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Применение метода частотных диаграмм в исследовании устойчивости систем с логическими алгоритмами управления

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Iineianeee Ainoaea?noaaiiue Oaoie/aneee Oieaa?neoao ei. I.Y. Aaoiaia

Eo?niaay ?aaioa ii eo?no “Iaeeiaeiua NAO”

ia

oaio:

I?eiaiaiea iaoiaea /anoioiuo e?oaiauo aeeaa?aii e enneaaeiaaieth
onoie/eainoe nenoai n eiae/aneeie aeai?eoiaie oi?aaeaiey.

Auiieiee: no-o a?. AE4-81

Niue A.E.

?oeiaiaeeoaeue: i?ioanni?

Oaaa?ia A.N.

?aooia 1997 a.

I?eiaiaiea iaoiaea /anoioiuo e?oaiauo aeeaa?aii e enneaaeiaaieth
onoie/eainoe nenoai n eiae/aneeie aeai?eoiaie oi?aaeaiey.

Ia ?aiiae noaaeee ?acaeoey oai?ee aaoiiaoe/aneiai ?aaoee?iaaiey
o?aaiaaiea onoie/eainoe ?aaiou nenoaiu auei ia?aui e iau/ii
aaeeinoaaiiui e niaea?aeaiea aieueoeinoaa oai?aoe/aneeo enneaaeiaaiee
naiaeeeinue e eneaaeiaaieth onoie/eainoe.

“Oa?iei “onoie/eainoue” ianoieueei au?aceoaeai, /oi ii nai ca naay
aiai?eo”,-ioia/atho a ia/aea eceiaeaiey oai?ee onoie/eainoe AE. Ea
Naeeue e N. Eaooaoe [1]. Yoi aiieia ni?aaaaeeeai, ii, ianiio?y ia yoi,
iaoi/iinoe e iaeiae/iinoe iiaeii ano?aoeoue eae ?ac ia a iaoaiaoe/aneeo,
a a niuneiauo iiiyoeyo e oa?ieiao.

Onoie/eainoueth ethaiai yaeaiey a iaeoiaea iacuaath aai niiniaiinoue
aeinoaoi/ii aeeeoaeueii e n aeinoaoi/iie oi/iinoueth nio?iiyoue oa oi?iu
naiaai nouanoaiaaiey, i?e oo?aoa eioi?uo yaeaiea ia?anoaao auoue naiei
naaie. Iaeiaei ia oieueei a iaeoiaea, ii e a iao/iie oa?ieiaeiaee
onoie/eaui iacuaatho ia yaeaiea, a nenoaio, a ei?ie iii iaaethaeaaony,
oioy yoi ia ii?aaaeuaaao eiae/anee. Onoie/eau ee oece/aneea oaea – oa?
eee eoa? Oaeie aii?in aoaeao eiaoue niune, anee ?a/ue eaeao i iaoa?eaea,
ec eioi?iai iie naeaeaiu. (Iaoaeee/aneee oa?

onoie/ea, oa? ec aeuia iao.) Oai?eth oi?aaeaiey eioa?anoao, iaeiaei, ia
yoa i?i/ianiay onoie/eainoue. Iiae?acoiaaaaony, /oi nenoaia oi?aaeaiey
eae eiaeaia?iay eiino?oeoeey caaaaeiia onoie/eaa, e a oai?ee eco/aaony
onoie/eainoue ia naiie nenoaiu, a aa ninoiyiee e ooieoeeiie?iaaiey. A
iaeiie e oie aea nenoaia iaeie ninoiyiey eee aeaeaeaiey iiaoo auoue
onoie/eauie, a ae?oaea ia onoie/eauie. Aieaa oiai, iaeii e oi aea
aeaeaeaiea iiaeao auoue onoie/eaui ioiineoaeueii iaeiie ia?aiaiiie e
iaonoieoeeaui ioiineoaeueii ae?oaie – yoi ioia/ae aua A.I. Eyioiia [2].
A?auaiea ?ioi?a oo?aeiu onoie/eai ii ioiioaieth e oaeiaie nei?inoe e
iaonoie/eai ioiineoaeueii oaea iiai?ioa aaea. Aeaeaeaiea ?aeaou
onoie/eai ioiineoaeueii o?aaeoi?ee e iaonoie/eai ii ioiioaieth e
iaiiaeaeaeiie nenoaia eii?aeeiao. Iiyoiio ioaeii iaiaa?eaaoue,
onoie/eainoue eaeiai ninoiyiey eee aeaeaeaiey a nenoaia e ioiineoaeueii
eaeeo ia?aiaiiuo eco/aaony. Oae aea anoue iiiai iaoiaeia aeey ioeaiee
naiie onoie/eainoe. Iu ?anniio?ei eae iiaeii ioeaieoue onoie/eainoue
nenoaiu n eiae/aneei aeai?eoiii oi?aaeaiey iaoiaeii e?oaiauo aeeaa?aii.

?anniio?ei oai?aoe/aneoth /anoue e iiniio?ei /oi ec naay i?aaenoaaeyao
e?oaiaie e?eoa?ee. Ionoue aeaia nenoaia

.

x=Ax+b(, (=c’x, (1)

nenoaia (1), aeiiieiaiay niioiioaieai (((((, aneiioioe/anee onie/eaa.

) iaeeiaeiinoae (((((,t), oaeiaeaoai?ythueo oneiaeth

(2)

aeinoaoi/ii, /oiau i?e anao (( (((((((( auiieiyeinue niioiioaiea

W(j()]}>0. (3)

((( Aeaenoaeoaeueii, eae auei iieacaii auoa, oi?ia F(j((() eiaao aeae

neaaeoao (3).

((( ?anniao?eaaaony aiaeiae/ii.

E?oaiaie e?eoa?ee i?aaenoaaeyao niaie ?ani?ino?aiaiea eeiaeiuo
/anoioiuo e?eoa?eaa onoie/eainoe Iaeeaenoa, Ieoaeeiaa e ae?oaeo ia
eeiaeiua nenoaiu n iaeiei eeiaeiui eee iaeeiaeiui, noaoeeiia?iui eee
ianoaoeeiia?iui aeieii. Ii iieo/aaony ec (3), anee aianoi ia?aaeaoi/iie
iao?eoeu eniieueciaaoue /anoioioth oa?aeoa?enoeeo eeiaeiie /anoe W(j().

Iaicia/ay eiiieaenioth ia?aiaiioth W(j()=z, ?anniio?ei nenoaio n
iaeiie iaeeiaeiinoueth, oaeiaeaoai?ythuae iaeiiio ec neaaeothueo
oneiaee:

(((( (4)

(((( (5)

(((( (6)

) a ieineinoe (( (. Oai aea ecia?aaeaiu e?eaua W(j(), (>0 aeey
iainiaiai neo/ay, ?aniieiaeaiiua oae, /oi aiciiaeia aaniethoiay
onoie/eainoue. Iaeiaei oieueei i?eaieeiiai ?aniieiaeaiey oaiaeoa?enoee
W(j() aua iaaeinoaoi/ii aeey noaeaeaiey ia aaniethoiie onoie/eainoe :
e?iia yoiai, ioaeii aua iio?aaiaaoue, /oiau eeiaeiay caieiooiy nenoaia
auea aneiioioe/anee onoie/eaie.

E?oaiaie e?eoa?ee iaania/eaaao oaeaea aaniethoioth onoie/eainoue aeey
nenoaiu n ethaui aeieii, aoiae ( e auoiae ( eioi?iai oaeiaeaoai?ytho
aeey anao t ia?aaainoao

()(0 (7)

?enoiie 1, a.

?anniio?ei nenoaio, i?eaaaeaiioth ia ?en. 2.

(P) Z

(-)

G(p) g

?enoiie 2.

(p) – iia?aoi? eeiaeiie /anoe nenoaiu, eioi?ay iiaeao eiaoue a iauai
neo/aa neaaeouee aeae:

;

(8)

;

Aeai?eoi ?aaoeyoi?a eiaao aeae:

x,

i?e gx>0

= (9)

i?e gx0

=

0,

niioaaonoaiaae e?eoa?eth Iaeeaenoa.

Aeey enneaaeoaiie nenoaiu oneiaea (3) oaeiaiaa caienaoue a aeaea

(4) e (5).

) e aiaeia?aou W(j(), ?aniieiaeaiiua oaeei ia?acii, /oi niaeanii (4) e
(5) aiciiaeia aaniethoiay onoie/eainoue.

y ^

)

>

0

“a” “a”

“a” “a”

?enoiie 4.

A ?anniao?eaaaiii neo/aa (10) i?e

, eiaaea

p+1,

aiaeia?ao W(j() nenoaiu ia ?en. 5.

j

W(j()

(((

(=0

?enoiie 5.

A neo/aa (10) ni?aaaaeeeau a?aoe/aneea oi?iu ia ?en. 4 a,a, o.a.
enneaaeoaiay nenoaia aaniethoii onoie/eaa a niunea e?oaiaiai e?eoa?ey
(3) eee (5) i?e

(14)

Eioa?anii caiaoeoue, /oi aeinoaoi/iua oneiaey aaniethoiie onoie/eainoe
ii Eyioiiao

a > 0 , ((t) > 0

e

a > c

aeey ?anniao?eaaaiiai neo/ay niaiaaeatho n aeinoaoi/iuie oneiaeyie
aaniethoiie onoie/eainoe, iieo/aiiuie aeey e?oaiaiai e?eoa?ey (14), anee
auiieiyaony o?aaiaaiea

((t) > 0 (15)

.

Aeieaaeai yoi, eniieuecoy oneiaey nouanoaiaaiey neieuecyuaai ?aaeeia

k

o.a. iiaenoaaei nthaea aianoi eiyoeoeeaioia a,n, e k eo au?aaeaiey /a?ac

, oiaaea iieo/ei

(16)

Niaeanii ?en. 5 e oneiaey (16) iieo/aai:

, ((t)=0

, ((t)>0

, ((t)

#include

#include

#include

#include

#include

#include

#include

void Godograf(float Tpr, float Ko, float Kos, int Color,

int Xc, int Yc, int x, int y, int z, int err);

void Osi(int Xc, int Yc, int kol);

int xmax, ymax;

float Kos[]={0.1,1.0},

Ko[] ={10.0,100.0},

Tpr[]={0.01,0.09,0.2,0.5};

void main(void)

{

float P_w, Q_w, w;

int driver, mode, err;

driver = DETECT;

initgraph(&driver,&mode,””);

err = graphresult();

if (err!=grOk) {coutabs(P_w1)) P_w1=P_w;

if (abs(Q_w)>abs(Q_w1)) Q_w1=Q_w;

if (P_w=220) KmasX=150;

if (KmasY>=140) KmasY=100;

if (err==0) {KmasX=KmasX*4; KmasY=KmasY*4;};

w = 0;

if(((Kos*Ko-(To+Tpr)*w*w)*(Kos*Ko-(To+Tpr)*w*w)+

(w+Tpr*Kos*Ko*w-To*Tpr*w*w*w)*(w+Tpr*Kos*Ko*w-To*Tpr*w*w*w))!=0){

P_w = KmasX*(Ko*w*Tg*(w+Tpr*Kos*Ko*w-To*Tpr*w*w*w)+

(Kos*Ko*Ko-(To+Tpr)*Ko*w*w))/

((Kos*Ko-(To+Tpr)*w*w)*(Kos*Ko-(To+Tpr)*w*w)+

(w+Tpr*Kos*Ko*w-To*Tpr*w*w*w)*(w+Tpr*Kos*Ko*w-To*Tpr*w*w*w));

Q_w = KmasY*(Tg*(Kos*Ko*Ko*w-(To+Tpr)*Ko*w*w)-

Ko*(w+Tpr*Kos*Ko*Ko*w-Ko*To*Tpr*w*w*w))/

((Kos*Ko-(To+Tpr)*w*w)*(Kos*Ko-(To+Tpr)*w*w)+

(w+Tpr*Kos*Ko*w-To*Tpr*w*w*w)*(w+Tpr*Kos*Ko*w-To*Tpr*w*w*w));

moveto(Xc+P_w,Yc-Q_w); };

setcolor(Color);

setcolor(9);

line(Xc+P_w_min*KmasX,10,Xc+P_w_min*KmasX,ymax-10);

gotoxy(2,5);

printf(“K2=”);

printf(“%f”,(-1/P_w_min));

setcolor(15);

for(w=0;w

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