kn ca h thng Xy dng b iu khin PID Chnh nh thng s ca b u khin v kho st p ng ca h thng.

Hnh 5.1 Mt m hnh h thng iu khin tiu biu

THAM KHO

[1]. The Mathworks Inc., Matlab Notebook Users Guide Control toolbox, 2003.

[2]. Phm Vn Tn, Bi ging mn C s T ng hc, B mn Vin Thng v T ngha, khoa Cng ngh Thng tin, i hc Cn Th, 2001.

[3]. Nguyn Cng nh, Phn tch v Tng hp cc h thng iu khin bng my tnh,NXB Khoa hc v K thut, 2002.

M hnh h thng iu khin t ng

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www.princexml.comPrince - Non-commercial LicenseThis document was created with Prince, a great way of getting web content onto paper.

[4]. http://www.engin.umich.edu/group/ctm

[5]. http://www.shu.ac.uk/schools/eng/teaching/rw/pidtutorial.htm

THC HNH

c th thc hin tt bi th nghim, sinh vin cn nm vng cc kin thc c bn viu khin t ng (C s t ng hc). Do , bi ny khng bt buc i vi cc sinhvin Tin hc (nu c) v cc sinh vin in t theo hng Vin thng. Trong trnghp , c th sinh vin thc tp bi 4 hoc sinh vin c th chuyn sang bi 7.

Hm truyn v phng trnh trng thi ca h thng

Trong iu khin t ng, ngi ta thng biu din mt h thng vt l bng hmtruyn (transfer function) hay phng trnh trng thi (state-space equation) ca n (ivi cc h phi tuyn, t c iu ny, ngi ta phi dng phng php tuyn tnhha tng on).

Gi s c h thng iu khin tc motor DC nh hnh v 5.2 [4]. Trong :

J = 0.01 kgm2/s2 l moment qun tnh ca rotor

b = 0.1 Nms h s ma st

K=Ke=Kt=0.01 Nm/Amp cc hng s sc in ng

R = 1 ohm in tr

L = 0.5 H in cm

I: dng in chy trong cun dy ca motor

V: in p trn hai u cun dy motor ng vo

: v tr trc ng ra

Hnh 5.2 M hnh ton mt h iu khin tc motor DC


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http://www.engin.umich.edu/group/ctmhttp://www.shu.ac.uk/schools/eng/teaching/rw/pidtutorial.htm

Phng trnh vi phn m t h thng nh sau:

Jd2

dt2+ bddt = Ki

Ldidt + Ri = V Kddt

1. Hm truyn: Bin i Laplace 2 v ca phng trnh trn ta c:

s(Js+b)(s) = KI(s)(Ls+R)I(s) = V Ks(s)

Suy ra: [(Ls+R)(Js+b) + K2]s = KV hay V = K(Ls+R)(Js+b) + K2

Biu din hm truyn ny trong Matlab ta thc hin nh sau (sinh vin nn lu thnhfile.m):

>>J=0.01;

>>b=0.1;

>>K=0.01;

>>R=1;

>>L=0.5;

>>num=K; % t s ca hm truyn

>>den=[(J*L) ((J*R)+(L*b)) ((b*R)+K^2)]; % mu s hm truyn

>>hamtruyen = tf(num,den)

p ng bc vng h:

>>step(num,den) % hoac

>>step(hamtruyen)


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p ng xung vng h:

>>impulse(hamtruyen)

2. Phng trnh trng thi: Dng tng qut:

X = AX + BU

Y = CX+DU

vi X l vct trng thi, U l vct tn hiu vo v Y l vct tn hiu ra.

Bin trng thi v phng trnh trng thi: T phng trnh vi phn m t hthng, nu t x1 = v x2 = i, ta c:


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Biu din phng trnh trng thi trong Matlab nh sau:

>>J=0.01;

>>b=0.1;

>>K=0.01;

>>R=1;

>>L=0.5;

>>A = [-b/J K/J; -K/L -R/L];

>>B = [0; 1/L];

>>C=[1 0];

>>D=0;

p ng bc vng h:

>>step(A,B,C,D)

p ng xung vng h:

>>impulse(A,B,C,D)

3. Ta c th chuyn i qua li gia hm truyn v phng trnh trng thi bng lnhsau:

>>[num,den]=ss2tf(A,B,C,D) % t PT trng thi sang hm truyn

>>[A,B,C,D]=tf2ss(num,den) % t hm truyn sang PT trng thi

4. Kho st p ng vng h ca h thng i vi tn hiu bt k


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(Hnh 5.3)

Phi m bo rng trong Workspace cn bin hamtruyen ca cu 1, sinh vin c thdng lnh lsim kho st p ng ca h i vi tn hiu bt k. Gi s l tn hiusin:

>>close all

>>t=0:0.1:2*pi;

>>u=sin(pi/4*t);

>>lsim(hamtruyen,u,t) % mo phong dap ung voi tin hieu vao u

B iu khin PID

Cu trc mt h thng iu khin PID nh hnh sau:

Hnh 5.4 S khi h iu khin PID

Trong hm truyn ca khu PID l: KP +KIs + KDs =

KDs2 + KPs + KI

s

vi: KP l li ca khu t l (Proportional gain)


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KI l li ca khu tch phn (Integral gain)

KD l li khu vi phn (Derivative gain)

Vic hiu chnh ph hp 3 thng s KP, KI v KD s lm tng cht lng iu khin.nh hng ca 3 thng s ny ln h thng nh sau:

1. B iu khin t l P:

Hnh 5.5 B iu khin t l P

Thc hin trong Matlab: Ta c hm truyn ca motor DC nh III.1.1:

>>J=0.01;

>>b=0.1;


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>>K=0.01;

>>R=1;

>>L=0.5;

>>num=K;

>>den=[(J*L) ((J*R)+(L*b)) ((b*R)+K^2)];

Khi thm vo khu t l P, ta c hm truyn vng h:

>>Kp=100;

>>numa=Kp*num;

>>dena=den;

Xc nh hm truyn vng kn ca h thng ta dng lnh cloop:

>>[numac,denac]=cloop(numa,dena)

p ng Step vng kn ca b iu khin t l nh sau:

>>t=0:0.01:2;

>>step(numac,denac)


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Sinh vin hy so snh vi p ng ca h khi cha c b iu khin t l, cuIII.1.1 (lu n cc thng s: thi gian ln, vt l, thi gian qu ).

Tng t, sinh vin hy so snh vi p ng xung.

2. B iu khin Vi tch phn t l PID:

Hnh 5.6 B iu khin PID

Khi thm b iu khin PID, hm truyn h ca h thng l:

>>Kp=100;

>>Ki=1;

>>Kd=1;

>>numc=[Kd, Kp, Ki];

>>denc=[1 0];

>>numa=conv(num,numc); % tch chp t s


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>>dena=conv(den,denc); % tch chp mu s

Hm truyn vng kn hi tip m n v:

>>[numac,denac]=cloop(numa,dena);

p ng Step ca h iu khin PID:

>>step(numac,denac)

Sinh vin so snh vi p ng ca b iu khin t l P cu 1, nhn xt. Da vo bng tng kt nh hng ca KP, KD v KI i vi h thng iu

khin, sinh vin hy thay i 3 thng s ny v kim chng p ng ca hthng.

Hiu chnh thng s ca b iu khin PID

Mt phng php c in nhng n gin v hiu qu chnh nh 3 thng s KP, KIv KD ca b iu khin PID l phng php Ziegler-Nichols (Ziegler Nichols TuningMethod). Th tc chnh nh nh sau:

1. Ch iu khin h thng bng b iu khin t l KP (t KI=KD=0).

2. Tng KP n gi tr KC m h thng bt u bt n (bt u xut hin s giaong - im cc ca hm truyn kn nm trn trc o j). Xc nh tn s c ca giaong va t.

T 2 gi tr KC v c va t, cc thng s s KP, KI v KD c xc nh nh bngsau:


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3. Tinh chnh li 3 thng s ny t c p ng nh mong mun.

1. V d: Gi s cn thit k b iu khin PID cho h thng sau:

Bc 1: iu khin h thng ch vi b iu khin t l:

Bc 2: Xc nh KC v c m h thng bt u giao ng - dng hmrlocus ca Matlab (sinh vin nn lu thnh file .m hoc thao tc trong MatlabEditor sau copy v dn vo Workspace c on lnh d dng cho vichiu chnh cc thng s phn sau):

>>close all

>>num=5;

>>den=[1 10 100 0];

>>[numc,denc]=cloop(num,den);

>>htkin=tf(numc,denc) % ham truyen vong kin

>>rlocus(htkin); %ve qui dao nghiem

>> axis([-10 10 -15 15])


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Xc nh Kc v c bng hm rlocfind:

>>[Kc,Omegac] = rlocfind(htkin)

Nhp chut vo im giao nhau gia qu o nghim v trc o ca th, trongWorkSpace ta c:

Kc =

199.5793

Omegac =

-10.0145

0.0072 +10.0072i

0.0072 - 10.0072i

Nh vy ta c KC=200 v c = 10. Suy ra thng s ca b iu khin PID:

KP = 0.6KC = 120

KI = 0.318KPc = 381.6

KD = 0.785KP/c = 9.4

Th p ng ca h:

>>Kp=120; Ki=381.5; Kd=9.4;


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>>numc=[Kd, Kp, Ki];

>>denc=[1 0]; % ham truyen cua PID

>>[numac,denac]=cloop(conv(num,numc),conv(den,denc))

>>step(numac,denac)

Bc 3: Thc hin tng t nh III.2.2, sinh vin hy iu chnh mt lngnh 3 thng s KP, KD v KI c p ng tt hn.

2. Sinh vin hy thit k b iu khin PID cho h thng sau:

T CHN

1. Sinh vin hy thit k b iu khin Vi phn t l (Proportional-Derivative controller):

2. Sinh vin hy thit k b iu khin Tch phn t l (Proportional-Integral controller):


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M hnh h thng iu khin t ngM HNH H THNG IU KHIN T NGMC TIUTHAM KHOTHC HNHHm truyn v phng trnh trng thi ca h thngB iu khin PIDHiu chnh thng s ca b iu khin PID

T CHN

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