Symbolic v SimulinkBi:

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SYMBOLIC V SIMULINK

MC TIU

Hiu mt cch c bn v hai cng c mnh v hu hiu ca Matlab, l Symbolic vSimulink, t sinh vin c th t mnh pht huy cc chc nng cao hn ca haicng c ny trong tnh ton v m phng h thng.

THAM KHO

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

[2]. Nguyn Hoi Sn - Thanh Vit - Bi Xun Lm, ng dng MATLAB trongtnh ton k thut, Tp 1, NXB HQG Tp. HCM, 2000

[3]. Nguyn Ch Ngn, Bi th nghim K thut m phng trong iu khin t ng, Bmn Vin Thng & T ng ha, khoa Cng ngh thng tin, i hc Cn th, 2002.

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

[5]. http://www-h.eng.cam.ac.uk/help/tpl/programs/Matlab/Symbolic.html

THC HNH

Symbolic v Simulink u cha th vin chc nng rt phong ph, bi th nghim nych c th cp n nhng g gi l c bn nht. T , sinh vin c th t mnh nghincu v pht trin tip.

Symbolic

Phin bn mi nht ca Symbolic toolbox c Mathworks gii thiu trong Matlab 6.5vo thng 6-2003. l mt th vin ton hc kiu k t, c pht trin t Symbolic

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Maple ca trng i hc Waterloo, Canada. c ci nhn tng qut v cc chc nngca Symbolic, sinh vin hy g:

>>help symbolic

Mt s hm thng dng ca Symbolic:

Tn hm Chc nng Tn hm Chc nng

diff o hm fourier Bin i Fourier

int Tch phn ifourier Bin i Fourier ngc

taylor Khai trin Taylor laplace Bin i Laplace

det nh thc ca ma trn laplace Bin i Laplace ngc

numden T v mu ca phn s ezplot V hm, ? plot

subs Thay bin sym bng tr s ezpolar V hm, ta cc ? polar

dsolve Gii phng trnh vi phn ezmesh V mt li ? mesh

solve Gii phng trnh i s ezsurf V mt ? surf

bin i mt s, mt bin hay mt i tng no thnh kiu Symbolic ta c ths dng mt trong cc cch sau:

>>s=sym(A)

>>x=sym(x)

>>syms x y z % khai bo kt hp x, y v z l bin symbolic

1. Tnh o hm bng hm diff ca symbolic: Nu S l biu thc symbolic th:

diff(S) o hm ca S theo bin t do

diff(S,v) o hm ca S theo bin v

diff(S,v,n) o hm cp n ca S theo v.

V d: Tnh o hm ca y = sinx3.

>> syms x % khai bao x la bien kieu symbolic

>> y=sin(x^3);

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>> z=diff(y) % dao ham cua y

z =

3*cos(x^3)*x^2 % sinh vien kiem tra ket qua

>>pretty(z) % hien thi dang quen thuoc

3 cos(x3) x2

>>ezplot(x,y) % ve y theo x

Hnh 3.1 V th hm symbolic

2. Tnh vi phn bng hm int - Nu S l biu thc Symbolic th:

int(S) tch phn khng xc nh ca S theo bin mc nhin (mun bit bin mc nhinny ta dng hm findsym).

int(S,v) tch phn khng xc nh ca S theo v.

int(S,a,b) tch phn xc nh ca S trn cn [a,b]

int(S,v,a,b) tch phn xc nh ca S theo v trn cn [a,b]

V d: Tnh10

2x2(19+12x2)7(x2 + 1)

dx

>>syms x

>>S=2*x^2*(19+12*x^2)/(7*(x^2+1))

>>y=int(S,x,0,1) % tch phn S theo x trn cn [0,1]

>>subs(y) % i sang kiu s

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3. Gii h phng trnh bng hm solve:

>>help solve

>>syms x y

>>[x,y]= solve('x^2*sin(x^2)-3*y=7','x+y=1')

Sau khi thu c nghim x v y, sinh vin hy thay vo 2 phng trnh trn v nhn xtkt qu.

4. V mt 3D bng hm ezsurf: V d v mt S = f(x,y) = y1 + x2 + y2

trn min xc nh:-5S=y/(1+x^2+y^2)

>>ezsurf(S, [-5 5 2*pi 2*pi])

Hnh 3.2 V th 3D cho hm s symbolic

Simulink

Simulink 5.0 (Simulation and Link - R13) c MatWorks gii thiu vo thng 6 nm2003. N cho php phn tch, m hnh ha v m phng cc h thng ng tuyn tnhv phi tuyn, lin tc v ri rc mt cch trc quan trong mi trng giao tip ha,bng cc thao tc chut n gin. C th ni, khng tn dng c Simulink l mt thitthi ln cho ngi lm cng tc m phng!

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Khi ng Simulink bng mt trong cc cch sau:

nhp: >>simulink

hoc nhp chut vo

trn menubar ca Matlab

Th vin simulink hin ra nh hnh 3.3:

Trc tin, sinh vin hy nhp chut vo cc thanh cun ca th vin c ci nhnthn thin v simulink.

T y, c th to m hnh bng simulink, hy:

nhp chut vo biu tng

ca th vin simulink chn: File New Model trong Menu ca th vin Simulink chn: File New Model trong ca s lnh ca Matlab

Hnh 3.3 Ca s chnh ca th vin Simulink

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Hnh 3.4 Mi trng son tho ca Simulink

Ca s ny (hnh 3.4) cho php ta nhp - ko - th vo tng khi chc nng trong thvin simulink. V d, t vo y khi Sine Wave trong th vin

ca

(hnh 3.5):

Hnh 3.5 Ly mt khi t th vin

Sau khi t tt c cc khi cn thit ca m hnh, ta ni chng li bng cch nhp - giv ko mt ng t ng ra ca khi ny n ng vo ca khi khc ri th phm trichut, mt kt ni s c thit lp.

1. Xy dng m hnh h thng xe ti:

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Hnh 3.6 M hnh xe ti

cho bi phng trnh: mdvdt = u bv haydvdt =

1m (u bv).

Trong m l khi lng xe, u l lc tc ng ca ng c (ng vo ca m hnh), b lh s ma st v v l vn tc t c (ng ra ca m hnh).

Xut pht im ca vic xy dng cc m hnh h thng t cc phng trnh vi phntng ng l cc khi tch phn (Integrator). Nu trong phng trnh m t h thng cvi phn bc n th ta s t vo m hnh n khi tch phn, do quan h dvdt = v.

M mt ca s m hnh mi. t vo m hnh khi Integrator t th vin Continuous v k cc ng

thng ni n ng vo v ng ra ca khi ny. t nhn vdot (dv/dt) cho cho ng ni n ng vo v v cho ng ni

n ng ra bng cch nhp p chut ngay pha trn cc ng ny.

T phng trnh h thng ta thy dv/dt (vdot) bng tch ca thnh phn (1/m) v thnhphn tng (u-bv), nn ta thm khi 1/m ngay trc khi tch phn:

t vo khi Gain trong th vin

. Nhp p chut vo khi ny thay i li thnh 1/m. t nhn inertia cho khi ny tng trng cho qun tnh ca xe (nhp p

vo nhn Gain bn di khi).

By gi ta t khi tng vi 2 ng vo +-, ng vo + s c ni vi u, ng vo -s c ni vi thnh phn bv c (u-bv)

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t vo khi Sum trong th vin

Nhp p vo khi ny i ng vo t ++ sang +-

c thnh phn bv ta ch cn t thm khi Gain vi li b:

t khi Gain c li b t nhn l damping tng trng cho thnh phn lc cn ca xe.

n y vic xy dng m hnh xe ti vi ng vo u v ng ra v coi nh hon thnh.Tuy nhin, m phng m hnh ny, ta cn t thm khi Step vo u v hin th vtrn khi Scope

t khi Step trong th vin

bin u ngay ng vo. t khi Scope trong th vin

ngay ng ra v.

Nh rng m, b v u l cc bin cn c gn tr trc khi m phng.

>>m=1000

>>b=50

>>u=500

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Thi gian m phng h thng ty thuc vo thng s Stop time trong menuSimulationSimulation paramrters,gi s t 120 (Hnh 3.7).

chy m phng, ta c th thc hin bng 1 trong cc cch:

nhp chut vo biu tng

trn menubar ca m hnh chn: Simulation Start Ctrl-T

Nhp p vo Scope xem kt qu m phng.

Hnh 3.7 Thay i thng s m phng

2. Xy dng m hnh h thng iu khin v tr motor DC cho bi phng trnh vi phnsau:

d2dt2

= 1J (Kti bddt )didt =

1L ( Ri + V Ke ddt )

Trong :

J = 0.01 Kgm2/s2l moment qun tn ca rotor

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b = 0.1 Mms l h s ma st ca cc b phn c kh

K = Ke = Kt = 0.01 Nm/A l hng s sc in ng

R = 10 ohm l in tr dy qun

L = 0.5 H l h s t cm

V l in p t ln cun dy ca motor

l v tr trc quay (ng ra ca m hnh)

i l dng in chy trong cun dy ca motor.

Hnh 3.8 M hnh ton h iu khin v tr motor DC

Quan st tng phng trnh m t h thng ta thy cu trc ca chng cng tng tnh phng trnh ca cu ?. Sinh vin ln lt thc hin trn tng phng trnh c(hnh 3.9):

(Hnh 3.9)

Kt hp 2 phng trnh:

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(Hnh 3.10)

t vo m hnh khi Step lm tn hiu tham kho, khi Scope quan st png. Sinh vin hy gn tr cho tt c cc thng s ca m hnh, thc hin m phng vquan st p ng (Hnh 3.11).

Hy thay i ng vo m hnh bng khi to xung vung. M phng, quan st kt quv nhn xt.

T CHN

1. Sinh vin hy tnh o hm cp 2 ca hm y = xe(1 x2) bng tay v kim chng ktqu bng symbolic.

3. Tnh tch phn sau v kim chng kt qu bng symbolic:0

e x2

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Hnh 3.11 - M hnh Simulink hon chnh ca h iu khin v tr motor DC

3. Xy dng m hnh h thng xe la cho bi phng trnh:

M1d2x1dt2

= F k(x1 x2) M1gdx1dt

M2d2x2dt2

= k(x1 x2) M2gdx2dt

(Hnh 3.12 Photo courtesy: Dr. Howard Blackburn)

Trong cc thng s tng trng nh sau:

M1=1 kg l khi lng toa ko;

M2=0.5 kg l khi lng toa khch;

k=1 N/sec l cng l xo kt ni gia 2 toa;

F=1 N l lc tc ng ca u my (ng vo m hnh);

=0.002 sec/m l h s ma st ln;

g = 9.8 m/s^2 l gia tc trng trng

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x1, x2 v tr 2 toa (ng ra).

Hnh 3.13 M hnh ton ca h thng xe la

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Symbolic v SimulinkSYMBOLIC V SIMULINKMC TIUTHAM KHOTHC HNHSymbolicSimulink

T CHN