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МІН&= #1030;СТЕРСТВО  ОСВІТИ  ТА  НАУКИ= ;  УКРАЇНИ<= o:p>

&= #1044;ОНЕЦЬКИЙ  ДЕРЖАВНИЙ  ТЕХНІ= ;ЧНИЙ  УНІВЕРСИТh= 5;Т

МАГ&= #1044;ЕБУРГСЬКИЙ= ;  УНІВЕРСИТh= 5;Т  ім. ОТТО-ФОН-ГЕР= 030;КЕ

&= #1044;ЕРЖАВНИЙ  УНІВЕРСИТh= 5;Т  “ЛЬВІ= ;ВСЬКА  ПОЛІТЕХНІi= 0;А”

 

 

 

 

 

 

 

 

&= #1050;алашніков  В.І. , Паліс  Ф. , Лозинськ&= #1080;й  О.Ю.=

<= o:p> 

<= o:p> 

<= o:p> 

<= o:p> 

<= o:p> 

<= o:p> 

<= o:p> 

<= o:p> 

&#= 1054;снови  теорі= ;ї  фази-логік = 80; 

та  фази-регул = 02;вання

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Донец = 00;к , Магдебург , Львів

2= 000

УДК  62-83-52-0313

 

“Ос= 085;ови  теорії  фази-логік = 80;  та  фази-регул = 02;вання”: учбовий  посібник/       Калашнікоk= 4; В.І. , Паліс Ф. , Лозинський О.Ю. - Донецьк,  Магдебург  ,Львіk= 4;, - 2000 - 69с.

&n= bsp;

&n= bsp;

Роз&= #1075;лянуто  основи  теорії   &= #1092;ази-логіки  та  фази-регул = 02;вання  стосовно  впроваджеl= 5;ня  інтелектуk= 2;льних  систем  керування  в  галузі  керованогl= 6;  електропрl= 0;воду.  Учбовий  посібник  спрям= ;овано  на  придбання  студентамl= 0;  навичок  дослі= дження  та  проек= ;тування  подібних  систем  за  допомогою  програмноk= 5;о  пакета  MATLAB / SIMULINK.  Це  дозволяє  без  будь-яких  обмежень  на  лабораторl= 5;е  оснащення  використоk= 4;увати  посібник  як  методичні  матеріали  для  організацo= 0;ї  навча= ;льного  процесу  в  будь-якому  вищому  навчальноl= 4;у  закладі.=

&= #1053;авчальний  посібник  підго= ;товлено  в  рамках  прогр= ;ами  інтеграціo= 1;  вищої= ;  школи= ;  України  в  європейсьl= 2;у  систему  інженерноo= 1;  освіти  і  орієнтоваl= 5;о  на  студентів  спеціальнl= 6;сті  “Електромk= 7;ханічні  системи  автоматизk= 2;ції  та  електропрl= 0;вод”.

&= #1040;втори  виражають  щиру  подяку  студентам, магістрантk= 2;м  та  науковим  співр= ;обітникам  Донецькогl= 6;  техні= ;чного  університk= 7;ту,  Магде= ;бургського  ім.  Отто-фон-Ге= 088;іке  університk= 7;ту  та  Львівськоk= 5;о  університk= 7;ту  “Льві= вська  політехніl= 2;а”, які  допомогалl= 0;  в  підго= ;товці  посібника  та  його  практичніl= 1;  реалізаціo= 1;  в  навчальноl= 4;у  проце= ;сі  вузів-парт = 85;ерів.

<= o:p> 

&= #1050;омп'ютерна верстка Александроk= 4;ої Ю. І.

<= o:p> 

<= o:p> 

<= o:p> 

<= o:p> 

&= #1056;ецензенти:=

Клеп&#= 1110;ков  В.Б. – д.т.н., проф., завідувач  кафедри  “Авто= ;матизовані  електро-ме = 93;анічні  системи”  Харківскоk= 5;о  технічногl= 6;  університk= 7;ту.

 

&= #1050;оцегуб  П.Х. – д.т.н., проф., завідувач  кафедри  “Електропl= 8;ивод  та  автоматизk= 2;ція  проми= ;слових  установок̶= 1;  Донец= ;ького  державногl= 6;  технічногl= 6;  університk= 7;ту.

<= o:p> 

 

З&= #1052;ІСТ

 

= 42;СТУП………………&#= 8230;…………………………= …………………………̷= 0;………..

4

1 ОСНОВИ ТЕОРІЇ ФАЗИ-ЛОГІКИ ТА ФАЗИ-РЕГУЛЮ&#= 1042;АННЯ…………….<= /o:p>

7

1.1 Фази-множин&#= 1080; та основні операції над ними………&#= 8230;…………………….…

7

1.2 Фази-контро&#= 1083;ер……………………= …………………………̷= 0;………………..

13

1.3 Основні етапи проектуван= 085;я фази-контро&#= 1083;ерів………………= ……………….

25

1.4 Типи фази-контро&#= 1083;ерів………………= …………………………̷= 0;…………….

27

1.5 Варіанти побудови контурів регулюванн= 103; із фази-регуля&#= 1090;ором……………..=

29

2 МОДЕЛЮВАНН= 071; СИСТЕМ ФАЗИ-РЕГУЛЮ&#= 1042;АННЯ ЗА ДОПОМОГО&#= 1070; ПРОГРАМНОГ= 054; ПАКЕТА MATLAB/SIMULINK………….…………&= #8230;………

 

34

3 ПРАКТИЧ= НЕ ЗАСТОСУВАН= 053;Я ФАЗИ - ЛОГІКИ В СИСТЕМАХ РЕГУЛЮВАНН= 071;…………………………&= #8230;…………………………= ;……………...

 

44

3.1 Постановка завдання……= 230;…………………………&= #8230;……………………….

44

3.2 Лабораторн= 080;й практикум…= 230;…………………………&= #8230;…………………….<= /span>

48

Лабора&#= 1090;орна робота 1. Використан= 085;я неадаптивн= 086;го фази-регуля&#= 1090;ора в системі автоматиза= 094;ії……………………&= #8230;…………………………= ;………..

 

48

Лабора&#= 1090;орна робота 2. Адаптація фази-логіки в системах регулюванн= 103;…...

59

ЛІТЕРАТ&#= 1059;РА……………………= …………………………̷= 0;………………………..

69


ВСТ= 059;П

 

Давні&= #1084; прагненням людства бул = 86; створення приладів, що були б здатн= 110; полегшl= 0;ти людську працю. Спочатку йшлося про інструментl= 0; та машини, які механізуваl= 3;и тільки фізичну працю, але пізніше постало питання розробки "розумних машин", які ф= 091;нкціонувал&= #1080; б подібно до людського мозку. Така постановка завдання викликає на = 89;тупні принципові питання:=

ü      = чи є взагалі можливим створення машини, здат= 085;ої до інтелектуаl= 3;ьної діяльності;

ü      = чим характеризm= 1;ється інтелектуаl= 3;ьність людини та на чому вона ґрунтуєтьсn= 3;;

ü      = які = 075;оловні принципи мають лягти = 074; основі так з= 074;аного "штучного інтелекту".

Спо= 095;атку треба пояснити, що означає поняття "інтелектуа= ;льність" стосовно до людини. Інтелектуаl= 3;ьність (розумність) у такому контексті можна визначити я = 82; наявність комплексноo= 1; когнітивноo= 1; здатності, з= 072; допомогою я = 82;ої людина впізнає об'єкти, явища та відповідно до ситуації на них реагує. Сере= 076; типових характерниm= 3; рис інтелектуаl= 3;ьності слід зазнач = 80;ти такі:

<= ![if !supportLists]>ü     усвідо= ;млення ситуації, виходячи із багатозначl= 5;ої або суперечливl= 6;ї інформації;

<= ![if !supportLists]>ü     знаход= ;ження аналогій, здатність д = 86; класифікацo= 0;ї;

<= ![if !supportLists]>ü     здатні= ;сть до вивчення нових понят = 00; та встановл = 77;ння зв'язків між різними поняттями.=

Зав= 076;анням теорії штучного інтелекту я = 82; області прикладної математики = 08; знаходженнn= 3; засобів формалізацo= 0;ї процесів усвідомленl= 5;я та пізнавання та переніс ї= 093; на мову алгоритмів. При цьому розумова діяльність постає як засіб обробки інформації. Це означає, що теорія штучного інтелекту виходить з того, що діяльність людського розуму в певній мірі може бути розглянута незалежно від функцій мозку, тобто достатньо знати основ = 85;і принципи розумної поведінки, щоб записат = 80; їх у вигляді алгоритмів, зрозумілих для комп'юте= 088;а. Таким чином, інженерно-н = 72;уковий аспект теорії штучного інтелекту полягає в пр= 086;ектуванні складних систем обробки інф = 86;рмації. Це завдання включає в себе розроб = 82;у як методів обробки інформації, так і відпов= 110;дних пристроїв т = 72; програмногl= 6; забезпеченl= 5;я.

В даний час можна виділити чотири напрямки розвитку комп'ютерно = 75;о інтелекту:=

ü      = фази-лl= 6;гіка;

ü      = експер= ;тні системи;

ü      = нейрос= ;ітки;

ü      = еволюц= ;ійне моделюваннn= 3;.

Пер= 077;д теорією штучного інтелекту стоїть завд = 72;ння створення комп'ютерни = 93; систем, які були б здатн= 110; вирішувати такі задачі:

<= ![if !supportLists]>1.     . Розв'язання знаходитьсn= 3; шляхом зведення на = 03;вної інформації до відомих елементарнl= 0;х висловлень та пошуку в базі знань необхідної інформації;

<= ![if !supportLists]>2.     ;

<= ![if !supportLists]>3.     , тобто впізнаваннn= 3; із візуальної інформації окремих об'єктів та груп об'єктів. Цей процес вимагає класифікацo= 0;ї об'єктів за певними характерниl= 4;и ознаками;=

<= ![if !supportLists]>4.     . Знанн = 03; має автоматичнl= 6; накопичуваm= 0;ись з метою покращення властивостk= 7;й системи;

<= ![if !supportLists]>5.     . Специфічні для певної області знання мают = 00; бути збережені т = 72; оброблені комп'ютером таким чином, щоб система могла самостійно приймати рішення, подібно спеціалістm= 1; з цієї галузі;

<= ![if !supportLists]>6.     . Ця область застосовуєm= 0;ься при аналізі процесів, як= 110; мають не чіт= 082;ий кількісний, = 072; якісний опи = 89;.

Ви= 088;ішення першого, четвертого та шостого з= 072;вдань тісно пов'язане із фази-логіко = 02;. Фази-логіка використовm= 1;ється в інформати = 94;і, техніці регулюваннn= 3; та математиці для моделюв = 72;ння експертногl= 6; знання та вирішення задач автом = 72;тизації. Експертні знання при цьому предс = 90;авляються у формі якщо...то-пр&#= 1072;вил із якісними поняттями, такими, як велика, маленька. Застосуванl= 5;я такого методу обробки інф = 86;рмації є доцільним при створенні систем регу = 83;ювання для об'єктів, які описуються через велик = 91; кількість параметрів (особливо якщо ці параметри змінюються за нелінійнимl= 0; законами) і мають досит = 00; складну математичнm= 1; модель.

Слід зазначити, щ= 086; фази-логіка була взята і= 085;женерами на “озброєння̶= 1; ще в сімдеся= 090;і роки. Звичайно, що сьогодні вона не відп= 086;відає сучасним вимогам, які ставляться до систем програмногl= 6; керування, і тому застос = 91;вання її у “чистом= 091; вигляді” є дуже рідкіс = 85;им. Удосконалиm= 0;и фази–логікm= 1;, зробити її спроможною до адаптаці = 11; в системах р= 077;гулювання були покликані інші типи штучного ін = 90;електу. Насамперед це нейросітки, експертні системи та еволюційні методи.

Дані методичні вказівки містять основи теор = 10;ї фаззи-логік = 80; та фаззи-регул = 02;вання, огляд засобів побудови на її основі фаззи-регул = 03;торів, основних типів контурів регулюваннn= 3; із фази-конт= 088;олером. Практичномm= 1; застосуванl= 5;ю фази-логіки = 074; системах автоматизаm= 4;ії присвячені дві лабораторнo= 0; роботи.

  &nbs= p;    оператори, що пов'язуют= 100; фази-множин = 80; єдиної базової множини;

ü  &nbs= p;    оператори, що обробляють фази-множин = 80; окремих базових множин.

<= /sub>

=  

<= !--[if gte mso 9]>

Трикут&#= 1085;а

= <= /sub>

<= !--[if gte mso 9]>

Трапец&#= 1110;єподібна

=  

= <= /sub>

<= !--[if gte mso 9]>

Прямок&#= 1091;тна

=  

= <= /sub>

<= !--[if gte mso 9]>

= 060;ункція Гауса

=  

=  

= <= /sub>

<= !--[if gte mso 9]>

= 057;инглетон-фу= нкція

=  

=  

= <= /sub>

<= !--[if gte mso 9]>

 

 

 

В першій груп = 10; операцій із фази-множин = 72;ми виділяють три основни = 93; операції:=

ü  &nbs= p;    І. Реалізує перетин фази-множин. Перетин фаз = 80;-множин A1ÇA2 визначаєтьl= 9;я таким чином:

ü  &nbs= p;  АБО. Реалізує поєднання фази-множин. Поєднання двох фази-множин A1ÈA2 визначаєтьl= 9;я таким чином:

ü  &nbs= p;    НІ. Реалізує логічне запереченнn= 3; фази-множин = 80;. Логічне запереченнn= 3; Ø= A фази-множин = 80; ­A визначаєтьl= 9;я таким чином:

На рис. 1.1 подається графічне зображення поданих вищ = 77; визначень. Логічні операції на = 76; фази-множин = 72;ми можуть бути розглянуті = 03;к узагальненl= 5;я класичних операцій на = 76; множинами.=

Рисун= ;ок 1.1 – Операції із фази-множ= 080;нами

 

В процесі подальшого розвитку фази-логіки були визначені також інші оператори для фази-мно= 078;ин. Ці оператор = 80; розрізняютn= 0;ся загальновжl= 0;ваністю, сумісністю та насампер = 77;д ступенем вірогідносm= 0;і, що змінюєть = 89;я в межах від інтуїтивно аргументовk= 2;них до аксіомат = 80;чно обґрунтоваl= 5;их визначень. Розрізняютn= 0; два основни = 93; класи таких операторів:

ü  &nbs= p;    Т-норми, що використовm= 1;ються для моделюв = 72;ння перетину фази-множин;

ü  &nbs= p;    Т-Со-норми (також інкол= 080; позначаютьl= 9;я як S-норми), що використовm= 1;ються для моделюваннn= 3; поєднання фази-множин.

Функція Т: [0,1]H[0,1]→[0,1] називаєтьсn= 3; Т-нормою, якщо вона відповідає таким умова = 84;:

Функція S: [0,1]H[0,1]→[0,1] називаєтьсn= 3; Т-Со-нормою або S-нормою, якщо вона відповідає таким умова = 84;:

Операт&#= 1086;ри обох цих класів можуть бути параметризl= 6;ваними та непараметрl= 0;зованими. Табл. 1.2 надає огляд найбільш відомих непараметрl= 0;зованих Т-норм та Т-Со-норм.

 

Таблиц&#= 1103; 1.2 – Непараметрl= 0;зовані оператори<= /span>

 

Непарам&#= 1077;тризовані оператори

T-норма:

T(μA1(x), μA2(x)) = =3D

T-Co-норма або S-норма:

S(μA1(x), μA2(x)) = =3D

максиму&#= 1084;/мінімум

Tmin/Smax

min{μA1(x), μA2(x)}=

max{μA1(x), μA2(x)}=

Обмежен&#= 1072; різниця/

Обмежен&#= 1072; сума

Tобмеж/Sобмеж

 

max{0, μA1(x)+μA2(x= )-1}

 

min{1, μA1(x)+μA2(x= )}

Продов&#= 1078;ення табл. 1.2

&= #1040;лгебраїчни= ;й добуток/

&= #1040;лгебраїчна сума

T= алгебр/Sал&= #1075;ебр

<= o:p> 

<= o:p> 

μA1(x).μA2(x)

<= o:p> 

<= o:p> 

μA1(x)+μA2(x)-μ= ;A1(x).μA2(x)

D= rastisches-добуток/

D= rastisches-сума

T= drastisch/Sdrastisch

m= in{μA1(x), μA2(x)}

&= #1103;кщо max{μA1(x), μA2(x)} =3D 1

0 інакше

m= ax{μA1(x), μA2(x)}

&= #1103;кщо min{μA1(x), μA2(x)} =3D 0

1 інакше

H= amacher-добуток/

H= amacher-сума

T= Hamacher/SHamacher

<= sub><= /sub>

<= sub><= /sub>

&= #1044;обуток Ейнштейна/

&= #1057;ума Ейнштейна

T= Eйншт/SEйншт= ;

 <= sub><= /sub>

<= /sub>

 

Властивост = 10; параметризl= 6;ваних операторів на відміну від непараметрl= 0;зованих можуть змінюватисn= 3; в широких межах залеж = 85;о від області їх застосуванl= 5;я за допомого = 02; відповідноk= 5;о параметра. Деякі прикл = 72;ди таких операторів наведені в табл. 1.3.

 

Таблиця 1.3 – Параметризl= 6;вані оператори<= /span>

 

&= #1055;араметризо= ;вані оператори

T= -норма:

T= (μA1(x), μA2(x), γ) =3D

T= -Co-норма або S-норма:

S= (μA1(x), μA2(x), γ) =3D

H= amacher-перетин/

&= #1087;оєднання

T= Ham_перетин/SHam_= поєднання<= /o:p>

<= sub><= /sub>

γ³0

<= sub><= /sub>

γ³0

Y= ager-перетин/

&= #1087;оєднання

T= Yager_перетин/SYa= ger_поєднання

 <= /sub>γ³0

<= /sub>γ³0

 

Ще більш узагальненl= 0;м, ніж фа= ;зи-І- та фаз= ;и-АБО-операm= 0;ори є γ-оператор (також в літературі = 79;устрічаєть&#= 1089;я позначення Zкомп), який дозволяє здійснити певну компенсаціn= 2; однієї величини іншою. Цей оператор ст = 72;новить комбінацію алгебраїчнl= 6;го добутку й алгебраїчнl= 6;ї суми. Можна сказати, що γ-оператор може бути безперервнl= 6; визначений між перетином т = 72; поєднанням фази-множин:

Змінюючи γ в інтервал = 10; [0,1] можна реалізуватl= 0; моделюваннn= 3; від логічного І до логічного АБО з = 72; допомогою лише одного оператора:=

 

γ =3D 0:            &n= bsp;            = ;  Zкомп → Tалгебр

γ =3D 1:            &n= bsp;            = ;  Zкомп → Sалгебр

 

До другої груп = 80; операторів, що визначають = 74;ідношення між фази-множин = 72;ми, які містять до себе різн= 110; базові елементи, належать фа = 79;и-співвідно&= #1096;ення. Щоб пояснит = 80; це поняття, необхідно звернутись до визначення = 74;екторного добутку.

Векторний добуток A13...3Am фаззи-множи = 85; A1...,Am із базовими множинами X1...,Xm визначаєтьl= 9;я в просторі добутку X13...3Xm таким чином:

На основі поняття векторного добутку можна визначити фази-співві = 76;ношення. Фази-співві = 76;ношення можуть розглядатиl= 9;я як узагальн = 77;ння співвідношk= 7;нь класичних м = 85;ожин. Фази-співві = 76;ношення являє собою фази-множин = 91;, яка є підмножиноn= 2; простору до = 73;утку X13= ...3Xm базових множин X1...,Xm. Фази-співві = 76;ношення (нечітке співвідношk= 7;ння) R у просторі добутку X13...3Xm із базовими множинами X1...,Xm визначаєтьl= 9;я таким чином:

Зворотне фази-співві = 76;ношення R-1 бінарного фаззи-співв = 10;дношення (1.8) визначаєть= ;ся як

Нечіткі бінарні співвідношk= 7;ння R1(X1, X2) та R2(X2, X3) з різними просторами добутку та спільним ба = 79;овим елементом X2 поєднуютьсn= 3; за допомого = 02; оператора композиції (оператора з'єднання) "°". З'єднання (зчеплення) R12(X1, X3= ) двох бінарних фази-співві = 76;ношень R1(X1, X2) та R2(X2, X3) із базовими множинами X1, X2, X3 <= /p>

R12(X1= , X3) =3D R1(X1, X2)<= span lang=3DUK style=3D'font-family:TechnicLite;mso-ascii-font-family:"Times New= Roman"; mso-hansi-font-family:"Times New Roman";mso-ansi-language:UK;mso-char-type: symbol;mso-symbol-font-family:TechnicLite'>°R2(X2, X3)<= span style=3D'mso-tab-count:2'>        &= nbsp;       або R12 =3D R1°R2            =                    &= nbsp;   (1.10)

може бути визначене з = 72; допомогою деяких опер = 72;торів, найбільш відомі з них наведені у табл. 1.4.

 

Таблиц&#= 1103; 1.4 – Оператори з'єднання=

 

R12 =3D R1°R2<= /p>

<= /sub>

max-= min

(= 084;аксимум мінімуму)

= <= /sub>

max-= prod

(= 084;аксимум добутку)

= <= /sub>

max-= average

(= 084;аксимум середнього значення)

= <= /sub>

 

1.2&= nbsp;           Фази= -контролер

&n= bsp;

У попередньоl= 4;у розділі бул = 80; представлеl= 5;і основні поняття та механізми ф = 72;зи-теорії без огляду н= 072; практичні аспекти її використанl= 5;я в техніці регулюваннn= 3;. В цьому розділі розглядаютn= 0;ся засоби побу = 76;ови на основі нечіткої логіки фази-контро = 83;ерів та їх практичне застосуванl= 5;я в межах техніки авт = 86;матизації.

Основ&= #1085;у структуру фаззи-контр = 86;лера можна представитl= 0; у вигляді трьох блокі = 74;
(рис. 1.2):

ü      = вхідний фільтр;

ü      = фази-бло= 082;;

ü      = вихідни = 81; фільтр.

Рисун= ;ок 1.2 – Структура фази-контро = 83;ера

Вхідн&= #1110; та вихідні фільтри фази-контро = 83;ера служать для узгодження параметрів об'єкта регулюваннn= 3; із параметрамl= 0; фази-блока. В&#= 1093;ідні та вихідні фільтри можуть включати в себе динамічні компоненти фази-контро = 83;ера (наприклад, інтеграторl= 0; та ланки диференціюk= 4;ання) або складатися із чисто статичних компонентіk= 4; (наприклад, суматори та підсилювачo= 0;). Фази-блок утворює центральну частину фаз = 80;-контролера. Передавальl= 5;а функція фаз = 80;-блока є чисто статичною, фази-блок не містить у собі жодних динамічних компонентіk= 4; та внутрішніх змінних стану.

Завда&= #1085;ням вхідного фільтра є перетворенl= 5;я вимірюваниm= 3; величин системи E1...Ee на вхідні величини X1...Xm фази-блока. У випадку, якщ= 086; для утворення з = 85;ачення однієї вхідної величини потрібні значення декількох змінних системи , кіл&#= 1100;кість е величин системи E1...Ee може відрізнятиl= 9;ь від кількості m вхідних величин X1...Xm фази-блока. Найпростішl= 0;м прикладом цього є використанl= 5;я помилки регулюваннn= 3; як вхідної величини фази-блока. Помилка регулюваннn= 3; Xd обчи&= #1089;люється виходячи із заданого значення величини r, що регулюєтьсn= 3;, та поточног = 86; значення цієї ж величини y (Xd  =3D  r  −  y).

Зав&= #1076;анням вихідного фільтра є узгодження значення вихідної величини фази-блока і= 079; керуючою величиною перетворювk= 2;ча або безпосе = 88;едньо об'єкта регулюваннn= 3;. Принципово вихідний фільтр може містити будь-які ста= 090;ичні та динамічн = 10; функції, проте як правило він містить тільки підсилювач або інтегра = 90;ор. Інтегратор = 91; вихідному фільтрі зді = 81;снює перетворенl= 5;я форми керуючого сигналу.

Ядр&= #1086; фази-контро = 83;ера утворює фази-блок. Ви&#= 1097;е було зазначено, щ= 086; фази-блок не містить жод = 85;их динамічних компонентіk= 4;. Це означає, щ&#= 1086; будь-який фази-блок можна представитl= 0; за допомого = 02; статичної функції F: X→C, що пов'язує базові множини X1,...,Xm вхідних величин із базовою множиною вихідної величини С. Цей зв'язок здійснюєтьl= 9;я за допомого = 02; якісних знань експерта. Це означає, що функція c =3D F(x), де  xÎ= X, cÎC, не записуєтьсn= 3; математичнl= 6; в аналітичн = 10;й формі, а встановлюєm= 0;ься за допомого = 02; лінгвістичl= 5;их термів (фази-множин) та правил на основі інши = 93; ступенів свободи. Функція F(x) є як правило нелінійною. Це викликає питання: що власне ново = 75;о привносить фази-регулю = 74;ання? Адже неліні = 81;на передавальl= 5;а функція із багатьма вх = 10;дними змінними може бути реалізованk= 2; за допомого = 02; багатовиміl= 8;ного регулятора. = 053;овим є метод розробки системи регулюваннn= 3;, вербальне формулюванl= 5;я експертних знань за допомогою лінгвістичl= 5;их правил.

Стр&= #1091;ктура фази-блока показана на рис. 1.3. Фази-бл = 86;к складаєтьсn= 3; з трьох частин:

 

 

<= ![if !supportLists]>ü  &nbs= p;  блок фазифікаціo= 1;;

<= ![if !supportLists]>ü  &nbs= p;  блок інференції;

<= ![if !supportLists]>ü  &nbs= p;  блок дефазифікаm= 4;ії.

 

Рисун= ;ок 1.3 – Структура фази-блока=

 

У техніці регулюваннn= 3; можуть бути виміряні тільки однозначні величини, і тільки одно = 79;начні керуючі величини можуть бути задані об'єкту регулюваннn= 3;; тому використанl= 5;я фази-множин безпосередl= 5;ьо як технічно = 75;о сигналу неможливе. Фазифікаціn= 3; та дефазифі = 82;ация здійснюють перетворенl= 5;я відповідно однозначниm= 3; вхідних величин на в= 093;ідні фази-множин = 80; та вихідних фази-множин на однозначні вихідні величини.=

У процесі фазифікаціo= 1; кожному елементарнl= 6;му висловленнn= 2; ЯКЩО-ч&#= 1072;стини правила ставиться д = 86; відповідноl= 9;ті ступінь приналежноl= 9;ті. Ступінь приналежноl= 9;ті розраховуєm= 0;ься із функції приналежноl= 9;ті лінгвістичl= 5;ого терма та актуальногl= 6; вхідного значення елементарнl= 6;го висловленнn= 3;. Графічне зображення фазифікаціo= 1; надається н = 72;
рис. 1.4.

Р= 080;сунок 1.4 – Фаззифікацo= 0;я

Зав&= #1076;анням інференції = 08; перетворенl= 5;я якісного експертногl= 6; знання на закон регул = 02;вання, що може бути реалізованl= 0;й технічно. Вх= 110;дними даними для процесу інференції = 08; фази-правил= а та ступінь приналежноl= 9;ті, з яким є справедливl= 0;м елементарнk= 7; висловленнn= 3; Ek,i(xk). На основі результатіk= 4; фазифікаціo= 1; та фази-прав= 080;л в процесі інференції відбуваєтьl= 9;я формування вихідної фази-множин = 80; B*. Інференцію можна умовн = 86; поділити на три етапи:

= ü  &nbs= p;  агрегація;

= ü  &nbs= p;  імплікація;<= o:p>

= ü  &nbs= p;  акумуляція.<= o:p>

У процесі агрегації визбируютьl= 9;я різні елементарнo= 0; висловленнn= 3;, що належать до одного правила, та утворюєтьсn= 3; ступінь приналежноl= 9;ті, з яким є справедливl= 0;м елементарнk= 7; висловленнn= 3; ЯКЩО-ч&#= 1072;стини фази-правил = 72;. Кожна ЯКЩО-частин= 072; правила складаєтьсn= 3; з декількох елементарнl= 0;х висловлень, які зводять = 89;я за допомого = 02; логічних зв'язків до єдиного комплексноk= 5;о висловленнn= 3;. Як результа = 90; для кожного активного правила виз = 85;ачається ступінь приналежноl= 9;ті, з яким висловленнn= 3; у ЯКЩО= ;-частині є справедливl= 0;м. Операторамl= 0; агрегації м = 86;жуть бути будь-як= 110; з наведених вище операторів, але в техніц= 110; регулюваннn= 3; використовm= 1;ється як правило лише І-опера= 090;ор. І-оператор може бути реалізованl= 0;й двома способами, тому можна виділити дв = 72; типи реалізації оператора агрегації:=

= ü  &nbs= p;  мінім= ;ум-агрегаці= 103;:

<= ![if !supportLists]>ü  &nbs= p;  добут= ;ок-агрегаці= 103;:

Гра&= #1092;ічне зображення мінімум-агр = 77;гації надається н = 72; рис. 1.5. Розглядаєтn= 0;ся правило, ЯКЩО-части= 085;а якого має вигляд:

ЯКЩ= ;О Помилка регулюваннn= 3; позитивна ТА Похідна від помилки регулюваннn= 3; позитивна велика,...

Помилка регулюваннn= 3; є позитивною зі ступенем приналежноl= 9;ті 0.7 та По&#= 1093;ідна від помилки регулюваннn= 3; є позитивно = 02; великою зі ступенем приналежноl= 9;ті 0.6. Відповідно до формули (1.11), агрегація дає результат – ступінь приналежноl= 9;ті, з яким виконуєтьсn= 3; ЯКЩО-ч&#= 1072;стина правила, – 0.6.<= /span>

Р= 080;сунок 1.5 – Мінімум-агр = 77;гація

 = ;

В процесі імплікації для кожного активного правила залежно від ступеня приналежноl= 9;ті Ei(x), k= 9; яким воно виконуєтьсn= 3;, визначаєтьl= 9;я фази-множин = 72; B*i. Для здійснення імплікації використовm= 1;ються оператори композиції. Фази-множин = 72; B*i є складовою частиною базової множини Ci вихідної величини C фази-блока. Існує декіл = 00;ка методів імплікації, найбільш відомі з них наведені в табл. 1.5. Найчастіше як оператор імплікації = 74; техніці регулюваннn= 3; використовm= 1;ється І-опе&= #1088;атор. Графічне уявлення імплікації, = 097;о здійснюєтьl= 9;я за допомого = 02; І-опе = 88;атора, представлеl= 5;е на рис. 1.6.

 

Таб&= #1083;иця 1.5 – Методи імплікації=

 

Опе= ратор імплікації

<= /sub>

Zadeh

<= /sub>

Lukasiewicz

<= /sub>

Minimum Mam= dani

<= /sub>

Kleene-Dienes

<= /sub>

Produkt

<= /sub>

 

Р= 080;сунок 1.6 – Імплікація=

 = ;

Ост&= #1072;ннім етапом інференції = 08; акумуляція. = 047;авданням акумуляції = 08; об'єднання р= 077;зультатів інференції окремих фази-правил. Результатоl= 4; акумуляції = 08; фази-множин = 72; B*, що утворюєтьсn= 3; шляхом об'єднання окремих фаз = 80;-множин B*i:

Аку&= #1084;ульована фази-множин = 72; B* являє собою остаточний результат процесу інференції. Функція при = 85;алежності результуючl= 6;ї фази-множин = 80; утворюєтьсn= 3; за допомого = 02; оператора акумуляції Akk:

Опе&= #1088;атор акумуляції Akk здійснює об'єднання фази-множин, тому для йог= 086; реалізації можна застосовувk= 2;ти будь-який з розглянутиm= 3; вище операторів для фази-множин. Оператори, щ= 086; є найбільш п= 086;ширеними, наведені в табл. 1.6.

 

Таб&= #1083;иця 1.6 – Оператори акумуляції=

 

Опер = 72;тори акумуляції Akk

T-Co-норм= ;а bzw. S-норма

Макс = 80;мум (за Mамдані)

Smax

Обме = 78;ена сума

Sобмk= 7;ж

 

Най&= #1095;астіше як оператор акумуляції виступає максимум-оп = 77;ратор. У цьому випадку акумульоваl= 5;а фази-множин = 72; визначаєтьl= 9;я таким чином:

Фун&= #1082;ція приналежноl= 9;ті результуючl= 6;ї фази-множин = 80;, що визначаєтьl= 9;я за допомого = 02; максимум-оп = 77;ратора, наведена на рис. 1.7.

Р= 080;сунок 1.7 – Акумуляція=

 = ;

У техніці регулюваннn= 3; як керуючі сигнали мож = 91;ть бути використанo= 0; лише однозначні = 74;еличини, тому акумульоваl= 5;а у процесі ін= 092;еренції фази-множин = 72; не може бути використанk= 2; як керуюча величина об'єкту регулюваннn= 3;; необхідна дефазифікаm= 4;ія отриманого результату. = 059; процесі деф = 72;зифікації відбуваєтьl= 9;я перетворенl= 5;я акумульоваl= 5;ої фази-множин = 80; на однознач = 85;у вихідну величину. Існує велик = 72; кількість методів дефазифікаm= 4;ії, метою яких є визначення такої однозначноo= 1; вихідної величини, як= 072; б як можна точніше представилk= 2; акумульоваl= 5;у фази-множин = 91;. Серед найбільш поширених с = 83;ід зазначити такі методи дефазифікаm= 4;ії:

ü     м= 077;тод мінімуму, коли як вихідне значення виступає максимальнk= 7; значення множини Сmin, яку утворюють елементи, що належать до терму із мін= 110;мальними значеннями функції приналежноl= 9;ті акумульоваl= 5;ої фази-множин = 80; (рис. 1.8).=

ü     м= 077;тод максимуму<= span lang=3DUK style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;line-height:1= 50%; mso-ansi-language:UK'>, коли як вихідне значення виступає максимальнk= 7; значення множини Сmax, яку утворюють елементи, що належать до терму із максимальнl= 0;ми значеннями функції при = 85;алежності акумульоваl= 5;ої фази-множин = 80; (рис. 1.8).=

ü     г= 088;авітаційни&= #1081; метод, коли розраховуєm= 0;ься центр ваги площі функц = 10;ї приналежноl= 9;ті вихідної величини, як= 072; складаєтьсn= 3; зі всіх лінгвістичl= 5;их змінних (рис. 1= .8). Вихідна величина визначаєтьl= 9;я таким чином:

ü     с= 110;нглетон - метод – спрощений варіант гравітаційl= 5;ого метода. Застосуванl= 5;я цього метод = 72; дозволяє зм = 77;ншити витрати час = 91; на розрахунки, тобто збіль = 96;ити швидкість обчислювалn= 0;них процесів та зменшити витрати пам'яті. Відхилення результатіk= 4;, отриманих з = 72; допомогою цього метод = 72;, від результ = 72;тів розрахункіk= 4; за гравітаційl= 5;им методом незначні.

Рисун= ;ок 1.8 - Методи дефазифікаm= 4;ії

 

Розгл= ;янемо докладніше найпростішl= 0;й і тому найбільш поширений метод дефазифікаm= 4;ії – сінглетон-м = 77;тод. Цей метод базується н = 72; гравітаційl= 5;ому методі і том= 091; передбачає розрахунок проекції центра ваги фігури, яка утворюєтьсn= 3; шляхом накладення усіх усічених площ, що відп&#= 1086;відають результату кожного активного п = 88;авила. Звичайно, це стосується випадку ная = 74;ності декількох активних термів вихідної змінної.

Я= 082; було зазначено вище, центр ваги j= 1;S результуючl= 6;ї площі визначаєтьl= 9;я шляхом інте = 75;рування результатиk= 4;ної функції μ(с) (рис. 1.9).=

Р= 080;сунок 1.9 - Визначення центра ваги результуючl= 6;ї площі

Я= 082;що усічені функції приналежноl= 9;ті розглядати окремо, а значення усічених функцій визначати шляхом множення<= /p>

 

то методика значно спрощуєтьсn= 3;:

 

 

Я= 082;що розглянути останнє рівняння, то можна помітити, що тепер під інтегралом стоять тільки функції μАО(с) та μВО( = 93;), а ці функції не залежать від процесу, тобто площа під ними мож= 077; бути розрахованk= 2; ще під час проектуванl= 5;я.

І= 085;теграл в чисельник = 91; дробі відповідає = 86;бертальном&#= 1091; моменту М, а інтеграл в знаменнику відповідає усіченій площі А. Відповідно до цього рівняння спрощуєтьсn= 3; ще:

З цього рівняння видно, що форма функцій при = 85;алежності вихідної фази-змінно = 11; не впливає н= 072; кінцевий результат. Зараз важливими є тільки площ = 10; та їхнє розташуванl= 5;я на осі. Якщо вибрати функції приналежноl= 9;ті μАО(&#= 1089;) і μВО<= /sub>(с) незалежним&= #1080; від с, наприклад, прямокутниl= 2;и з висотою, яка дорівню = 08; одиниці, то ці функції можна винести за знак інтеграла і скоротити. У цьому випад = 82;у ми отримаєм = 86; формулу розрахунку центра ваги за сінглето = 85; - методом:

Н= 072; рис. 1.10 показані сінглетон-ф = 91;нкції усічених функцій приналежноl= 9;ті μАО(&#= 1089;) і μВО<= /sub>(с).

Р= 080;сунок 1.10 - Сінглетон-ф = 91;нкції усічених фу = 85;кцій приналежноl= 9;ті

Усі ступені свободи фази-блока можна розподілитl= 0; на два класи:

<= span lang=3DUK style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;line-height:1= 50%; mso-ansi-language:UK'>1.        &= nbsp;       П= 072;раметричні:=

= ü      =           л= 110;нгвістичні терми (форма та параметр = 80; функцій приналежноl= 9;ті);

= ü      =           ф= 072;зи-правила;<= /o:p>

= ü      =           в= 072;гові коефіцієнтl= 0;.

<= span lang=3DUK style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;line-height:1= 50%; mso-ansi-language:UK'>2.        &= nbsp;       А= 083;горитмічні:=

<= span lang=3DUK style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;line-height:1= 50%; font-family:Wingdings;mso-fareast-font-family:Wingdings;mso-bidi-font-famil= y: Wingdings;mso-ansi-language:UK'>ü      =           о= 087;ератори агрегації;=

<= span lang=3DUK style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;line-height:1= 50%; font-family:Wingdings;mso-fareast-font-family:Wingdings;mso-bidi-font-famil= y: Wingdings;mso-ansi-language:UK'>ü      =           о= 087;ератори імплікації;

<= span lang=3DUK style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;line-height:1= 50%; font-family:Wingdings;mso-fareast-font-family:Wingdings;mso-bidi-font-famil= y: Wingdings;mso-ansi-language:UK'>ü      =           о= 087;ератори акумуляції;

= ü      =           м= 077;тод дефазифікаm= 4;ії.

Виз&= #1085;ачальну роль при настроюванl= 5;і фази-блока грають пара = 84;етричні ступені свободи, том= 091; що саме база &#= 1087;равил та лінгвістичl= 5;і терми представляn= 2;ть експертне знання. При розробці фази-блока оператори інференції та метод дефазифікаm= 4;ії завжди розглядаютn= 0;ся підпорядкоk= 4;ано, головна увага приділяєтьl= 9;я визначенню параметричl= 5;их ступенів свободи. Значно легш = 77; помітити зміни в роботі системи, що викликані з = 84;іною лінгвістичl= 5;их термів або правил, ніж зміни, що спричиняютn= 0;ся варіацією методу дефазифікаm= 4;ії або операторів інференції. Алгоритмічl= 5;і ступені свободи здебільшогl= 6; встановлююm= 0;ься виходячи із вимог до швидкодії (ц= 077; стосується насамперед до вибору методу дефа = 79;ифікації) та сталості системи. В техніці регулюваннn= 3; існують установки, яким традиц = 10;йно надається перевага пр = 80; проектуванl= 5;і фази-блоків. Як оператор = 80; інференції, наприклад, найчастіше вживаються Max-Min- та Max-Prod-інф = 77;ренція. Огляд найбільш поширених операторів інференції представлеl= 5;ий в табл. 1.7.

 

Таб&= #1083;иця 1.7 – Оператори інференції=

 

= Мето = 76; інференції

= Агре = 75;ація (І)

= Імпл = 10;кація

= Акум = 91;ляція

= Max-Min

= Міні = 84;ум або добуток

= Міні = 84;ум

= Макс = 80;мум

= Max-Prod

= Міні = 84;ум або добуток

= Добу = 90;ок

= Макс = 80;мум

= Sum-Prod

= Міні = 84;ум або добуток

= Добу = 90;ок

= Сума

= Sum-Min

= Міні = 84;ум або добуток

= Міні = 84;ум

= Сума

 

Мат&= #1077;матичний опис операторів інференції = 91; вигляді формул надається в = 090;абл. 1.8.

 

Таб&= #1083;иця 1.8 – Формульне представлеl= 5;ня деяких операторів інференції=

 

Метод інференції

Фор= мула

Max-Min=

<= /sub>

Max-Prod

<= /sub>

 = ;

П= 088;одовження табл. 1.8

Sum-Prod

<= /sub>

Sum-Min=

<= /sub>

 

Заг&= #1072;льна структура фаззи-контр = 86;лера зображена н = 72; рис. 1.11. Ця схем= 072; може служит = 80; допоміжним матеріалом при проектуванl= 5;і фази-контро = 83;ерів.

 

 = ;

Р= 080;сунок 1.11 – Загальна структура фази-контро = 83;ера

 = ;

1.3   &n= bsp;   Основні етапи проектуванl= 5;я фази-контро = 83;ерів

 

Процес проектуванl= 5;я фази-контро = 83;ера складаєтьсn= 3; з чотирьох етапів.

1.        &= nbsp;  Аналіз системи. На початку проектуванl= 5;я обов'язково треба провести аналіз системи. Процедура аналізу включає в себе як вибі= 088; структури контуру регулюваннn= 3;, так і вибір в&#= 1080;мірюваних величин та вхідних величин фаз = 80;-контролера, що визначаютьl= 9;я виходячи із результатіk= 4; вимірюваннn= 3;; визначення = 74;ихідних величин фази-контро = 83;ера, тобто керую = 95;их величин об'єкта регулюваннn= 3;. На цьому етапі можут = 00; також бути встановленl= 0;ми вхідні й вих= 110;дні фільтри, що вимагає вірного добору коеф = 10;цієнтів підсилюванl= 5;я або масштабних коефіцієнтo= 0;в у вхідних та вихідних фільтрах. Ця процедура є обов'язково = 02; при застосу = 74;анні нормованогl= 6; фази-блока, тому що в так&#= 1086;му випадку необхідно узгодити величини системи із вхідними та вихідними величинами фази-блоку, що змінюються = 74; одиничному інтервалі (наприклад, [-1,1] або [1,100]). Використанl= 5;я нормованих фази-блоків дозволяє інколи стандартизm= 1;вати їх, використовm= 1;вати той самий фа= 079;и-блок в різних системах керування і = 79; різними параметрамl= 0;, змінюючи лише масшта = 73;ні коефіцієнтl= 0; вхідних та вихідних фі = 83;ьтрів. Масштабні коефіцієнтl= 0; вхідних та в= 080;хідних фільтрів грають таку = 078; важливу рол = 00;, як і коефіцієнтl= 0; підсилення = 74; класичних регулятораm= 3;. Перший етап проектуванl= 5;я є дуже відпо= 074;ідальним і потребує глибоких знань в обла= 089;ті класичних методів регулюваннn= 3; та цифрової обробки сигналу. Помилки, що виникають н = 72; цьому етапі, набагато складніше в = 80;правити, ніж ті, що виникають н = 72; наступних е = 90;апах.

2.        &= nbsp;  Встанов = 83;ення алгоритмічl= 5;их ступенів св = 86;боди. На цьому етапі здійснюєтьl= 9;я визначення = 86;сновних властивостk= 7;й фази-блока. Наприклад, метод дефазифікаm= 4;ії визначає швидкодію фази-блока т= 072; його сталість.=

3.        &= nbsp;  Встанов = 83;ення параметричl= 5;их ступенів св = 86;боди. Цей етап є центральниl= 4; в усьому процесі про = 77;ктування, його можна розподілитl= 0; на три кроки:

<= ![if !supportLists]>ü      = встанов = 83;ення можливих інтервалів зміни вхідн = 80;х та вихідних величин. При цьому припу = 89;кається, що на попередньоl= 4;у етапі були в= 080;значені властивостo= 0; об'єкта регулюваннn= 3; та масштабн = 10; коефіцієнтl= 0; фільтрів;=

ü      = встанов = 83;ення лінгвістичl= 5;их термів та їх функцій приналежноl= 9;ті для всіх лінгвістичl= 5;их змінних. Як правило у техніці регулюваннn= 3; обираються трикутні, трапецієпоk= 6;ібні та сінглетон-ф = 86;рмені функції приналежноl= 9;ті. Слід зауваж = 80;ти, що наявніст = 00; невизначенl= 0;х областей є н= 077;бажаною, всі функції приналежноl= 9;ті вхідних фази-множин обов'язково мають перекриватl= 0;сь;

<= ![if !supportLists]>ü      = складан = 85;я бази правил. На жаль, для цього не існує жодного систематизl= 6;ваного алгоритму, тому центральниl= 1; етап проектуванl= 5;я фази-регуля = 90;ора не має такої загальнопрl= 0;йнятої систематикl= 0;, як при проектуванl= 5;і класичних регуляторіk= 4;. Це значно ускладнює процес проектуванl= 5;я - дуже часто трапляютьсn= 3; випадки, кол= 080; різні настройки фази-блока зумовлюють майже ідентичні його передавальl= 5;і властивостo= 0;.

4.        &= nbsp;  Моделюв = 72;ння спроектоваl= 5;ого контуру рег = 91;лювання. На цьому етапі відбуваєтьl= 9;я перевірка р = 86;зробленого фази-контро = 83;ера. У випадку, якщо результати моделюваннn= 3; є незадовільl= 5;ими, потрібно змінити певні параметри фази-контро = 83;ера.

На рис. 1.12 процес розробки фази-контро = 83;ера представляn= 8;ться у наочній формі.

Рисун= ;ок 1.12 – Процес розробки фази-контро = 83;ера

 

1.4       Тип= 080; фази-контро = 83;ерів

 

Фази-контро= ;лери, як і класичн= 110; регулятори, = 084;ожуть бути реалізованo= 0; у вигляді П-регулятор = 10;в, ПІ-регулято = 88;ів, ПД-регулято = 88;ів та ПІД-регул= 103;торів [4]. Проте слід пам'ятати, що ця аналогія не є повною, і = фази-П-регул= 103;тор, наприклад, н= 077; є аналогом к= 083;асичного П-регулятор = 72;. Нижче розглянуті = 86;сновні типи фази-контро = 83;ерів.

1.&n= bsp;    Фази-П-ре&#= 1075;улятор

Фази-П= -регуляторо = 84; називаєтьсn= 3; фази-контро = 83;ер з однією вхідною величиною, причому при зростанні вхідної величини е вихідна величина u та= 082;ож зростає або принаймні залишаєтьсn= 3; незмінною, тобто:

u =3D F(e)<= /p>

Це визначення збігається = 79; вимогами до монотонної (проте не строго монотонної) передавальl= 5;ої функції та являє собою значне пом'я= 082;шення поняття пропорційнl= 6;сті. Як фази-П-регул= 103;тор може розглядатиl= 9;я, наприклад, зона нечутл = 80;вості.

2.&n= bsp;    Фази-ПІ-р&#= 1077;гулятор

Фази-П= І-регулятор = 86;м називаєтьсn= 3; фази-контро = 83;ер, вхідними величинами якого є поми= 083;ка регулюваннn= 3; e та швидкість ї = 11; змінювання (тобто перша похідна) ė, а вихідною величиною є похідна від керуючого сигналу ů, причому як при зростанні помилки регулюваннn= 3; e, так і при зростанні ї = 11; похідної ė вихідна величина ů зростає або принаймні залишаєтьсn= 3; незмінною:=

ů =3D F(e, ė)<= /o:p>

3.&n= bsp;      Фази-ПД-р&#= 1077;гулятор

Фази-П= Д-регулятор = 86;м називаєтьсn= 3; фази-контро = 83;ер, вхідними ве = 83;ичинами якого є помилка регулюваннn= 3; e та швидкість ї = 11; зміни (тобто перша похідна) ė, а вихідною величиною є керуючий сигнал u, причому як при зростанні помилки регулюваннn= 3; e, так і при зростанні ї = 11; похідної ė вихідна величина u зростає або принаймні залишаєтьсn= 3; незмінною:=

u =3D F(e, ė)=

4.&n= bsp;      Фази-ПІД-&#= 1088;егулятор

Фази-= ПІД-регулят = 86;р може бути реалізованl= 0;й за допомого = 02; двох алгоритмів R= 11; алгоритму встановленl= 5;я керуючої величини та алгоритму встановленl= 5;я швидкості зміни керую = 95;ої величини:

= ü     при реалізації за першим алгоритмом фаззи-ПІД-ре= 075;улятором називаєтьсn= 3; фази-контро = 83;ер, вхідними величинами якого є помилка рег = 91;лювання e, її перша похідна ė та інтеграл ві = 76; помилки регулюваннn= 3; ∫edτ, а вихідною величиною є керуючий сигнал u:

u =3D F(e, ∫edτ, ė)

= ü     при реалізації за другим алгоритмом фази-ПІД-рег= 091;лятором називаєтьсn= 3; фази-контро = 83;ер, вхідними величинами якого є помилка рег = 91;лювання e, її перша ė та друга ë похідні, k= 2; вихідною величиною є похідна кер = 91;ючого сигналу ů.

ů =3D F(e, ė, ë)

 

1.5   &n= bsp;   Варіант&#= 1080; побудови контурів регулюваннn= 3; із фази-регу= 083;ятором

 

Існ&= #1091;є велика кількість різноманітl= 5;их варіантів побудови контурів регулюваннn= 3; із фази-регуля = 90;ором. Цей розділ присвячениl= 1; розгляду найбільш поширених з них.

Найпростіш = 72; структура показана на рис. 1.13. Ця структура представляn= 8; собою одноконтурl= 5;у систему регулюваннn= 3;, аналогічну класичній одноконтурl= 5;ій системі. Замість кла = 89;ичного регулятора контур містить фаз = 80;-регулятор, що має одну вхідну та одну вихідн = 91; величини.=

 

Рисун= ;ок 1.13 – Одноконтурl= 5;а система регулюваннn= 3; з фази-регул= 103;тором

 

Трохи ускладнениl= 1; варіант ціє = 11; структури є система, показана на рис. 1.14. Фази-контро = 83;ер в цьому випадку має більш, ніж одну вхідну величину, тому в системі з'являється додатковий блок підготовки вимірюваниm= 3; величин. Йог= 086; завданням є розрахунок вхідних величин регулятора, виходячи із значення помилки регулюваннn= 3; та надання отриманих величин регулятору. Принципово при реалізації цього блока можливе вик = 86;ристання будь-яких динамічних та статични = 93; операторів.

Рису&= #1085;ок 1.14 - Одноконтурl= 5;а система регулюваннn= 3; з фази-регуля = 90;ором

Слід зауважити, щ= 086; структури, подібні до н= 072;ведених, на практиці вживаються дуже обмеже = 85;о. Причиною є те, що проектувалn= 0;ники ще "не довіряють" фази-контро = 83;еру, теорія фази-регулю = 74;ання в даний час ще не має однозначниm= 3; простих методів оцінки фази-= 089;истем регулюваннn= 3;. Тому досить часто структур із одним лише фази-регуля = 90;ором намагаютьсn= 3; уникнути. В більшості випадків проектувалn= 0;ники систем фази-регулю = 74;ання прагнуть поєднати достоїнствk= 2; фази-регуля = 90;орів та класични = 93; регуляторіk= 4;. Дуже часто в= 080;користовую&= #1090;ься структури, в яких до випр= 086;буваного класичного контуру регулюваннn= 3; (наприклад, до контуру з ПІД-регулят = 86;ром) підключаєтn= 0;ся фази-регуля = 90;ор, що має компе= 085;сувати недоліки класичного регулятора або втрутит = 80;ся у разі особливих режимів роботи. Це да&#= 1108; можливість переключатl= 0;сь залежно від = 087;оточного режиму роботи системи між двома конце = 87;ціями регулюваннn= 3;: при незначних в = 10;дхиленнях від робочої точки є доцільним в = 80;користання класичного регулятора (наприклад, ПІД-регулят = 86;ра), при значних швидких змінах збуд = 78;ення або завданн = 03; хороші результати дає фази-рег= 091;лятор. Одним із варіантів реалізації такого підходу є структура, наведена на рис. 1.15. Контур регулюваннn= 3; містить фази-контро = 83;ер, що підключаєтn= 0;ся паралельно до класично = 75;о регулятора. Вхідною величиною ф = 72;зи-контроле&= #1088;а може бути, наприклад, помилка регулюваннn= 3; та похідна від неї, на виході фази-контро = 83;ер утворює коригувальl= 5;ий сигнал, що складаєтьсn= 3; із сигналом на виході класичного регулятора.

Рисун= ;ок 1.15 – Контур регулюваннn= 3; з паралельн = 86;ю фази-корекц = 10;єю

 

Широкі можливості для фази-регулю = 74;ання відкриваютn= 0;ся в області адаптивногl= 6; регулюваннn= 3;. Йдеться про on-line-покl= 8;ащення властивостk= 7;й контуру регулюваннn= 3;, що є, наприклад, доцільним у системах, в яких вид перехідногl= 6; процесу залежить ві = 76; моменту йог = 86; початку. В таких системах шл = 03;хом модифікаціo= 1; структури регулюваннn= 3; розробляєтn= 0;ся фази-контро = 83;ер, здатний до самоорганіk= 9;ації, який через зміну своїх = 087;араметрів залежно від стану системи функціонує можливо оптимально. Найпростішk= 2; структура регулюваннn= 3; такого типу надається н = 72; рис. 1.16.

Рисунок 1.16 – Структура контуру регулюваннn= 3; з адаптивни = 84; фази-контро = 83;ером (пряма адапт= 072;ція)

 

Осново&#= 1102; для адаптації фази-контро = 83;ера служать в цьому випадку спостерігаl= 5;ня за величино = 02; помилки регулюваннn= 3;, виходячи з якої визначаєтьl= 9;я через певни = 81; критерій як = 86;сті індекс якості, що характеризm= 1;є якість регу = 83;ювання. "Розум" адаптивногl= 6; регулятора міститься у блоці Алгоритм адаптації у вигляді різноманітl= 5;их команд, що виконуютьсn= 3; залежно від значення індексу якості. Таки= 084; чином, алгоритм адаптації проектуєтьl= 9;я як фази-алгори = 90;м у формі ЯКЩО...ТО-пр&#= 1072;вил. Ця структур = 72; являє собою так звану пр= 103;му адаптацію. Більш складною є структура непрямої адаптації. Найпростішk= 2; форма таког = 86; контуру рег = 91;лювання наведена на рис. 1.17. В цьому випадку стр = 91;ктура алгоритму адаптації ускладнюєтn= 0;ся. Блок А= ;лгоритм адаптації складаєтьсn= 3; з двох блоків: Ідентифік= 072;ція системи та Проек= 090;увальник фази-контро = 83;ера. Протягом процесу адаптації виконуєтьсn= 3; аналіз поточних значень регульованl= 6;ї координати та заданого значення цієї ж коорд= 080;нати. На основі даних аналізу відбуваєтьl= 9;я зміна параметрів фази-контро = 83;ера. Здійснення зміни параметрів = 08; завданням блока Проектувал = 00;ник фази-контро = 83;ера.

Рисунок 1.17 – Структура контуру регулюваннn= 3; з адаптивни = 84; фази-контро = 83;ером (непряма ада= 087;тація)

Така стратегія адаптації може бути реалізованk= 2; в концепції регулюваннn= 3;, що ґрунтуєт = 00;ся на моделі процесу. Структура контуру регулюваннn= 3; такого типу представлеl= 5;а на рис. 1.18. В цьо&#= 1084;у випадку зміна параметрів фази-контро = 83;ера відбуваєтьl= 9;я на основі порівняння процесів, що протікають = 74; реальній системі, з процесами в ідеалізоваl= 5;ій моделі (так з&#= 1074;аної моделі процесу). Відхилення регульованl= 6;ї координати, що вимірюєтьсn= 3; в реальній системі, від значення цієї ж координати = 74; моделі процесу (у разі необхідносm= 0;і може також аналізуватl= 0;ся похідна від нього) викор= 080;стовується як сигнал навчання. Це відхилення та його похідні (у більшості випадків до уваги приймаєтьсn= 3; лише перша похідна) можуть бути проаналізоk= 4;ані за допомого = 02; ще одного фази-контро = 83;ера (не адаптивногl= 6;), але це значн= 086; ускладнює структуру контуру рег = 91;лювання.

 

 

Рис&#= 1091;нок 1.18 – Реалізація концепції регулюваннn= 3;, що ґрунтуєт = 00;ся на моделі процесу

 

Більш консерватиk= 4;на структура адаптивногl= 6; контуру регулюваннn= 3; надається н = 72;
рис. 1.19. В цьому випадку власне адаптивний регулятор є традиційниl= 4; (наприклад, ПІД-регулят = 86;р), і зміна його параметрів відбуваєтьl= 9;я за допомого = 02; фази-алгори = 90;му.

 

Рис&#= 1091;нок 1.19 – Контур регулюваннn= 3; з адаптивни = 84; класичним регулятороl= 4;

Вибір структури контуру регулюваннn= 3; є одним з найбільш відповідалn= 0;них кроків у роз= 088;обці системи рег = 91;лювання. Складна система із адаптивним = 92;ази-контрол&= #1077;ром або адаптивним класичним регулятороl= 4;, настроюванl= 5;я якого відбу = 74;ається за допомого = 02; фази-алгори = 90;му, демонструє кращі результати, ніж одноконтурl= 5;а система (рис. 1.13). Слід зауважити, щ= 086; взагалі пра = 82;тичне застосуванl= 5;я одноконтурl= 5;ої системи із фази-контро = 83;ером є дуже обмеженим через проблеми у забезпеченl= 5;і необхідногl= 6; ступеня стабільносm= 0;і. Проте правильне настроюванl= 5;я складних систем потребує дуже велики = 93; витрат часу (насамперед через відсу = 90;ність загальновжl= 0;ваних методів розробки фази-систем). Задовільні результати можуть бути отримані пр = 80; вдалій настройці в системі із паралельноn= 2; фази-корекц = 10;єю
(рис. 1.15). Настроюванl= 5;я такої системи не потребує значних витрат часу = 091; порівнянні = 79; настроюванl= 5;ям адаптивних систем, але така систем = 72; має відносн = 86; високу надійність: при "випадінні" із контуру регулюваннn= 3; фази-контро = 83;ера система про = 76;овжує задовільно функціонувk= 2;ти.

2 МОДЕЛЮВАННk= 1; СИСТЕМ ФАЗИ-РЕГУЛЮ = 42;АННЯ ЗА ДОПОМОГО = 70; ПРОГРАМНОГi= 4; ПАКЕТА MATLAB/SIMULINK

 

Як зазначалосn= 3; вище, важливим етапом розробки системи із фази-регуля = 90;ором є моделюваннn= 3; контуру регулюваннn= 3;. В даний час розроблюваm= 5;і програмногl= 6; забезпеченl= 5;я пропонують різні моделюючі програми, що дозволяють проводити розробку та тестування фази-блоків. Деякі з них дають можливість інтегруватl= 0; модель фази-= 088;егулятора до загально = 11; моделі системи регулюваннn= 3; та дослідит = 80; роботу системи в цілому, інші дозволяють лише перевірити = 88;оботу фази-блока окремо від системи, до якої він інтегруєтьl= 9;я, при різних значеннях в = 93;ідних величин. Велика кількість проектувалn= 0;ників користуєтьl= 9;я при моделюваннo= 0; програмним пакетом Matlab та моделюючою програмою Simulink, що входить д= 086; його складу. Simulink дає можливість = 89;творювати наочні математичнo= 0; моделі сист = 77;м регулюваннn= 3; та досліджуваm= 0;и їх функціонувk= 2;ння.

Для моделюваннn= 3; фази-блоків = 074; програмномm= 1; пакеті Matlab/Simulink було розроблено Fuzzy Logic Toolbox, що являє собою набір функцій, створених у числовому обчислювалn= 0;ному середовищі Matl= ab. Fuzzy Logic Toolbox містить k= 4; собі засоби створення т = 72; редагуваннn= 3; фази-блоків = 074; межах струк = 90;ури Matlab. Fuzzy Logic Toolbox дає можливість створювати фази-блоки трьох типів [6]= :

ü      = система інференції Мамдані (Mamdani’s fuzzy inferen= ce method) – фази-блок, вхідні та вихідні функції при = 85;алежності якого можут = 00; мати будь-яку з наведених в табл. 1.1 форму);

ü      = система інференції Сугено<= /span> (Sugeno’s fuzzy inference method) &#= 8211; фази-блок, вхідні та вихідні функції при = 85;алежності якого можут = 00; бути лише константні або лінійні);

ü  &nbs= p;    адаптивна нейро-фаззи система інференції (adaptive neuro-fuzzy inference system) – фази-блок, добір параметрів функцій при = 85;алежності якого відбуваєтьl= 9;я на основі за= 076;аних бажаних значень вхідних та вихідних величин фази-блока з= 072; допомогою методів тренування нейросіток.

В цих методичних вказівках розглядаєтn= 0;ся моделюваннn= 3; систем лише першого тип = 91;.

Ство&#= 1088;ені за допомого = 02; Fuzzy Logic Toolbox фази-систем = 80; можуть бути промодельоk= 4;ані моделюючою програмою Simulink. Недоліком Fuzzy Logic Toolbox є відсутністn= 0; можливості використанl= 5;я у системі інференції Мамдані фун = 82;цій приналежноl= 9;ті із змінними параметрамl= 0;, тобто промоделювk= 2;ти фази-блок, параметри функцій приналежноl= 9;ті якого динам = 10;чно змінюються = 74; процесі моделюваннn= 3;. Промоделювk= 2;ти в Matlab/Simulink такий адаптивний фази-блок можна, лише написавши функцію користувачk= 2;, що містить алгоритм обробки інформації таким регулятороl= 4;, у середовищ = 10; Matlab або С та помістивши цю функцію д= 086; Simulink-моделі за допомогою блока Matlab Fcn (функція Matlab) або S-Function (S-функція).

Засо&#= 1073;и, що входять д= 086; складу Fuzzy Logic Toolbox, можна поділити на дві групи. До першої груп = 80; входять редактор фази-блоків (FIS Editor), редактор правил (Rule Editor) та редактор функцій приналежноl= 9;ті (Membership Function Editor). Ці засоби служать для встановленl= 5;я вхідних та вихідних змінних фази-блока, їх функцій приналежноl= 9;ті та фази-прав= 080;л. Друга група я = 74;ляє собою read-only Tools, тобто інструментl= 0;, які не дозволяють вносити зміни в фази-систем = 91;, а використовm= 1;ються тільки для діагностикl= 0;. До цієї груп= 080; належать переглядач тривимірноo= 1; функції (Surface Viewer) та переглядач правил (Rule Viewer).

Для того, щоб викликати Fuzzy Logic Toolbox, необхідно набрати в командному рядку Matlab fuzzy та натиснут = 80; клавішу Enter. Після цього відкриваєтn= 0;ся вікно, вигля= 076; якого представлеl= 5;ий на рис. 2.1.

 

Рисунок 2.1 – Редактор фази-блоків

 

В цьому вікні Ви можете створити власний фаз = 80;-блок. В тому випадку, якщ= 086; фази-блок мі= 089;тить більш, ніж одну вхідну чи вихідну змінну, треб= 072; вибрати в меню відповідно Edit→Add input або Edit→A= dd output. Щоб відредагувk= 2;ти функції приналежноl= 9;ті, треба клацнути двічі лівим клавішем миші на ікон= 094;і вхідної або вихідної змінної або = 074;ибрати в меню View→Edit Membershipsfunctions. Після цього на екрані з'яви= 090;ься вікно редактора функцій приналежноl= 9;ті (рис. 2.2), за допо&#= 1084;огою якого можна задати функції приналежноl= 9;ті певної лінгвістичl= 5;ої змінної або відредагувk= 2;ти вже існуючі.

Рисунок 2.2 – Вікно редактора функцій приналежноl= 9;ті

 

Для того, щоб ввести нову функцію приналежноl= 9;ті, необхідно вибрати в меню Edit&= #8594;Add MFs... або E= dit→Add custom MFs.... В першому випадку відкриваєтn= 0;ся таке вікно:

 

 

Рисун= 086;к 2.3 – Вікно параметрів стандартноo= 1; функціі приналежноl= 9;ті

В другому випадку відкриваєтn= 0;ся таке вікно:

 

Рисунок 2.4 – Вікно параметрів функціі приналежноl= 9;ті користувачk= 2;

 

В цьому вікні можна ввест = 80; будь-яке ім'я терму, тип та <= /span>межі функції приналежноl= 9;ті.

Як видно із рис. 2= .2, Fuzzy Logic Toolbox пропонує для системи інференції Мамдані 11 тип&= #1110;в функцій приналежноl= 9;ті. Їх назви та с&#= 1090;ислий опис представлеl= 5;і в табл. 2.1.

 

= Таблиця 2.1 – Тип функцій приналежноl= 9;ті лінгвістичl= 5;их термів в Matlab

 

Тип функції приналежно= 089;ті

Опис

Матема&#= 1090;ичне визначення

Графіч&#= 1085;е зображення

dsigmf (a1,c1,a2,= c2)=

різниц&#= 1103; двох сигмоїдаль= 085;их функцій приналежно= 089;ті

<= /sub>

<= /p>

gaussmf (σ, с)

симетр&#= 1080;чна функція Гауса

<= /sub>

<= /p>

gauss2mf (σ1,с1<= /sub>,σ2,с2)

несиме&#= 1090;рична крива, утворена двома функц&#= 1110;ями Гауса

<= /sub><= /sub>

<= /p>

 

 

Продовжен&= #1085;я табл. 2.1

gbellmf (a,= b,c)

дзвіно&#= 1087;одібна крива

<= /sub>

<= /p>

pimf (a,b,c,d)

сплайн&#= 1086;ва крива, що проходить через точки <= /span>a, b, c, d

 

 

−

<= /p>

psigmf (a1,c1,a2,= c2)

добуто&#= 1082; двох сигмоїдаль= 085;их функцій приналежно= 089;ті

<= /sub>

<= /p>

sigmf (a,c)

сигмої&#= 1076;альна функція приналежно= 089;ті

<= /sub>

<= /p>

smf (a,b)

S-под = 10;бна сплайнова крива, що проходить через точки <= /span>a, b=

 

 

−

<= /p>

trapmf (a,b,c,d)

трапец&#= 1110;єподібна функція приналежно= 089;ті

<= /sub>

<= !--[if gte mso 9]>

trimf (a,b,c)

трикут&#= 1085;а функція приналежно= 089;ті

<= /sub>

<= !--[if gte mso 9]>

zmf (a,b)

Z-под = 10;бна сплайнова крива, що проходить через точки <= /span>a, b=

−

<= /p>

 

Для введення фази-правил використовm= 1;ється редактор правил. Щоб його відкрити, треба вибрати в меню View&= #8594;Edit rules. Після цього відкриваєтn= 0;ся вікно редактора правил
(рис. 2.5). Складання фази-правил проводитьсn= 3; автоматичнl= 6; на основі опису вхідних та вихідних лінгвістичl= 5;их змінних, яки= 081; був зроблен = 80;й за допомого = 02; редактора фази-блоків. Для того, щоб утворити нове правил = 86;, треба натиснути н = 72; кнопку Add rule, після чого обрати значення кожної вхідної змінної, логічний зв'язок між вхідними зм = 10;нними та значення вихідної змінної, що відповідає створеній ЯКЩО-ч&#= 1072;стині фази-правил = 72;. У випадку, якщ= 086; правило не містить якоїсь вхід = 85;ої величини, треба обрат = 80; як вхідну величину none. Якщо змінна має бути проінвертоk= 4;ана, треба поставити прапорець напроти not.

 

<= !--[if gte vml 1]>

 

Рисунок 2.5 – Вікно введення фази-правил

 

Діаг&#= 1085;остика розробленоk= 5;о фази-блока здійснюєтьl= 9;я за допомого = 02; переглядачk= 2; тривимірноo= 1; функції (Surface Viewer) та переглядачk= 2; правил (Rule Viewer). Для того= ;, щоб викликати вікно переглядачk= 2; правил, треб= 072; обрати в мен= 102; View→View rules, після чого на екрані з'яв= 080;ться вікно:

 

Рисунок 2.6 – Вікно тестування фази-правил

 

Пере&#= 1075;лядач правил дає можливість для будь-яко= 111; комбінації числових значень вхідних змінних (звичайно, із області зміни цих зм= 110;нних!) визначити відповідне числове зна = 95;ення вихідної змінної.

Пере&#= 1075;лядач тривимірноo= 1; функції дає можливість представитl= 0; залежність вихідної змінної від вхідних змі = 85;них у вигляді тривимірноk= 5;о графіка; осо= 073;ливо добре це дозволяє проаналізуk= 4;ати фази-блоки, що мають дві вхідні та одну вихідн = 91; змінні. У випадку, якщ= 086; фази-блок ма= 108; більш, ніж одну вихідн = 91; змінну, або більш, ніж дв&#= 1110; вхідні змінні, можн= 072; обрати таку комбінацію двох вхідни = 93; та однієї вихідної змінної, яка дозволяє найліпше представитl= 0; передавальl= 5;і властивостo= 0; фази-блока. Для того, щоб викликати переглядач тривимірноo= 1; функції, необхідно обрати в мен= 102; View→View surface, після чого на екрані з'явиться вікно:

 

Рl= 0;сунок 2.7 – Вікно переглядачk= 2; тривимірноk= 5;о графіка передавальl= 5;ої функції фази-блока=

 <= /o:p>

Для того, щоб дати користувачm= 1; можливість = 87;ереглянути установки фази-блока, що знаходит = 00;ся в робочому просторі Matlab, у більш зручній формі, ніж це пропонує редактор фази-блоків, із можливістю копіювання = 10;нформації до буферу обміну для подальшого редагуваннn= 3; за допомого = 02; інших прогр = 72;м, було розроблено ряд функцій виводу на ек= 088;ан (System Display Functions). Огляд цих функцій представлеl= 5;ий в табл. 2.2.

 

Таблиц&= #1103; 2.2 – Функції виводу на установок ф = 72;зи-блока екран

 

&#= 1030;м'я та параметри функції

&#= 1054;пис функцій

plotfis (fismat)

&#= 1057;творює в вікні фігури діаграму фази-блока, що міститься в робочому просторі Matlab п&#= 1110;д ім'ям fismat. На діаграмі позначають= 089;я вхідні та вихідні змінні, вигляд їх термів, кількість фази-правил та тип системи інференції.

plotmf (fismat,varType,varIndex)

&#= 1042;иводить на екран графік функції приналежно= 089;ті лінгвістич= 085;ої змінної фази-блока fismat. У спис= 082;у параметрів вказуються тип змінної (= 'Input' або 'Output') та її індекс.<= /p>

Продовжен&= #1085;я табл. 2.2

gensurf (fismat)

&#= 1042;иводить на екран тривимірни= 081; графік пере&#= 1076;авальної функції фази-блока fismat.

getfis (fismat)

&#= 1042;иводить на екран установки фази-блока fismat – тип фази-блока, кількість вхідних та вихідних змінних, їх імена, тип дефазифіка= 094;ії, тип операторів інференції.

 

Для того, щоб інтегруватl= 0; розроблениl= 1; фази-блок до Si= mulink-моделі, що має містити фази-регуля = 90;ор, та промодел = 02;вати цю систему регулюваннn= 3;, треба спочатку переконатиl= 9;ь, що фази-блок, &= #1089;творений за допомого = 02; редактора фази-блоків, є збережени = 84; до робочого простору Matlab під іменем, яке використовm= 1;ється при парамет = 88;изації Simulink-блока Fuzzy-Logic-Controller. Для того, щоб зберегти фази-блок до робочого простору Matlab, треба обрат = 80; в меню редактора фази-блоків File→Save to workspace аб&= #1086; File→Save to workspace as. У випадку, якщ= 086; фази-блок бу= 074; раніше спроектоваl= 5;ий та збережений на твердому диску, цю операцію можна виконати безпосередl= 5;ьо в робочому просторі Matlab. Для цього в командному рядку необхідно набрати ком = 72;нду:

fuz =3D readfis('Controller')

fuz – ім= ;'я FIS-матриц= і – матриці, що відображує фази-блок у робочому просторі Matlab;

Controller<= span lang=3DDE style=3D'mso-ansi-language:DE;layout-grid-mode:line'> - і&#= 1084;'я файлу, який містить фази-блок.

Післ&#= 1103; цього треба відкрити Simulink-б&#= 1110;бліотеку fuzblock. = 059; результат&= #1110; відкриваєтn= 0;ся вікно:

 

Рисун= 086;к 2.8 – Simulink-бібл= 110;отека фази-блоків

З ціє&= #1111; бібліотеки до Simulink-моделі к&= #1086;піюється один із таки= 093; блоків:

ü   Fuzzy Logic Controlle= r;

ü   Fuzzy Controller with ruleviewer.

Вико&#= 1088;истання блока Fuzzy Controller with ruleviewer дає можливість у процесі моделюваннn= 3; спостерігаm= 0;и за змінами вхідних та вихідних величин фази-блока з= 072; допомогою переглядачk= 2; правил.

Обра&#= 1085;ий блок необхідно параметризm= 1;вати. Для цього треба двічі кла= цнути ліви&= #1084; клавішем миші на іконці блок = 72;. Якщо викори = 89;товується блок Fuzzy= Logic Controller, то після цього на екрані з'яви= 090;ься вікно:

 

Рисунок 2.9 – Вікно параметрів блока Fuzzy Logic Controller

Блок Fuzzy Controller with ruleviewer має досить складну структуру, яка представлеl= 5;а на рис. 2.10.

Рисунок 2.10 – Структура блока Fuzzy Controller with ruleviewer=

Параметри= 079;ація блока Fuzzy Controller with ruleviewer = здійснюєтьl= 9;я, як показано на рис. 2.10.

велике значення передавальl= 5;ого числа в реду= 082;торі, яке може сягати десятків та сотень, призводить до виникнення розбіжностk= 7;й на виході редуктора;=

üмасивна та відносно еластична механічна к = 86;нструкція у поєднанні = 079; великим значенням передавальl= 5;ого числа в реду= 082;торі робить можливою появу низькочастl= 6;тних механічних коливань;=

üкоефіці= 108;нт моменту пружності<= /span>

праг= 085;е досягти одиниці, тобто електродвиk= 5;ун досить слабко демпфірує виникаючі м = 77;ханічні коливання. Затухання коливань зд = 10;йснюється завдяки дії сил сухого тертя в механічній частині приводу. Слі= 076; зауважити, щ= 086; здатність с = 80;стеми до коливань зменшуєтьсn= 3; із зростанн = 03;м величини γ. Ц= 077; ілюструє ри = 89;. 3.1, на якому наk= 4;едені графіки перехідних процесів у д= 074;омасовій системі електроприk= 4;оду, що враховує наявність зазору в редукторі, при трьох значеннях коефіцієнтm= 1; моменту пружності. Найбільшу схильність до коливань демонструє система з γ =3D 1.2, при
γ =3D 10 перехідний процес носить аперіодичнl= 0;й характер.=

Рисунок 3.1 – Відпрацьовm= 1;вання завдання на = 096;видкість двомасовою системою електроприk= 4;оду

Такі ознаки властиві цілій низці слідкуючих приводів у широкому діапазоні потужностеl= 1;. До цього класу належать, наприклад, е= 083;ектроприво&= #1076;и радіотелесl= 2;опів, антен, соняч= 085;их печей. При складанні математичнl= 0;х моделей так = 80;х приводів досить часто потрібно враховуватl= 0; вплив таких = 103;вищ, як зазор у редукторі, дія сил сухого терт = 03;, наявність еластичносm= 0;і механічногl= 6; вала.

Наявність еластичносm= 0;і притаманна багатьом типам передавальl= 5;их ланцюгів – довгим вала = 84;, пружинам, пасовим передачам. Ц= 110; ланцюги мають еластичні й коливальні властивостo= 0;, які не можна ігнорувати. При наявності таких ланцюгів в механічній частині електроприk= 4;оду при перенос = 10; моменту виникає перекручувk= 2;ння вала. Це явище призводить, = 079; одного боку, до появи кол= 080;вань, з іншого, до перевантажk= 7;ння передавальl= 5;их пристроїв т = 72; самого електродвиk= 5;уна. В системах регулюваннn= 3; положення будь-які кол= 080;вання вихідної величини взагалі неп = 88;ипустимі, тому що ці системи мають здебі = 83;ьшого досить високі вимоги до точності.=

На рис. 3.2 наведене зображення моделі двомасової = 89;истеми. Електродвиk= 5;ун та робоча машина поєд = 85;ані між собою за допомогою еластичногl= 6; вала.

Рису&= #1085;ок 3.2 – Двомасова система електроприk= 4;оду

Припу&= #1089;тимо, що маса вала дорівнює нулю. Рівнян= 085;я руху систем = 80; має вигляд:

де J1 – сумарний момент інерції з боку двигун = 72;;

J2 – сумарний момент інерції з боку робочо = 11; машини, приведений до швидкост = 10; двигуна;

m – момент двигуна;

mO – момент опор = 91;;

ω1 – швидкість двигуна;

ω2 – швидкість робочої машини, приведена д = 86; швидкості д = 74;игуна.

Елас&#= 1090;ичний вал з коефіцієнтl= 6;м жорсткості С переносить обертаючий момент m12:

Цикл&#= 1110;чна частота власних незатухаючl= 0;х коливань системи [3]:

Доси&#= 1090;ь часто при аналізі систем електроприk= 4;оду необхідно враховуватl= 0; вплив сил сухого терт = 03; та залежног = 86; від швидкості моменту демпфіруваl= 5;ня. Обертаючий момент сухого терт = 03; визначаєтьl= 9;я за формулою:

де К= 058; – коефіцієн = 90; сухого терт = 03;.

Моме&#= 1085;т демпфіруваl= 5;ня визначаєтьl= 9;я за формулою:

В деяких механічних передавальl= 5;их ланцюгах досить част = 86; спостерігаn= 2;ться зазори. При цьому в динамічномm= 1; режимі не відбуваєтьl= 9;я жорсткий перенос моменту в межах кута ±Δα. Результатоl= 4; цього є те, що при лінійні = 81; зміні вхідної величини вихідна величина є нелінійною, внаслідок чого виника = 08; часовий зсу = 74; фаз між вхідною та вихідною ве = 83;ичинами та усталена помилка (рис. 3= .3).

Рисунок 3.3 – Вплив зазорів

 

Стру&#= 1082;турна схема механічної частини сис = 90;еми електроприk= 4;оду, складена згідно з рівняннями (3.2= ), (3.3) з врахуванl= 5;ям дії моменту сухого терт = 03; (3.5), моменту де = 84;пфірування (3.6) та зазору в редукторі наведена на рис. 3.4 [3].

Зваж&#= 1072;ючи на усі вказані особливостo= 0; двомасової системи, слі= 076; зазначити, щ= 086; побудова класичних регуляторіk= 4; для неї, які б враховувалl= 0; вплив нелінійносm= 0;ей, є досить складним завданням, яке не завжд= 080; має однозначне рішення. Мет= 086;ди фаззи-логік = 80;, які засновані н = 72; обробці нечіткої інформації, дають при регулюваннo= 0; значно кращ = 10; результати, особливо ко = 83;и до контуру регулюваннn= 3; входять також і клас= 080;чні регулятори, оптимізоваl= 5;і за традицій = 85;ими методами (модульний оптимум, сим= 077;тричний оптимум, настроюванl= 5;я за мінімумо = 84; резонансноk= 5;о максимуму), що дозволяє поєднати достоїнствk= 2; класичної концепції р = 77;гулювання та методів, які засновані н = 72; теорії штучного інтелекту. Треба зауважити, щ= 086; фаззи-логік = 72; в "чистому вигляді" використовm= 1;ється зараз дуже обмежено, набагато перспективl= 5;ішим є її поєднання і = 79; нейросіткаl= 4;и, що дозволяє створювати гнучкі системи регулюваннn= 3;, здатні до самонастроn= 2;вання.

 

 

Рисуl= 5;ок 3.4 – Структурна схема механічної частини двомасової системи електроприk= 4;оду

 

3.2 Лабораторнl= 0;й практикум

 

= 051;абораторна робота 1. Використанl= 5;я неадаптивнl= 6;го фази-регуля = 90;ора в системі автоматизаm= 4;ії

 

1 Постановка завдання<= /b>

Об'єк&= #1090;ом дослідженнn= 3; є електроприk= 4;ід постійного струму, що приводить д = 86; руху робочу = 084;ашину (параметри системи представлеl= 5;і в табл. 3.1).

 

Таб&= #1083;иця 3.1 – Параметри системи, що підлягає до = 89;лідженню

<= o:p> 

Найменуван= ;ня параметру

Ч&= #1080;слове значення

Одиниця виміру

Номінальна потужність електродви= 075;уна P

160

кВ

Кількість пар полюсів 2p

6

−

Номінальни= ;й струм електродви= 075;уна I

390

A

Номінальна напруга електродви= 075;уна U

440

В

Номінальна частота обертання електродви= 075;уна n

 <= /span>

980

 <= /span>

об/= 093;в

Величина опору якірного ланцюга RЯ

0,025

Ом

Момент інерції електродви= 075;уна J1=

58,7

кг.м2

Стала двигуна k

4,18

В.с

Стала часу якірного ланцюга TЯ

82

мс

Механічна стала часу TM

84

мс

Коефіцієнт підсилення перетворюв= 072;ча KП=

68,35

В

Стала часу перетворюв= 072;ча TП

1,7

мс

Коефіцієнт жорсткості вала = 57;

2,06.105

Н.м

Момент інерції робочої машини J2

29,35

кг.м2

 

Мате&#= 1084;атична модель системи складаєтьсn= 3; з урахування= 084; еластичних властивостk= 7;й довгого вал = 72;, наявності зазору в редукторі т = 72; дії моменту сил сухого терт = 03; в двигуні та робочому механізмі. Система міс = 90;ить класичні регулятори струму, швид= 082;ості двигуна та положення, які оптимізоваl= 5;і за модульни = 84; оптимумом (табл. 3.2). Структурна схема системи, що підлягає дослідженнn= 2;, надається н = 72; рис. 3.6.

&= #1058;аблиця 3.2 – Розрахунок системи підпорядкоk= 4;аного регулюваннn= 3; положення<= /span>

 

Рег= улятор

Розрахунок параметрів

= 55;І-регулятор струму

<= /sub>

= 55;-регулятор швидкості

<= /sub>

= 55;-регулятор положення

<= /sub>

 

Зада&#= 1085;е значення вихідної величини системи змінюється за лінійним законом.

Сист&#= 1077;ма, що підлягає розгляду, ма= 108; високі вимо = 75;и до точності, тому що йдеться про регулюваннn= 3; положення, а будь-які коливання т = 72; усталена помилка в цьому випадку є неприпустиl= 4;ими. Класичні регулятори не здатні за= 073;езпечити задовільну точність (рис. 3.5). Одним із засобів покращення передавальl= 5;их властивостk= 7;й системи є застосуванl= 5;я фази-регуля = 90;ора. Пропонуєтьl= 9;я використатl= 0; неадаптивнl= 0;й фази-регуля = 90;ор, що підключа = 08;ться паралельно до класичного регулятора положення (рис. 1.15). Така система регулюваннn= 3; є досить стабільною та дозволяє значно покращити вид перехідногl= 6; процесу, отримавши н = 72; виході системи майже експоненціk= 2;льну криву вихідної величини – кута повороту ро = 73;очого механізму.

Рисун&#= 1086;к 3.5 – Перехідні процеси в двомасовій системі електроприk= 4;оду підпорядкоk= 4;аного регулюваннn= 3; з класичним = 80; регулятораl= 4;и



3D"Подпись:3D"П=

Двl= 0;гун
 

Роk= 3;очий механізм
 

Рисунок 3.6 – Структурна схема системи електропри= воду постійного струму з врахування= м еластичних властивост= ей довгого вала, наявнl= 6;сті зазору в редукторі та дії моменту сил сухого тертя в двигуні та робочому ме= ;ханізмі
 
2 Мета роботи

Мета лабораторнl= 6;ї роботи полягає в дослідженнo= 0; системи еле = 82;троприводу постійного струму за допомогою програмногl= 6; пакета Matlab/Simulink з метою порівняння передавальl= 5;их властивостk= 7;й системи з підпорядкоk= 4;аним регулюваннn= 3;м положення з класичними ПІ-регулято = 88;ом струму і П-регулятор = 72;ми швидкості і положення т = 72; системи з поєднанням класичного підпорядкоk= 4;аного регулюваннn= 3; і фази-корекц = 10;ї.

 

3 Зміст роботи

3.1    Досл= ідження системи електроприk= 4;оду з класичною структурою підпорядкоk= 4;аного регулюваннn= 3;:

ü   запустити середовище програмуваl= 5;ня Мatlab 5.2;

ü   ввійти до програмногl= 6; пакету Simulink, набравши = 74; командному рядку команду simulink;

ü   додати директорію x:\...\alex до списку активних директорій, для чого виб= 088;ати в меню File→Set Path. Після цього відкриєтьсn= 3; вікно списк = 91; активних директорій (Path Browser), в якому слід вибрати в меню Path&= #8594;Add to Path та ввести шлях до директорії x:\...\alex;

ü   відкрити в середовищі Simu= link файл x:\..= .\alex\system.mdl;

ü   ввести параметри системи, що підлягає до = 89;лідженню, до робочого простору Мatlab 5.2, для чого клацнути двічі лівим клавішем миші на блоц= 110; Enter Parameter. Встановленo= 0; параметри можна переглянутl= 0; в робочому просторі Мatlab;

ü   промоделю&#= 1074;ати систему, для чого в меню Simulink вибрати Simulation→Start;

ü   проаналіз&#= 1091;вати результати моделюваннn= 3;, для чого клацнути двічі лівим клавішем ми = 96;і на блоці Plot, який виконує функції виводу на екран графі = 82;ів величин, що мають бути проаналізоk= 4;ані – завдання н= 072; положення, положення двигуна, положення робочого механізму, помилки рег = 91;лювання й її похідної, швидкості двигуна та переданого через редуктор моменту m12. За допо = 84;огою графіків визначити величину пе = 88;ерегулюван&#= 1085;я положення робочого механізму, інтервал зміни швидкості двигуна, пом= 080;лки регулюваннn= 3; й її похідної;

ü   зафіксува&#= 1090;и результати моделюваннn= 3;.

 

 

 

3.2    Досл= ідження системи електроприk= 4;оду з класичною структурою підпорядкоk= 4;аного регулюваннn= 3; та паралельноn= 2; фази-корекц = 10;єю

3.2.1       Розр= обка фази-регуля = 90;ора

Процес розробки фази-регуля = 90;ора здійснюєтьl= 9;я за алгоритмом, розглянутиl= 4; у розділі 1.3 (рис. 1.12).

1.     Проведенн&#= 1103; аналізу системи. Встановленl= 5;я структури контуру регулюваннn= 3; та вхідних і вихідних величин фази-регуля = 90;ора.

Обир&#= 1072;ється одна з найбільш стабільних та простих для настроюванl= 5;я структур – контур з паралельноn= 2; фази-корекц = 10;єю, загальна ст = 88;уктура якого представлеl= 5;а на рис. 1.15). Фази-&= #1088;егулятор підключаєтn= 0;ся паралельно до класично = 75;о регулятора положення. Вхідними величинами фази-регуля = 90;ора є помилка регулюваннn= 3; положення робочого механізму
(αза= ;в-α2) та похідна від неї (αзаk= 4;-α2)'. Вихідною величиною фази-контро = 83;ера є коригува= 083;ьний сигнал, який складаєтьсn= 3; з вихідним сигналом традиційноk= 5;о пропорційнl= 6;го регулятора положення. Сума цих сигналів утворює завдання на = 096;видкість двигуна.

2.     Встановле&#= 1085;ня алгоритмічl= 5;их ступенів св = 86;боди.

Прак&#= 1090;ика показує, що на етапі моделюваннn= 3; тип фази-інфере = 85;ції не грає великої рол = 10; (це можна легко перевірити, = 087;роексперим&= #1077;нтувавши за допомого = 02; редактора фази-блоків Fuz= zy Logic Toolbox). Вибір операторів інференції має велике значення лише при пра= 082;тичній реалізації фази-блока, тому що він в&#= 1080;значає швидкодію контуру регулюваннn= 3; та стабільнісm= 0;ь передавальl= 5;их властивостk= 7;й фази-блока. Проте рекомендуєm= 0;ься дотримуватl= 0;сь певних рекомендацo= 0;й і використо = 74;увати загальнопрl= 0;йняті сполучення операторів окремих етапів інференції (= 090;абл. 1.7). Для проектованl= 6;го фази-блока пропонуєтьl= 9;я використатl= 0; такі установки:

= üоперато= 088; імплікації R= 11; мінімум-опе = 88;атор;

= üоперато= 088; агрегації – максимум-оп = 77;ратор.

Реком&= #1077;ндується використатl= 0; найбільш по = 87;улярний метод дефазифікаm= 4;ії - гравітацій= 085;ий (centroid).

3     Встановле&#= 1085;ня параметричl= 5;их ступенів св = 86;боди.

Цей етап є центральниl= 4; кроком процесу роз = 88;обки фази-регуля = 90;ора, він складаєтьсn= 3; з трьох крок= 110;в.

3.1       h= 2;становленн= 103; можливих інтервалів зміни вхідн = 80;х та вихідних величин

Резу&#= 1083;ьтати моделюваннn= 3; системи з класичною системою регулюваннn= 3; дозволяють визначити інтервали зміни вхідних та вихідних величин. Помилка рег = 91;лювання змінюється = 74; інтервалі [-0.5,0.5], похідна від неї змінюється = 74; інтервалі [-10,10]. Сумісний аналіз кривих змін = 80; помилки рег = 91;лювання, її похідної та швидкост = 10; двигуна дають можливість визначити інтервал зм = 10;ни вихідної величини як [-100,100].

 

3.2       h= 2;становленн= 103; форми та параметрів функцій приналежноl= 9;ті

Вхід&#= 1085;им змінним Error (помилка регулюваннn= 3;) та D-Error (похідна помилки регулюваннn= 3;) відповідає = 87;'ять лінгвістичl= 5;их термів:

ü     PL – Positive Large (позитивна велика);

ü     Р – Positive (позитивна);

ü     Z – Zero (нуль);

ü     N – Negative (негативна);

ü     NL – Negative Large (негативна велика).

Форм&#= 1072; граничних термів PL та NL приймаєтьсn= 3; трапецієпоk= 6;ібною (прямокутна трапеція, прямий кут якої відповідає точці на меж= 110; області визначення змінної). Фор&#= 1084;а термів Р, Z, N приймаєтьс= ;я трикутною. Трикутна та трапецієпоk= 6;ібна форми функцій приналежноl= 9;ті вживаються = 74; техніці регулюваннn= 3; найчастіше, тому що це дозволяє зменшити витрати машинного ч = 72;су.

Гран&#= 1080;ці термів були спочатку встановленo= 0; приблизно в межах інтервалів зміни вхідн = 80;х величин та визначені остаточно після моделюваннn= 3; системи. Остаточно прийняті дл = 03; лінгвістичl= 5;их змінних Error та D= -Error функції приналежноl= 9;ті зображені н = 72; рис. 3.7 та рис. 3.8, k= 2; параметри ї = 93; термів представлеl= 5;і в табл. 3.3-3.4.

 

 

Рисунок 3.7 – Функція приналежноl= 9;ті вхідної змінної Error

 

Табл&#= 1080;ця 3.3 – Параметри функції приналежноl= 9;ті вхідної змінної Error

 

Терм

Форма терму

Характерні точки

NL (Negative Large)

трапеція

[-0.5, -0.5, -0.14, -0.07]

N (Negative)

трикутник

[-0.14, -0.07, 0]

Z (Zero)

трикутник

[-0.005, 0, 0.005]

Р (Positive)

трикутник

[0, 0.07, 0.14]

PL (Positive Large)

трапеція

[0.07, 0.14, 0.5, 0.5]

 

 

Рисунок 3.8 – Функція приналежноl= 9;ті вхідної змі = 85;ної D-Error

 

Табл&#= 1080;ця 3.4 – Параметри функції приналежноl= 9;ті вхідної змінної D-Error

Терм

Форма терму

Характерні точки

NL (Negative Large)

трапеція

[-10, -10, -2 -1]

N (Negative)

трикутник

[-2, –1, 0]

Z (Zero)

трикутник

[-0.25, 0, 0.25]

Р (Positive)

трикутник

[0, 1, 2]

PL (Positive Large)

трапеція

[1, 2, 10, 10]

 

Вихі&#= 1076;ній змінній Korrektion (корекці&#= 1103;) відповідає дев'ять лінгвістичl= 5;их термів:

ü     PL – Positive Large (позитивна велика);

ü     PМ - Positive Middle (позитивна середня);

ü     PS - Positive Small (позитивн= 072; маленька);

ü     Р – Positive (позитивна);

ü     Z – Zero (нуль);

ü     N – Negative (негативна);

ü     NS – Negative Small (негативна маленька);

ü     NМ – Negative Middle (негативна середня);

ü     NL – Negative Large (негативна велика).

Як і у випадку вхідних змінних, форма грани = 95;них термів PL та NL приймаєтьсn= 3; трапецієпоk= 6;ібною, а форма "вну = 90;рішніх" термів PМ, PS, Р, Z, N, NS, NМ - трикутною. Обрати параметри термів для в= 080;хідної змінної складніше, ніж для вхідних змі = 85;них, точно встановити їх можна лиш= 077; після багаторазоk= 4;ого моделюваннn= 3;. Остаточно приймаєтьсn= 3; функція приналежноl= 9;ті, що зображен = 72; на рис. 3.9. Параметри функції при = 85;алежності лінгвістичl= 5;ої змінної Korrektion подаються в табл. 3.5.

 

 

Рисунок 3.9 – Функція приналежноl= 9;ті вихідної змінної Korrektion

 = ;

&= #1058;аблиця 3.5 – Параметри функції приналежноl= 9;ті вихідної змінної Korrektion

<= o:p> 

Терм

Форма терму

Характерні точки

NL (Negative Large)

трапеція

[-8, -8, –5.61, –3.77]

NМ (Negative Middle)

трикутник

[-5.6, -4, -2.4]

NS (Negative Small)

трикутник

[-4, -2.4, -0.8]

N (Negative)

трикутник

[-2.38, -0.8, 0]

Z (Zero)

трикутник

[-0.8, 0, 0.8]

Р (Positive)

трикутник

[0, 1.312, 2.624]

PS (Positive Small)

трикутник

[1.39, 2.83, 4.05]

PМ (Positive Middle)

трикутник

[2.64, 3.97, 5.65]

PL (Positive Large)

трапеція

[4.064, 5.44, 8, 8]

3.3       i= 7;кладання бази фази-правил

Прав&#= 1080;ла складаютьсn= 3; на основі інтуїтивниm= 3; знань експерта. В нашому випадку як експертні знання використовm= 1;ються результати аналізу перехідних процесів, що були отримані пр = 80; моделюваннo= 0; системи з кл= 072;сичною системою регулюваннn= 3;. Деякі прави = 83;а після моделюваннn= 3; системи з паралельноn= 2; корекцією можуть бути уточненими.

Прин&#= 1094;ип складання ф = 72;зи-правил ілюструєтьl= 9;я за допомого = 02; рис. 3.10, на яком= 091; представлеl= 5;ий перехідний процес у системі з класичним регулятороl= 4;. Як зазначал = 86;ся вище, завдання паралельноo= 1; фази-корекц = 10;ї полягає в покращенні вигляду пер = 77;хідного процесу, зменшенні величини перерегулюk= 4;ання в ідеальном = 91; випадку до нуля. Тому найбільш небажаною є ділянка перехідногl= 6; процесу, кол= 080; величина кута повороту пе = 88;евищує величину завдання на кут поворот = 91;. На рис. 3.10 виділена саме ця ділянка та наведені у масштабі збільшення відповідні фрагменти кривих змін = 80; помилки регулюваннn= 3;, її похідної та швидкост = 10; двигуна.

Розг&#= 1083;янемо точки 1, 2, 3. В точці 1 помилка регулюваннn= 3; позитивна, а її похідна негативна в = 77;лика. Це означає, що помилка регулюваннn= 3; має тенденцію д = 86; зменшення, тому корекція ма = 08; бути незначна. Знак корекції +, тому що із кривої швид = 82;ості двигуна видно, що поблизу точки 1 швидк&#= 1110;сть зменшуєтьсn= 3;, тобто рух сповільнюєm= 0;ься, а його треба прискорити, щоб зменшит = 80; величину помилки. Отримуємо таке правил = 86;:

= ЯКЩО Помилка регулюваннn= 3; Позитивна І Пох = 10;дна помилки регулюваннn= 3; Негативна В = 77;лика, ТО Корекція Позитивна.=

В точці 2 помилка регулюваннn= 3; негативна т = 72; має досить велике числове значення, а її похідна майже дорівнює нуля, тобто помилка рег = 91;лювання поблизу точки 2 змінюється незначно. Це означає, що корекція не має бути досить сильною. Зна= 082; корекції визначимо, проаналізуk= 4;авши графік швидкості двигуна. Поблизу точки 2 швидк&#= 1110;сть двигуна негативна, тому для компенсаціo= 1; корекція ма = 08; бути позитивною R= 11; Р. Таким чином, отримуємо правило:

= ЯКЩО Помилка регулюваннn= 3; Негативна І Похідна помилки регулюваннn= 3; Нульова,
ТО Корекція Позитивна.=

В точці 3 помилка регулюваннn= 3; позитивна, а її похідна позитивна т = 72; має досить велике числ = 86;ве значення, тобто поблизу точки 3 помил&#= 1082;а регулюваннn= 3; має тенденцію д = 86; подальшого зростання. Виходячи з цього, можна стверджуваm= 0;и, що корекція має бути негативною = 79; метою обмеження швидкості. Аналіз кривої швид = 82;ості показує, що величина цієї корекції не має бути дуж= 077; великою, том= 091; що швидкіст = 00; на цій ділянці вже = 108; негативною = 10;, надмірно її знизивши, можна отримати велике значення перерегулюk= 4;ання. Таким чином отримуємо д = 74;а правила:

= ЯКЩО Помилка регулюваннn= 3; Позитивна І Похідна помилки регулюваннn= 3; Позитивна, ТО Корекція Негативна Маленька.=

=  

= ЯКЩО Помилка регулюваннn= 3; Позитивна І Похідна помилки регулюваннn= 3; Позитивна Велика, ТО Корекція Негативна Середня.

Скла&#= 1076;ені таким чином та уточнені після модел = 02;вання правила наведені в табл. 3.6.

 

Рису = 85;ок 3.10 – Перехідні процеси в двомасовій системі електроприk= 4;оду постійного струму

 

<= o:p> 

&= #1058;аблиця 3.6 – Фази прави= ;ла

 

 

 

Error

D-Error

 

PL

P

Z

N

NL

 

PL

NL

NM

Z

N

Z

 

P

NM

NS

Z

Z

P

 

Z

PM

PS

Z

P

PS

 

N

N

Z

Z

PS

PM

 

NL

Z

P

Z

PM

PL

 

 

3.2.2       Моде= лювання системи електроприk= 4;оду з класичною системою підпорядкоk= 4;аного регулюваннn= 3; та паралельноn= 2; фази-корекц = 10;єю:

ü      = створити з&= #1072; допомогою Fuzzy Logic Toolbox фаззи-блок з параметрамl= 0;, що наведені = 074; пункті 3.2.1. Утворену FIS-матрицю зберегти на = 078;орсткий диск та в робочий простір Matlab;

ü      = вставити д&= #1086; Simulink-моделі, що міститься в файлі x:\...\alex\system.mdl, паралельно до пропорційнl= 6;го регулятора положення фази-блок (Fuzzy Logic Controller або Fuzzy Controller with ruleviewer). Запараметрm= 1;вати цей блок;

ü      = зберегти н&= #1072; жорсткий диск створену Simulink-модель під іменем system1.mdl;

ü      = промоделю&#= 1074;ати систему;

ü      = за допомогою блока Plot вивести на екран графіки завдання на положення, положення двигуна, положення робочого механізму, п= 086;милки регулюваннn= 3; та її похідної, швидкості двигуна й переданого через редуктор моменту m12;

ü      = зафіксува&#= 1090;и результати моделюваннn= 3;;

ü      = порівняти результати, що були отримані в п= 077;ршій частині лабораторнl= 6;ї роботи, з результатаl= 4;и моделюваннn= 3; системи з паралельноn= 2; фази-корекц = 10;єю, зробити висновки.

&nbs= p;

&nbs= p;

&nbs= p;

4&nb= sp;            =     Зміст звіту

= В звіті повинні бут = 80; представлеl= 5;ими:

ü     структу = 88;на схема системи, що підлягала д = 86;слідженню;

ü     парамет = 88;и фази-регуля = 90;ора для паралел = 00;ної корекції – функції приналежноl= 9;ті лінгвістичl= 5;их змінних, фази-правил = 72;, тривимірніl= 1; графік передавальl= 5;ої функції фаз = 80;-блока;

ü     графіки зміни завдання на положення, положення двигуна, положення робочого механізму, помилки регулюваннn= 3; й її похідної, шв= 080;дкості двигуна та переданого через редуктор моменту m12 для системи електроприk= 4;оду з класичною = 087;ідпорядков&= #1072;ною системою регулюваннn= 3; та для системи з паралельноn= 2; фази-корекц = 10;єю;

ü     аналіз результатіk= 4;.

 

Лаборато= ;рна робота 2. Адаптація фази-логіки = 074; системах регулюваннn= 3;

 

1 Постановка завдання<= /b>

= Розглянута в попередні = 81; лабораторнo= 0;й роботі система регулюваннn= 3; з неадаптивнl= 0;м фази-регуля = 90;ором має декільк = 72; недоліків. Н= 072;самперед це її негнучкістn= 0;  та віk= 6;сутність особливої точності. Це є її основно= 102; вадою, яка зумовлює неможливісm= 0;ь використанl= 5;я фази-систем = 091; “чистому вигляді” дл = 03; виконання такого, напр= 080;клад, завдання, як точне позиціюванl= 5;я.

     &nb= sp;      Щоб зробити фази-систем = 91; більш досконалою, було запропоновk= 2;но об’єднати ї = 11; з іншими формами штучного інтелекту, які дозволя = 02;ть зробити сис = 90;ему фази-регулю = 74;ання більш гнучкою. В ці&#= 1081; роботі підлягає розгляду подібне об’ = 08;днання фази-систем = 80; з нейросіткаl= 4;и [9], а точніше з алгоритмамl= 0; навчання та тренування нейросіток.

Об’єкт&#= 1086;м досліджень = 08; система електроприk= 4;оду підпорядкоk= 4;аного регулюваннn= 3; швидкості. Як і в попередній роботі, з метою покращення якості роботи в систему вводиться паралельна фази-корекц = 10;я, що зумовлен = 72; необхіднісm= 0;ю демпфіруваl= 5;ня внутрішніх коливань в системі. Проте така система має невелику швидкодію, особливо коли йдетьс = 03; про відпрац = 00;овування стрибкоподo= 0;бного завдання. Причиною є класичний ПІ-регулято = 88; швидкості, який настроюєтьl= 9;я таким чином, щоб забезпечитl= 0; аперіодичнl= 0;й перехідний = 87;роцес в лінійній системі. Система відпрацьовm= 1;є завдання бе = 79; коливань, проте потре = 73;ує багато часу, що не є бажаним в слідкуючих системах. З м&#= 1077;тою виправленнn= 3; цього недоліку в систему вводяться 2 пропорційнl= 6;інтегральн= 110; фази-регуля = 90;ори, що здійснюють адаптацію класичного ПІ-регулято = 88;а швидкості. Один із них є неадаптивнl= 0;м фази-регуля = 90;ором (регулятор с= 090;алої часу), а інший (фази-регуля= 090;ор коефіцієнтm= 1; підсилення) має спроможнісm= 0;ь до самоадап = 90;ації. Причиною того, що фази-регуля = 90;ор сталої часу не потребує адаптації, є те, що зміна сталої часу пропорційнl= 6;інтегральн= 086;го регулятора = 91; відносно малих межах несуттєво впливає на процес регулюваннn= 3;, тому цим впл= 080;вом можна знехтувати.

Для адаптивногl= 6; регулятора сталої часу = 074;икористову&= #1108;ться непряма стратегія адаптації, щ= 086; ґрунтуєтьсn= 3; на моделі процесу (рис. 1.18). Як модель процесу виступає цільова фун = 82;ція, яку необхід = 85;о отримати на виході системи після певно = 11; кількості тренувань системи.

Структ&#= 1091;рна схема системи регулюваннn= 3;, що підлягає дослідженнn= 2;, надається н = 72;
рис. 3.11.

 

Рисун&#= 1086;к 3.11 – Структурна схема контуру рег = 91;лювання системи електроприk= 4;оду з адаптивни = 84; класичним ПІ-регулято = 88;ом та паралельноn= 2; фази-корекц = 10;єю

 

2 Мета роботи

М= 077;та лабораторнl= 6;ї роботи полягає в дослідженнo= 0; системи електроприk= 4;оду постійного струму за допомогою програмногl= 6; пакета Matlab/Simulink з метою порівняння ефективносm= 0;і використанl= 5;я двох різних = 072;лгоритмів навчання нейросіток (методу Відр= 086;у – Хоффа та методу Кохонена) дл= 103; адаптації фази-регуля = 90;орів в системах регулюваннn= 3; електроприk= 4;одів.

&nbs= p;

&nbs= p;

3 Теоретична частина

3.1 = Основи теорії нейросіток=

3.1.1 Біологічна та математичнk= 2; моделі нейр = 86;на

Нейросітки - це системи, що використовm= 1;ють деякі з відо= 084;их принципів організаціo= 1; людського мозку і базуються н = 72; біологічниm= 3; моделях [7]. Док= ;ладний розгляд цих біологічниm= 3; моделей доз = 74;оляє порівняти мозок людин = 80; або високо розвиненої тварини з комп'ютером. Найважливіm= 6;им результатоl= 4; такого порівняння = 08; висновки відносно паралельноo= 1; структури я = 82; першого, так і останньог = 86;, бо це робить можливим здійснюватl= 0; у комп'ютері імітацію роботи біологічниm= 3; нервових систем, а це, в свою чергу, дозволяє надати комп’ютеру таку власти = 74;ість, як спроможнісm= 0;ь до навчання.

Першою спроможною до навчання нейросіткоn= 2; був перцептрон, який базувався н = 72; аспектах відпрацьовm= 1;вання та збереження інформації. За допомого = 02; правил навчання після певно = 11; кількості тренувань перцептрон = 89;тавив у відповідніl= 9;ть вхідним величинам бажані вихідні. Про= 090;е ця нейросітка не була спроможна вирішувати більш важливі проблеми, що спонукало д = 86; розробки нових більш потужних нейросіток та пошуку нових прави = 83; навчання.=

  = ;          У протиріччя до біології або до нейрології для нейрона = 085;е використовm= 1;ється модель, яка чітко опису = 08; всі його аспекти, а тільки та модель, що са&#= 1084;а по собі є дуже грубим узагальненl= 5;ям [10]. Традиційна модель нейрона, яка представлеl= 5;а на рис. 3.12, розглядаєтn= 0;ся тут як різновид су = 84;атора з граничним значенням н = 72; його виході.

Б= іологічний нейрон складаєтьсn= 3; з тіла нейро= 085;а, до якого входить велика кількість д = 77;ндритів (від 10000 до 100000) і виходить тільки один = 072;ксон. Якщо сума вхідних сигналів перевищує певну межу (у випадку біологічноk= 5;о нейрона - граничний потенціал), то нейрон активізуєтn= 0;ся і посилає через вихід = 85;ий провідник (аксон) короткочасl= 5;ий електричниl= 1; імпульс до інших нейро = 85;ів [11]. Таким чиноl= 4;, нейрон явля = 08; собою проце = 89;ор з єдиною спроможнісm= 0;ю - посилати електричні імпульси залежно від суми вхідни = 93; сигналів.=

 

Рисунок 3.12 - Біологічна та математичнk= 2; моделі нейрона

 

М= іж входом одного нейрона (дендритом) та виходом попередньоk= 5;о (аксоном) є ще одна клітин = 72;, яка може підсилюватl= 0; або подавляти с = 80;гнал, який до неї надходить. Ц= 103; клітина наз = 80;вається сінапс і знаходитьсn= 3; найчастіше просто на тілі нейрон = 72;. Для процесу навчання сінапс має дуже велике значення, тому що з часом він може змінювати свою власти = 74;ість підсилюватl= 0; або подавляти сигнал.

Комуl= 5;ікація між нейронами завжди відбуваєтьl= 9;я тільки в такому напрямку:=

Сіна= 087;с → Дендрит → Тіло нейрона → Аксон = → Сінап&= #1089; і т. д.

Ш= тучний нейрон можн = 72; представитl= 0; як процесор, який прийма = 08; тільки два стани - активний та пасивний. Тому відповідно до бінарної логіки надамо активному стану значення 1, а пасивно= 084;у стану значення 0. Вхідними сигналами нейрона є імпульси, що &#= 1087;ередаються через дендрити, які, в свою чергу, є виходами інших нейронів. Проте перед = 090;им, як досягти тіла нейрон = 72;, вхідні сигнали про = 93;одять через сінапси. Цього можна легко досягти шляхом множ = 77;ння вхідних сигналів на позитивне (ефект підсилення) або негативне (ефект ослаб= 083;ення) число. Ці числа отримали назву вагов = 80;х коефіцієнтo= 0;в.

С= игнал на виході нейрона з’являєтьсn= 3; тільки тоді, коли сума всіх вхідни = 93; сигналів пе = 88;евищує певне граничне значення. Пр= 080; побудові моделі нейрона це досягаєтьсn= 3; шляхом порівняння суми множення всіх вхідни = 93; сигналів на величини сінапсів аб = 86;, що одне й те саме, на відповідні вагові коефіцієнтl= 0; з граничним значенням. Якщо сума більша, ніж г&#= 1088;аничне значення, то на виході нейрона буд = 77; встановленl= 6; одиницю, а якщо ні - то нуль. Наочно модель нейрона представлеl= 5;а на рис. 3.13.

Рисунок 3.13 - Функціоналn= 0;на модель нейрона

Для урахування граничного значення пр = 80; підсумовувk= 2;нні вхідних сигналів вводиться допоміжний вхід h= 2; – біас.=

В= 093;ідні сигнали Х1,…Хn m= 0;а В) проходять через вагов = 10; коефіцієнтl= 0; W(1,1),…W= (1, n+1), підсумовуюm= 0;ься і проходять через перед = 72;вальну функцію F на вихід. Вхідне значення біасу завжд = 80; дорівнює одиниці.

Виход&= #1103;чи із схеми рис. 3= .13, значення на виході сума = 90;ора розраховуєm= 0;ься за формулою:

Ця функція називаєтьсn= 3; функцією активності [7].=

Значення на виході нейрона є функцією ві = 76; функції активності:

Як передавальl= 5;а функція мож = 77; бути викори = 89;тана одна із стандартниm= 3; функцій або будь-яка інша, на розсуд проектувалn= 0;ника нейросітки.

 

3.1.2 Нейросітка

Д= 083;я того, щоб отримати найпростішm= 1; нейросітку, треба об’єднати між собою декілька не = 81;ронів. На рис. 3.14 представлеl= 5;а нейросітка = 79; двома нейронами, яка має три входи (Х1, Х2 та В) та два виходи (Υ1 та= Υ2).

.

Р= 080;сунок 3.14 - Схема нейросітки=

Щодо параметрів нейронів, з яких будується нейросітка, немає жодни = 93; усталених законів або правил. Наприклад, передавальl= 5;і функції нейронів можуть бути однакові за = 089;воїм виглядом та параметрамl= 0; або відрізн = 03;тися одна від одної. Це стосується також і зв’я= 079;ків між нейронами, щ= 086; є дуже актуальним при розгляд = 10; багатошароk= 4;их нейросіток.

 

3.1.3 Правила навчання і тренування нейросіток

На= йважливішоn= 2; складовою частиною моделі нейр = 86;сітки є процес нав= 095;ання. Метою процесу навчання є визначення таких вагових коефіцієнтo= 0;в W(1,1),…W(1, n+1), при яких сітка буде реагувати заданими ви = 93;ідними значеннями на задані вхідні значення. Що= 073; досягати цього, необхідно н = 72; кожному етапі трену = 74;ання порівнюватl= 0; дійсне вихідне значення не = 81;росітки з бажаним і на підставі цього змінювати вагові коефіцієнтl= 0; таким чином, щоб на подальших етапах трен = 91;вання дійсне та бажане вихідне значення сх = 86;дилися [10].

Існує велика кількість правил тренування нейросіток, саме від них залежить швидкість т = 72; точність навчання, звичайно, за інших рівни = 93; умов. Тому виникає проблема пошуку оптимальноk= 5;о правила навчання, як= 077; б задовольняl= 3;о вимогам швидкості т = 72; точності процесу нав = 95;ання.

Одним з алгоритмі = 74; навчання є перцептрон. Правило перцептрон відповідає Δ-правилу аб = 86; правилу Відроу-Хофф = 72; і має такий математичнl= 0;й опис:

  = ;         

де&nb= sp;            =             &nb= sp;          wki,j,wk-1= i,j − нове і попереднє значення ва = 75;ових коефіцієнтo= 0;в;

хj = − вхідний сигнал;

аi = − бажаний вихідний сигнал;

уi<= /sub> − дійсний вих = 10;дний сигнал.

Інші правила є більш досконалимl= 0;, вони містят = 00; в собі параметр швидкості навчання аб = 86; коефіцієнт навчання і належать до так званого другого покоління правил тренування. Одним з цих правил є правило Відроу - Хофф&#= 1072;, яке має таки= 081; вигляд:

де lr - коефіцієнт навчання.=

Др= угий клас алгоритмів навчання містить низ = 82;у правил, що мають спроможнісm= 0;ь до самоадап = 90;ації. Найвідомішl= 0;м з них є правило Кох = 86;нена:

 

= 3.3    Адап= тація фаззи-логік = 80; в системах регулюваннn= 3;

Метою об’єднання фаззи-логік = 80; з іншими формами штучного інтелекту є удосконалеl= 5;ня фаззи-логік = 80;. В цій роботі розглядаєтn= 0;ся об’єднання = 92;аззи-систем&= #1080; з алгоритмамl= 0; навчання та тренування нейросіток.

      &nb= sp;     Як зазначалосn= 3; при розгляд = 10; теоретичниm= 3; основ фаззи-регул = 02;вання, форма термі = 74; вхідної фаззи-змінн = 86;ї, площа термі = 74; вихідної фаззи-змінн = 86;ї та значення діапазонів зміни цих змінних визначаютьl= 9;я спеціалістl= 6;м, виходячи з його досвід = 91; та знань в галузі, де застосовуєm= 0;ься фаззи-систе = 84;а. Але спеціал = 10;ст - це людина, а людині властиво по = 84;илятись. Тому необхідно ввести певн = 91; корекцію вихідного значення фаззи-регул = 03;тора у вигляді змінних коефіцієнтo= 0;в, щоб не змінювати в процесі роботи самі лінгвістичl= 5;і правила.

      &nb= sp;     Формуl= 3;а розрахунку вихідного значення фа = 79;зи-регулято&= #1088;а має такий вигляд:

де W1, W2 - корегувальl= 5;і коефіцієнтl= 0;.

П= 088;опонується змінювати коригувальl= 5;і коефіцієнтl= 0; за правилам = 80; тренування нейросіток. При застосуванl= 5;і, наприклад, алгоритму навчання Відроу-= Хоффа кориг&#= 1091;вальні коефіцієнтl= 0; вихідного значення фаззи-регул = 03;тора розраховуюm= 0;ься за формулою:

де   Хзав − завдання н= 072; вході системи регулюваннn= 3;;

Хціл= 100;  − цільовий процес;

Х − дійсний процес на виході системи (рис. 3.15).

 

Рисунок 3.15 - Структурна схема адаптивної фази-систем = 80; електроприk= 4;ода

 

Резул= ;ьтати роботи адаптивної системи мож = 85;а оцінити за допомогою рис. 3.16.

<= !--[if gte mso 9]> 1 - Вхідна дія; 2 - Цільовий процес;
3 - Ненавчена система

<= !--[if gte mso 9]> 1 - Вхідна дія; 2 - Цільовий процес;

3 - П’ята епоха тренування коефіцієнт= 091; підсилення (навчена система)

 

Рисунок 3.16 – Перехідні процеси в системі еле = 82;троприводу з адаптивно = 02; системою регулюваннn= 3;

Зап&= #1088;опонована методика самоадаптаm= 4;ії фаззи-регул = 03;тора в системах регулюваннn= 3; є дуже ефективною = 74; тому плані, що дозволяє = 072;втоматично коригувати всі недолік = 80; і вади, зроблені пр = 80; проектуванl= 5;і тієї чи іншо= 111; фази–систеl= 4;и, не змінюючи самої фази– = 89;истеми. Слід також додати, що завдяки об’ = 08;днанню алгоритмів навчання нейросіток = 10; фази–логікl= 0; остання стала більш досконалою = 10; набула суттєвого з = 85;ачення для вирішення широкого спектру про = 73;лем в електроприk= 4;оді на рівні з іншими форм = 72;ми штучного інтелекту.=

<= ![if !supportLists]>4      =            Зміст роботи

4.1 Дослідженнn= 3; ненавченої системи регулюваннn= 3;:

ü   запустити середовище програмуваl= 5;ня Мatlab 5.2;

ü   ввійти до програмногl= 6; пакету Simulink, набравши = 74; командному рядку команду simulink;

ü   перейти до директорії (x:\...\Kollarov) командним шляхом, набравши в командному = 88;ядку:

>cd x:\...\Kollarov;

ü  відк= рити в середовищ = 10; Мatlab файл x:\...\Kollarov\Gain.m. Впевнитись, що перед відповідниl= 4;и рядками фай = 83;а Gain.m, які наведені далі, стоять коментарі " % ":=

%   &n= bsp;     w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * u(1) * u(4);

%     &n= bsp;   w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * (u(1)-w_KPI(pg,qg));

ü   ввести параметри регуляторіk= 4; та всі інші д&#= 1072;ні, які знаходятьсn= 3; у файлі daten.m, в середо = 74;ище Мatlab 5.2;

ü   виконат = 80; одноразове моделюваннn= 3; системи і зафіксуватl= 0; результати.

4.2 Дослідженнn= 3; правила навчання Відроу - Хофф&#= 1072;:

ü   ввести параметри регуляторіk= 4; та всі інші д&#= 1072;ні, які знаходятьсn= 3; у файлі daten.m, в середовище Мatlab 5.2;

ü   змінити рядки файла Gain.m

%   &n= bsp;       w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * u(1) * u(4);

%   &n= bsp;       w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * (u(1)-w_KPI(pg,qg));

н= 072; рядки

w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * u(1) * u(4);=

%   &n= bsp;       w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * (u(1)-w_KPI(pg,qg));

ü   виконат = 80; послідовно чотири епох = 80; тренування системи шляхом чотирикратl= 5;ого запуску мод = 77;лювання, зберігаючи результати після першо = 75;о та четвертого моделюваннn= 3;;

4.3 Дослідженнn= 3; правила навчання Кохонена:=

ü   ввести параметри регуляторіk= 4; та всі інші д&#= 1072;ні, які знаходятьсn= 3; у файлі daten.m, в середовище Мatlab 5.2;

ü   змінити рядки файла Gain.m:

w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * u(1) * u(4);=

%   &n= bsp;       w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * (u(1)-w_KPI(pg,qg));

н= 072; рядки:

%   &n= bsp;       w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * u(1) * u(4);

w_KPI(pg,qg) =3D w_KPI(pg,qg) + LR_KPI * (u(1)-w_KPI(pg,qg));

ü   виконат = 80; послідовно десять епох тренування системи шляхом десятикратl= 5;ого запуску моделюваннn= 3;, зберігаючи результати після першого, четвертого та десятого моделюваннn= 3;.

 

5 Зміст звітm= 1;

= В звіті повинні бут = 80; представлеl= 5;ими:

ü   графік перехідногl= 6; процесу в ненавченій = 89;истемі, графік вхідної дії та цільовог = 86; процесу на одному рисунку;

ü   графік перехідногl= 6; процесу при першій та че= 090;вертій епохах тренування за правилом = 042;ідроу-Хоффа на одному рисунку з вхідною діє = 02;;

ü   графік перехідногl= 6; процесу при першій, четв= 077;ртій та десятій епохах тренування за правилом Кохонена на одному рисунку з вхідною діє = 02;;

ü   порівняль&#= 1085;і висновки ефективносm= 0;і використанl= 5;я цих двох алгоритмів навчання не = 81;росіток для адаптації ф = 72;зи-регулято&= #1088;ів у системах ре = 75;улювання електроприk= 4;одів у плані швидкості і точності адаптації.

     Drechsel, D. Regelbasierte Interpolation und Fuzzy Control. - Braubschweig/Wiesbaden: Friedr. Vieweg&Sohn Verlagsgesellschaft mbH. - 1996.

2.     Passino K. M., Yurkovitch. F= uzzy Control. - ADDISON-WESLEY. - 1998.

3.     Vogel J. u.a. Elektrische Antriebstechnik. – Berlin: Verlag Technik GmbH. - 1991.

4.     Kahlert J., Frank H. Fuzzy-L= ogik und Fuzzy-Control. Eine anwendungsorientierte Einführung mit Begleitsoftware. - Braubschweig/Wiesbaden: Friedr. Vieweg&Sohn Verlagsgesellschaft mbH. - 1993.

5.     К= 072;лашников В.И., Палис Ф. Введение в интелектуаl= 3;ьные системы программноk= 5;о управления R= 11; Донецк: ДонГТУ. - 1997.

6.     Fuzzy Logic Toolbox User’s Guide: MathWorks. - 1998.

7.       Brause R. Neuronale Netze: eine Einführung in die Neuroinformatik. - Stuttgart: Teubner. - 1991.

8.       Kruse R., Gebhardt J., Klawonn F. Fuzzy-Systeme.- Stuttgart: Teubner. - 1993.

9.       Nauk D., Klawonn F., Kruse R. Neuronale Netze und Fuzzy-Systeme, Grundlagen des Konnektionismus, Neuronaler Fuzzy-Systeme und der Kombination mit wissensbasierten Methoden. - Braunschweig: Teubner. - 1992.

10.    К= 072;лашников В.И., Денисенко И.В. Теория нейросетей. - Донецк: ДонГТУ. - 1997.

 

&nbs= p;

&nbs= p;

 

 

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<= !--[if supportFields]>PAGE=   4

ОСНОВИ ТЕОРІЇ ФАЗЗИ-ЛОГІК = 48; ТА ФАЗЗИ-РЕГУЛ = 70;ВАННЯ

3

ЗМІi= 7;Т

5

1 ОСНОВИ ТЕОРІЇ ФАЗЗИ-ЛОГІК = 48; ТА ФАЗЗИ-РЕГУЛ = 70;ВАННЯ

42

ОСНОВИ ТЕОРІЇ ФАЗИ-= 051;ОГІКИ ТА ФАЗИ-РЕГУЛЮ = 42;АННЯ

5

ВСТi= 9;П

33

1 ОСНОВИ ТЕОРІЇ ФАЗИ-ЛОГІКИ ТА ФАЗИ-РЕГУЛЮ = 42;АННЯ

43

2 МОДЕЛЮВАННk= 1; СИСТЕМ ФАЗИ-РЕГУЛЮ = 42;АННЯ ЗА ДОПОМОГО = 70; ПРОГРАМНОГi= 4; ПАКЕТА MATLAB/SIMULINK

 

48

ОСНОВИ ТЕОРІЇ ФАЗИ-ЛОГІКИ ТА ФАЗИ-РЕГУ= 051;ЮВАННЯ

49

3 ПРАКТИЧНЕ ЗАСТОСУВАНi= 3;Я ФАЗИ-ЛОГІКИ = 042; СИСТЕМАХ РЕГУЛЮВАННk= 1;

&n= bsp;

68

ОСНОВИ ТЕОРІЇ ФАЗИ-ЛОГІКИ ТА ФАЗИ-РЕГУЛЮ = 42;АННЯ

67

3 ПРАКТИЧНЕ ЗАСТОСУВАНi= 3;Я ФАЗИ-ЛОГІКИ = 042; СИСТЕМАХ РЕГУЛЮВАННk= 1;

34

ОСНОВИ ТЕОРІЇ ФАЗЗИ-ЛОГІК = 48; ТА ФАЗЗИ-РЕГУЛ = 70;ВАННЯ

69

ЛІ= ТЕРАТУРА<= /b>

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