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СОДЕРЖАНИЕ
1.1.1.1
а)
б)
Рисунок 5.4 0
С ПИ-регулятором скоро=
сти
система является астатической по заданию второго порядка (см. рисунок 5.40б=
).
Рассогласование между задающим сигналом и сигналом датчика скорости имеет м=
есто
в начале и в конце линейно изменяющихся задающих сигналов, необходимых для
заряда и разряда Сос =
sub>.
В установившемся режиме разгона рассогласования нет.
Обратную связь по ЭДС
применяют в тех случаях, когда ЭП однозонный (Е =
º W ) и требования к поддержанию скорости не
высоки.
Контур тока в расчете
аналогичен системам с обратной связью по скорости. Структурная схема систем=
ы ЭП
с отрицательной обратной связью по ЭДС представлена на рисунке 5.41, где
принято обозначение: Тяц ¢ <=
/span>
– постоянная времени того участка ЯЦ двигателя, к которому подключается дат=
чик
напряжения.
1.=
2.1 =
Оптимизация контура ЭДС
В соответствии с рисун=
ком
5.42, в состав контура ЭДС входят регулятор ЭДС, ЗКТ, датчик ЭДС, интегриру=
ющее
звено.
где Т =
m э =3D Тт + Тяц =
¢ – малая постоянная врем=
ени
контура ЭДС.
МО:
;
.
С П-регулятором замкну=
тый
контур ЭДС является по заданию астатическим первого порядка, а по возмущению
статическим.
.
Наличие фильтра в кана=
ле
датчика ЭДС приводит к повышенному перерегулированию ЭДС двигателя. Настрой=
ка
контура на МО была проведена по отношению к сигналу датчика ЭДС. Для привед=
ения
перерегулирования к норме на входе контура необходимо поставить фильтр с то=
й же
постоянной времени, что и у датчика ЭДС.
Тогда передаточная фу=
нкция
замкнутого контура ЭДС будет иметь вид
.
;
УР:
.
;
;
;
.
Жесткость скоростных
характеристик при больших Тяц=
¢ может быть хуже, чем в
разомкнутой системе. Поэтому при подключении датчика напряжения подбирают т=
акие
точки съема сигнала, чтобы Тя=
ц ¢ была минимальной.
1.2.2
Принципиальная (блочная) схе=
ма с
обратной связью по ЭДС и датчиком напряжения
&nbs=
p;
Принципиальная (блочна=
я) схема
с ОС по ЭДС с датчиком напряжения представлена на рисунке 5.43. В этой схеме
сигнал датчика ЭДС получается в результате алгебраического суммирования
сигналов поступающих от ДН и ДТ. Этот сигнал измерить нельзя.
1.=
2.3 =
Расчет параметров и решающей=
цепи
контура ЭДС
Порядок расчета элемен=
тов
принципиальной схемы:
1) принимаем kдн =
® находим kрэ
;
2) задаемся Сдн ;
3) определяем
;
;
4) рассчитываем R=
оэ =3D kрэ × Rдн ;
5) находим
;
6) ищем
;
7) вычисляем резистор
токовой компенсации –
из режима стопор=
ения
двигателя W =3D 0 ® Е =3D 0 =
® Uдэ =3D 0. =
Iтк =3D Iдн ;
;
Uдт =3D Iд =
× kдт ; Uдн =3D Uд × =
kдн =3D Iд =
× Rяц =
¢ × kдн .
Пример расчета параметров и решающих цепей регулятора ЭДС.
Uдн =3D 220 В; Iдн =3D 50 А; Rа =
=3D 0,2
Ом; Rэ =3D 0,4 Ом; Rяц ¢ =3D Rа =3D=
0,2 Ом; Тэ =3D 0,04 с; Тяц =
¢ =3D 0,025 с; Тм =3D 0,02 с.
1)
; Uд ( max ) » Еdo =3D 300В;
;
2) Сдн =3D 1мкФ;
3)
;
4) Rоэ =3D kрэ × Rдн =3D2 × 100 =3D 200К;
5)
;
6)
;
7)
;
т.к. Rтк
> 500 кОм, то желательно принять Сдн
=3D 4 ¸ 5 мкФ;
8) R3 , R4
=3D ?
kдн =3D kдел × kпр =3D kдел , (kпр =3D 1);
;
R3 =3D kдн × R3 + k=
дн × R4 ;
.
Пусть R3 =
=3D 1K,
тогда <=
v:shape
id=3D"_x0000_i1057" type=3D"#_x0000_t75" style=3D'width:132.75pt;height:71=
.25pt'
o:ole=3D"" fillcolor=3D"window">
.
1.=
2.4 =
Построение скоростных
характеристик
Посадки скорости в зам=
кнутой
системе (рисунок 5.44)
;
;
.
Посадки скорости большие и статизм системы велик. При слишком больш=
их
посадках (слишком мягкие характеристики) систему с ОС по ЭДС строят с датчи=
ком
ЭДС, который при определенных решающих элементах может скомпенсировать
инерционность датчика напряжения. В этом случае могут быть получены скорост=
ные
характеристики такие же, как в системе с ОС по скорости с П-регулятором.
Фрагмент принципиальн=
ой схемы
с датчиком ЭДС представлен на рисунке 5.45.
На рисунке 5.45а Rодэ
=3D Rдн ; Rдэ
=3D Rдн .
Пусть на рисунке 5.45б=
R03 – очень мало. =
;
R02 <=
span
style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man";
mso-char-type:symbol;mso-symbol-font-family:Symbol'>× C0 <=
span
style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man";
mso-char-type:symbol;mso-symbol-font-family:Symbol'>@ Тяц ¢ ;
.
ЛАЧХ датчика ЭДС предс=
тавлена
на рисунке 5.46.
&nbs=
p;
Структурная схема конт=
ура
тока возбуждения представлена на рисунке 5.47.
МО: =
;
.
Получили ПИ-регулятор.
Если Тв å ³ 20Т m в , то регулятор тока
возбуждения может быть пропорциональным Wртв =3D kртв =
. С
П-регулятором в системе будет ошибка по заданию, которую можно скомпенсиров=
ать
увеличением задающего сигнала. (Если выбираем П-регулятор, то следует
определить сигнал задания, который необходимо подать, чтобы Iв =3D Iвн ). Uз
будет немного больше 10В.
Пр=
инципиальная
блочная схема стабилизации тока возбуждения и принципиальная схема тиристор=
ного
преобразователя возбуждения (ТПВ) представлены на рисунке 5.48.
Ди=
аграмма
работы ТПВ представлена на рисунке 5.49. Структурная схема ТПВ представлена=
на
рисунке 5.50.
=
Рисунок 5. 49 =
Рисунок 5.5=
1
В соответствии с рисун=
ком
5.50, можно записать
;
;
,
где U оп – опорное напряжение =
СИФУ
(см. рисунок 5.51).
Таблица 5.2. Зависимость угла управления a от
напряжения управления
Uув
a
0 <=
/p>
180 °
max
0 °
; <=
span
style=3D'position:relative;top:6.0pt;mso-text-raise:-6.0pt'>
;
<=
/span>®
;
.
;
.
;
.
Порядок расчета элемен=
тов
принципиальной схемы контура тока возбуждения (см. рисунок 5.48):
1) задаемся Сдтв =3D10 мкФ; =
span>
2) определяем
;
(Тф =3D Твт =
@ 0,1Тв S =3D0,04 с)
(
);
4) рассчитываем R=
отв =3D kртв × Rдтв =3D 16 × 41 =3D 656кОм;=
o:p>
5) находим
;
6) принимаем
;
7) вычисляем
.
&nbs=
p;
Двухзонный ЭП – это та=
кой
электропривод, в котором изменение скорости осуществляется как за счет
изменения напряжения на якоре, так и за счет изменения поля двигателя. Поэт=
ому
двухзонный АЭП состоит из двух подсистем: одна изменяет напряжение на якоре,
другая изменяет поле двигателя. Управление этими подсистемами может быть
зависимым и независимым. Современные системы АЭП зависимые, т.е. ослабление
поля начинается при достижении напряжения или ЭДС на якоре номинальных
значений.
Под управлением с пост=
оянным
моментом следует понимать, что в установившемся режиме момент двигателя не
должен быть больше номинального, а в переходных режимах меньше максимальног=
о (I
зона). Во II зоне ток двигателя в установившемся режиме I £ Iн , а в переходных режимах I=
£ Iмакс .
<=
/o:p>
1.=
4.1 =
Функциональная схема двухзон=
ного
АЭП
Функциональн=
ая схема
двухзонного АЭП (с реверсом по ЯД) с зависимым управляемым полем двигателя в
функции ЭДС приведена на рисунке 5.52, где приняты обозначения: ВМ – выявит=
ель
модуля (нужен, т.к. ЭП реверсивный по Я); ТПВ – нереверсивный; РЭ – регулят=
ор
ЭДС; РП – регулятор потока; ФП – функциональный преобразователь (в статичес=
ком
режиме воспроизводит кривую намагничивания); Rзэ – резистор подстроечный (его устанавливают в мом=
ент
наладки и дальше не трогают, причем Uзэ
º <=
/span> Ен ). =
p>
Ограничение контролиру=
емых
координат осуществляется либо за счет ограничения сигналов внешних регулято=
ров,
либо за счет ограничения сигналов, заданных на входе (с задатчиков скорости=
и
ЭДС). В общем случае за счет ограничения сигналов задания.
Работа схемы:
Uвп =3D Uзп(m) º Фн .
Пока сигнал задания на
скорость соответствует скорости, меньше номинальной (Uзс < Uзс(Н) ) сигнал с ДЭ по модул=
ю | Uзс | =
< Uзэ , поэтому РЭ находится на
ограничении, задавая максимальный поток двигателя, равный номинальному, поэ=
тому
ЭП работает как однозонный и скорость регулируется только за счет напряжени=
я на
якоре.
Пусть скорость двигате=
ля
равна номинальной. Так как РЭ обладает интегральными свойствами, то только =
при W =
> W н , сигнал ДЭ |
Uдэ | =
> Uзэ , регулятор ЭДС (РЭ) сойд=
ет с
ограничения и будет задавать Uзп
º Ф < Фн
(см. рисунок 5.53).
В первый мом=
ент
изменение напряжения на якоре двигателя вызывает увеличение напряжения якор=
я,
увеличивается скорость и увеличивается сигнал ДЭ. Последний вызовет выход Р=
Э с
ограничения и сформирует сигнал задания на поток, соответствующий полю мень=
ше
номинального, которое будет отработано контуром потока (КП). В результате в=
се
увеличение скорости, первоначально вызванное увеличением напряжения, будет
достигнуто за счет ослабления поля ЭД. Ослабление поля прекратится, когда
сигнал Uдэ =3D U=
зэ , который в свою очередь
установлен на уровне Ен .
1.=
4.2 =
Диаграмма пуска ЭД с выходом=
во
вторую зону
Временная диаграмма пу=
ска ЭД
с выходом во вторую зону представлена на рисунке 5.54. На всем протяжении п=
уска
во второй зоне ЭДС превышает номинальное значение на 3-5%, что вызывает
уменьшение поля ЭД. При торможении из второй зоны для того, чтобы шло
увеличение поля двигателя ЭДС должно быть меньше номинального. =
span>
1.4.3
Полная структурная схема
двухзонного АЭП с подчиненным регулированием параметров
&nbs=
p;
Полная структурная схе=
ма
двухзонной системы ЭП с подчиненным регулированием параметров представлена =
на
рисунке 5.55, где приняты обозначения: Кп
– коэффициент передачи магнитной цепи двигателя в данной рабочей точке; Дп – датчик потока; ВМ – выя=
витель
модуля.
Данная система является
четырехконтурной. Основным, самым высшим, является контур скорости, т.к. он
определяет цепь регулирования.
1.=
4.4 =
Оптимизация контуров регулир=
ования
Оптимизация контура то=
ка
якоря и скорости осуществляется так же, как в однозонном ЭП. При большом
диапазоне регулирования во второй зоне, т.е. за счет ослабления поля двигат=
еля,
требуется проводить линеаризацию контура скорости с целью поддержания
коэффициента в контуре скорости на одном и том же уровне при различных пото=
ках
двигателя.
Оптимизация подсистемы,
осуществляющей регулирование потока двигателя, начинается с внутреннего кон=
тура
потока.
1.=
4.4.1 =
Оптимизация контура потока
Структурная =
схема
контура потока представлена на рисунке 5.56. =
p>
<=
o:p>
Оптимизацию
проводим, полагая наличие датчика потока. Оптимизация на МО
Wкп p (p)=3DWpп (p)
=3D
;
Wрп (р)=3D
.
Получим ПИ-регулятор п=
отока.
.
С ПИ-регулятором контур
потока является астатическим как по заданию, так и по возмущению. Возмущени=
е –
изменение напряжения. Настройка контура является оптимальной только в одной
расчетной точке при фиксированных Кп ,
Тв S , Твт (см. рисунок 5.57).=
Передаточная функция о=
бъекта
W0 (p) =3D
;
К0 =3D
.
Постоянная времени обм=
отки
возбуждения
Тв =3D Lв /Rв<=
/span> ,
где Lв
=3D
– индуктивность
обмотки возбуждения.
Y =3D 2рwФ,
где =
Y – потокосце=
пление;
р – число пар
полюсов;
w – число ви=
тков на
полюс;
Ф – поток.
Тогда индуктивность об=
мотки
возбуждения равна
,
где Кп
– динамический коэффициент передачи магнитной цепи двигателя.
Тв =3D L в / R в =3D 2 pwK п<=
/span> / Rв ;
Тв S =3D 1,1Тв .
Передаточная функция о=
бъекта
будет равна
W0 (p) =3D <=
span
style=3D'position:relative;top:19.0pt;mso-text-raise:-19.0pt'>
.
Если w =
<
, то членами в скобках можно пренебречь и передаточная
функция объекта W0 (p) =
=3D
.
Если
< w =
<
, то W0 (p) =3D
,
где Ти
=3D
.
Если w =
>
, то W0 (p) =3D
.
Для диапазона частот <=
/span>w =
>
в выражении W0(p)
есть две переменных величины: W0 (p) =3D f(Кп ,Тв =
S ). =
p>
Тв =3D Lв /Rв<=
/span>
=3D 1,1 × 2pwKп /Rв ;
.
Получили выр=
ажение
для передаточной функции объекта, которая остается постоянной и не зависит =
от
рабочей точки на кривой намагничивания (КНМ). Поэтому частота среза
разомкнутого контура потока также будет оставаться неизменной при изменении
рабочей точки на кривой намагничивания. То есть, в соответствии с рисунком
5.58, положение участка с наклоном –20дБ/дек остается неизменным. <=
o:p>
Изменение ра=
бочей
точки на КНМ изменяет положение низкочастотного участка ЛАЧХ контура, котор=
ый
достаточно удален от частоты среза и поэтому существенного влияния на настр=
ойку
контура не оказывает, т.е. контур остается оптимальным практически во всех
рабочих точках.
Рисунок 5.58 <=
span
style=3D'mso-spacerun:yes'> =
Рисунок=
5.59
Изменение ЛАЧХ объекта=
при
настройке регулятора положения в точке с минимальным потоком изображено на
рисунке 5.59.
Если Тв S >> Т =
m , то вместо ПИ-регулят=
ора
положения можно применить более простой П-регулятор. С этим П-регулятором
характер переходных процессов будет практически такой же, но система будет
статической и по заданию и по возмущению.
Wрп (р) =3D
;
.
Определим ошибку по за=
данию
.
Величина ошибки будет =
менее
5% при Тв =
S >> =
2 0 =
T m .
Для непосредственного
измерения потока двигателя необходимы либо датчики Холла, либо специальные
обмотки, которые закладываются в пазы статора. Проще измерить поток косвенн=
о по
сигналу датчика потока возбуждения.
1.=
4.4.2 =
Оптимизация контура потока с датчиком тока возбуждения
Структурная схема кон=
тура
потока с датчиком тока возбуждения представлена на рисунке 5.60. =
.
Это условие необходимо
выполнить, чтобы настройка контура оставалась той же. Для выполнения условия
функциональный преобразователь ФП в определенном масштабе должен воспроизво=
дить
кривую намагничивания двигателя.
.
Реализация ФП
осуществляется с помощью операционного усилителя с нелинейным элементом в ц=
епи
обратной связи (см. рисунок 5.61). Нелинейный элемент – это переменное
сопротивление, которое изменяется с изменением выходного сигнала преобразов=
ателя. <=
o:p>
<=
o:p>
Реальная реа=
лизация
осуществляется методом кусочно-линейной аппроксимации (рисунок 5.62). <=
o:p>
К0 =3D
; R0 C=
0
=3D Tвт (Ф<=
span
style=3D'text-transform:uppercase'>мин );
K1 =3D
;
K2 =3D
.
При изменении рабочей =
точки
на КНМ величина постоянного времени функционального преобразователя, равная=
Твт , будет меняться автомати=
чески.
Для 1-го участка: R0 C0 =3D Твт (Фмин );
для 2-го участка: (R0 //R1 )C0=
sub> =3D
Твт 1 ; =
для3-го участка: (R0 //R1 //R2<=
/sub>)C0
=3D Твт 2 .=
o:p>
Если функционального
преобразователя в канале обратной связи нет, то оптимальная настройка конту=
ра
потока будет только в одной расчетной точке кривой намагничивания. Такое
допускается в системах АЭП с небольшим ослаблением потока (на 20-30%).=
Если оптимизация конту=
ра
была проведена при номинальном потоке Фн ,
то при ослаблении поля двигателя увеличивается Тв S , смещается вниз ЛАЧХ =
объекта
с наклоном –20дБ/дек, уменьшается частота среза в контуре. В этом случае
переходные процессы в контуре более демпфированные (быстродействие контура
снижается). Если оптимизация контура была проведена при минимальном потоке =
Фмин , то при его увеличении
снижается Тв S , поднимается вверх ЛА=
ЧХ
объекта и частота среза контура увеличивается, и контур может стать
неустойчивым при значительных изменениях.
1.4.4.3
Рисунок 5.63
Структурная схема кон=
тура ЭДС
представлена на рисунке 5.63.
,
где Тп =3D 2Т m – эквивалентная посто=
янная
времени контура потока, оптимизированного на МО.
,
где Т =
m э =3D Тп + Тяц / – малая постоянная времени контура Э=
ДС.
МО:
®
®
.
РЭ – интегрального тип=
а.
Оптимальная настройка
контура ЭДС будет выполняться только в одной расчетной точке, т.е. при
скорости, при которой была проведена оптимизация. Если оптимизация была
проведена для номинальной скорости, то при увеличении скорости (за счет
ослабления поля двигателя), коэффициент регулятора ЭДС увеличивается, что п=
риведет
к подъему ЛАЧХ.
Когда оптимизация конт=
ура
ЭДС проведена для максимальной скорости, то уменьшение скорости будет умень=
шать
коэффициент в объекте, уменьшать частоту среза, а, следовательно, уменьшать
быстродействие.
Снижение быстродействи=
я в
этом случае приводит к большему перерегулированию ЭДС при выходе во вторую
зону. Это приводит к аварийным ситуациям, которые могут вызвать опрокидыван=
ие
инвертора. Таким образом, перерегулирование не должно превышать 3%.
Для сохранения коэффиц=
иента
усиления в контуре ЭДС неизменным при изменении скорости, на выходе регулят=
ора
ЭДС включают делительное (рисунок 5.64а), либо множительное устройство (рис=
унок
5.64б).
На практике чаще приме=
няется
вариант а).
Включение делительных =
или
множительных элементов позволяет сделать контур ЭДС адаптивным, инверторным=
по
всем изменениям скорости.
1.4.5
Принципиальная (блочная) схе=
ма
управления возбуждением электродвигателя в двухзонном реверсивном по якорю АЭП
Принципиальн=
ая
(блочная) схема подсистемы двухзонной АЭП, управляющей полем двигателя
представлена на рисунке 5.65.
Uст VD1 =3D Uзп (max) º Фн
На диодах VD1, VD3 дио=
дная
схема ИЛИ.
Работа схемы: на вход
регулятора ЭДС подается сигнал, пропорциональный номинальной ЭДС. Если
двигатель неподвижен, то РЭ выходит на ограничение, задавая максимальный си=
гнал
на входе регулятора потока (уровень стабилизации стабилитрона), который
установит в двигателе Iвн ,
соответствующий номинальному полю. Если скорость двигателя меньше номинальн=
ой
(Е < Ен ),
то поле будет оставаться номинальным, и система останется в прежнем положен=
ии.
Когда ЭДС двигателя бу=
дет
превышать номинальный уровень, РЭ “сойдет” с ограничения, задавая Ф <=
span
style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man";
mso-char-type:symbol;mso-symbol-font-family:Symbol'><
Фн ,
который будет отрабатываться быстродействующим контуром потока. В результате
первоначальное увеличение скорости, полученное за счет увеличения напряжени=
я на
якоре, будет достигнуто за счет ослабления поля двигателя. В установившемся
режиме во второй зоне работы привода сигнал датчика ЭДС по модулю всегда ра=
вен
сигналу задания ЭДС.
Чтобы в процессе регул=
ирования
поток не ослабился ниже Фн ,
на входе РП установлена диодная схема ИЛИ. На диод VD3 подается сигнал,
соответствующий Фmin .
В режиме торможения сн=
ачала
работает вторая подсистема, усиливающая поле до номинального уровня. В этом
режиме ½ Uдэ =
½ < Uзэ ,
регулятор ЭДС (РЭ) увеличивает свой сигнал, выходя на ограничение, тем самы=
м,
задавая номинальный поток двигателя. Только после усиления потока до Ф=
н , вступает в работу первая
подсистема, уменьшая напряжение на якоре двигателя.
1.=
4.6 =
Линеаризация контура скорост=
и в двухзонном
АЭП
Структурная схема конт=
ура
скорости в двухзонном АЭП представлена на рисунке 5.66. <=
o:p>
Мдин =3D
;
M(p) =3D Jp W (p);
.
В двухзонном АЭП при
уменьшении потока уменьшается коэффициент в объекте регулирования контура
скорости (за счет ослабления поля двигателя). Если контур скорости был
оптимизирован на модульный оптимум, то эти изменения вызывают уменьшение
частоты среза и уменьшение быстродействия, т.е. контур становится более
демпфированным (рисунок 5.67а). Если контур скорости был оптимизирован на
симметричный оптимум (рисунок 5.67б), то при существующем уменьшении поля м=
ожет
произойти даже потеря работоспособности контура (если частота среза будет
приходится на участок ЛАЧХ с наклоном –40дБ/дек).
Настройка на симметрич=
ный
оптимум также может привести к потере работоспособности контура при
существующем увеличении коэффициента. Таким образом, настройка на СО дает
хорошие результаты только с коэффициентом регулятора, который рассчитан для
значения коэффициента в данной расчетной точке.
.
Для того чтобы коэффиц=
иент в
контуре скорости оставался неизменным при любом значении поля двигателя, на
выходе РС устанавливают делительное (рисунок 5.68а), либо множительное устр=
ойство
(рисунок 5.68б).
Сл=
едящие
системы – это системы, управляющие перемещением объекта регулирования. В та=
ких
системах главная обратная связь по
положению.
Следящие системы бывают
гидравлические, пневматические и электрические. В промышленных установках
находят применение в станках с ЧПУ, роботах-манипуляторах.
Основной характеристик=
ой
следящей системы является точность, с которой они отрабатывают заданное
перемещение, которое зависит от исполнения системы и режимов работы (режим
позиционирования, режим отработки линейно изменяющегося сигнала и т.д.). Са=
мый
простой из режимов – режим позиционирования. Эти системы и находят наибольш=
ее
распространение.
&nbs=
p;
Задачей позиционного А=
ЭП
является перемещение рабочего органа из одного положения в другое. Основной
характеристикой этой системы является быстрота и точность отработки задающих
сигналов. Т.к. в процессе отработки перемещения требуется контролировать то=
к и
скорость двигателя на определенном уровне, то все современные позиционные
системы АЭП являются трехконтурными с подчиненным регулированием параметров.
Структурная схема позиционного АЭП представлена на рисунке 6.1. <=
o:p>
Возможны три режима ра=
боты позиционного
АЭП:
<=
span
style=3D'mso-list:Ignore'>1)&n=
bsp;
Режим малых перемещений, при котором не один из
регуляторов не выходит на ограничение, т.е. система ведет себя как линейная=
. <=
o:p>
<=
span
style=3D'mso-list:Ignore'>2)&n=
bsp;
Режим средних перемещений – в этом режиме регуля=
торы
положения и скорости выходят на ограничение, т.е. система перестает быть
линейной, но скорость в процессе отработки не выходит на максимальный
установившийся уровень. Тахограмма режима средних перемещений изображена на
рисунке 6.2.
<=
span
style=3D'mso-list:Ignore'>3)&n=
bsp;
Режим больших перемещений – регуляторы положения=
и
скорости выходят на ограничение, привод разгоняется до максимальной скорост=
и,
некоторое время на ней работает. Тахограмма режима больших перемещений, в
соответствии с рисунком 6.3, имеет вид трапеции. =
p>
&nbs=
p;
Полагаем, что контура =
тока и
скорости уже оптимизированы и остается оптимизировать только контур положен=
ия.
Тогда структурная схема примет вид, представленный на рисунке 6.4.
Передаточная функция
замкнутого контура скорости, оптимизированного на модульный оптимум имеет в=
ид
,
где Тс =3D 4Тт – малая постоянная времени
оптимизированного контура скорости (Тсмо
=3D 2Тт , Т<=
span
style=3D'text-transform:uppercase'>с СО =3D 4Тт ).
Настроим контур на мод=
ульный
оптимум. При такой настройке ЛАЧХ имеет вид, представленный на рисунке 6.5.=
Тогда передаточная фун=
кция
разомкнутого контура положения, настроенного на модульный оптимум, примет в=
ид
,
где Кдп , Кдс – коэффициент передачи датчика положения и скоро=
сти
соответственно.
Передаточная функция
регулятора положения будет равна
,
где i – передаточное число редуктора. =
.
Получили П-регулятор
положения и астатическую систему по заданию.
,
где Тп =3D 2Тс – эквивалентная постоянная
времени оптимизированного на модульный оптимум контура положения.
Тп =3D 2Тс =3D ... =3D 8Т m
Полученная система по
заданию является астатической 1-го порядка по заданию. Если контур скорости=
был
оптимизирован на СО и регулятор скорости был ПИ, то данный контур положения
будет астатическим даже с П-регулятором.
Знак ошибки зависит от
направления действия статического активного момента (см. рисунок 6.6).=
Рисунок 6.5 =
Рисунок 6.6
Оценим точность позици=
онной
системы (см. рисунок 6.7).
;
;
– фактическое зн=
ачение
перемещения.
По аналогии находим за=
данное
перемещение
.
Считаем, что коэффицие=
нт
регулятора по заданию и каналу ОС одинаковы, т.е. Rзп =3D Rдп .
Определим величину оши=
бки
;
– не зависит от =
величины
задающего сигнала, а зависит от момента на валу и параметров системы.<=
/o:p>
Если контур скорости
настроен на СО (регулятор скорости ПИ), то
Функциональная схема
аналоговой позиционной системы АЭП представлена на рисунке 6.8, где приняты
обозначения: РП – регулятор положения; ФЧВ – фазочувствительный выпрямитель=
; Г
– задающий генератор (f =3D 400 ¸ =
1000Гц); СД, СП – сель=
синная
пара (сельсин-датчик и сельсин-приемник); ИО – исполнительный орган; Р –
редуктор с передаточным числом i.
Особенно=
сть
схемы: здесь используется датчик рассогласования на базе сельсинной пары и
фазочувствительного выпрямителя – это датчик положения. В этой схеме нет
электрических сигналов, пропорциональных задающей величине и сигналу
фактического положения, но есть сигнал, пропорциональный рассогласованию,
который определяется на выходе ФЧВ
.
О работе сел=
ьсинной
пары: переменное напряжение, подаваемое с генератора на обмотку
сельсина-датчика, создает пульсирующее поле, которое в трехфазной обмотке,
расположенной на роторе, наводит ЭДС (амплитуда каждой разности ЭДС зависит=
от
угла между осью поля и осью фазных обмоток). Так как трехфазные обмотки сел=
ьсинов
соединены, то токи, протекающие по этим цепям, создадут в сельсине-приемнике
пульсирующее поле, которое наведет в его однофазной обмотке ЭДС. =
Uод.обм=
.сп
=3D Uоосд cosd,
где cos d -=
угол рассогласования (=
угол
“неодинаковости” расположения роторов этих сельсинов по отношению к их
однофазным обмоткам). Если “неодинаковость =3D 0” , т.е. роторы сельсинов по
отношению к своим обмоткам расположены одинаково, то d =
=3D 0 и Uоосп
=3D Uоосд .<=
/o:p>
Для того=
чтобы
в согласованном положении сигнал рассогласовался (был равен нулю), производ=
ят
предварительную ориентацию сельсинов, поворачивающего ротор одного из сельс=
инов
на угол 900 .
В этом с=
лучае
Uоосп =3D U=
оосд sin d=
span>.
Напряжен=
ие
однофазной обмотки сельсина-приемника Uоосп
выпрямляется в ФВЧ и ему придается знак в зависимости от знака сигнала
рассогласования. Для этого с генератора на ФЧВ подается сигнал, определяющий
фазу Uоосд . Если
сигналы ООСП и ООСД в фазе, знак сигнала на выходе ФЧВ положительный, если в
противофазе – отрицательный.
Коэффициент =
датчика
положения
Кдп =3D Ксп Кфчв ,
где Ксп – коэффициент сельсинной=
пары.
ИР =3D С=
ПР +
ФЧВ,
где ИР – измеритель
рассогласования =3D сельсинная пара.
.
У соврем=
енных
сельсинных пар Ксп
.
Работа
системы: Поворотом ротора сельсина-датчика формируется сигнал задания q зад . На ООСП наводится ЭДС
соответствующей амплитуды, которая выпрямляется ФЧВ с приданием знака
зависимости от знака от знака рассогласования. В результате для сигнала
рассогласования на выходе РП сформируется сигнал задания на скорость U=
зс , который также сформирует
сигнал задания на ток Uзт .
Сформированный ток двигателя создаст момент, и двигатель начнет отрабатывать
сигнал задания до тех пор, пока рассогласование
между ротором СД и СП не станет равным нулю d <=
/span>=3D 0, т.е. пока угол
рассогласования не будет равным нулю.
&nbs=
p;
Режимы малых перемещен=
ий не
являются типичным для позиционных систем. Регуляторы положения (РП) для реж=
има
средних и больших перемещений рассчитываются иначе, чем для режима малых
перемещений. Для удобства сравнительной оценки различных настроек позиционн=
ой
системы перейдем к расчету и оптимизации позиционной системы в относительных
единицах.
При выборе базовых зна=
чений
принимают во внимание следующее:
- в с=
иловой
цепи за базовые значения принимают номинальные параметры привода Uн , I н , n Н ;
- в системе
рассогласования за базовые принимают значения, при которых ОС становятся
единичными с учетом того, что в узлах суммарные базовые значения должны быть
одни и те же.
U зт ( =
d ) =3D U дт ( d ) =3D I н Кдт ;
Uзc (d ) =3D Uдc (d )
=3D =
W н Kдс ;
U зп ( d ) =3D U дп ( d ) =3D q d <=
/sub>Кдп .
– базовое перемещение – поворот вала
исполнительного двигателя за 1с при вращении со скоростью, равной номинальн=
ой W н . Произведение =
W н × =
1 c с учетом коэффициента
редукции редуктора
Структурная схема позиционного АЭП в относительн=
ых
единицах приведена на рисунке 6.9. Сама система осталась 3-х контурной, но =
мы
свернули контур тока.
Передато=
чная
функция в относительных единицах имеет вид
С учетом
принятых базовых значений получим передаточные функции в относительных един=
ицах
;
;
.
Структур=
ная
схема в относительных единицах контура положения представлена на рисунке 6.=
10.
Оптимизи=
руем
контур положения на МО
;
;
;
=3D
=3D
Крп =3D
.
Получим
тот же результат, который был получен при оптимизации контура положения при=
его
настройке на МО в абсолютных единицах.
Найдем
величину ошибки d c * .
W* =3D 0;
d C * К* рп
К* рс =
=3D I3 * =3D I*=
sup>C ;
d C * =3D
.
<=
/o:p>
=
<=
/o:p>
Наилучшим
считается такой процесс отработки средних перемещений, при которой скорость
двигателя изменяется по треугольному графику (это позволяет максимально
использовать перегрузочную способность двигателя, т.к. он работает только в
пусковых и тормозных режимах). Чтобы обеспечить такой процесс отработки,
коэффициент регулятора положения должен быть своим для каждого задающего
сигнала, т.е. Крп =3D f( q 3 ). =
p>
Принимаем
упрощающее допущение: Тт =3D
0 – эквивалентная постоянная времени контура тока, отсюда =
1)
– контур тока ст=
ал безинерционным;
2)
– т.е. при таком
регуляторе малейший сигнал на входе регулятора будет вызывать ограничение, =
т.е.
задание будет на максимальный ток, который тут же будет отработан.
Диаграмма
сигналов при отработке средних перемещений представлена на рисунке 6.11.
Будем
полагать, что система статическая, но несмотря на то, что d* C
0 полагаем, что она очень мала и стремится к нулю.=
o:p>
В
момент t0 скачком подается сигнал задания
и если он велик,=
то
регулятор положения выходит на ограничение. Сразу же выйдет на ограничение =
и регулятор
скорости, т.к. Крс
, что определяет максимальный сигнал задания на ток, кото=
рый
будет мгновенно отработан, т.к. контур тока является безинерционным. Начина=
ется
разгон с постоянным ускорением. В момент времени t1 регулятор
положения (РП) сойдет с ограничения и в дальнейшем его выходной сигнал будет
изменяться по закону Uрп *
=3D
. Двигатель продолжает разгон с тем же d=
span>* ускорением (т.к. зада=
нная
скорость больше фактической и РС находится на ограничении того же знака). В
момент t2 заданная скорость будет равна фактической
.
В следующие =
моменты
фактическая скорость будет превышать заданную величину, поэтому РС выходит =
на
ограничение этого другого знака, что мгновенно отрабатывается контуром тока.
Двигатель переходит в тормозной режим с постоянным ускорением. Процесс
заканчивается в точке t3 , когда фактическое перемещение станет
равным заданному (при условии d С =3D 0).<=
o:p>
Рисунок 6.11 =
Рисунок 6.12
<=
o:p>
Целью
последующего расчета будет нахождение Крп
=3D f( q 3 ) – коэффициента регул=
ятора
в функции задающего сигнала.
tP
=3D ? M м - Mc =3D J=
span>
=3D
=3D <=
/span>
;
tT
=3D ? –MM – MC =3D J
=3D –
=3D <=
/span>
;
tP + tT =3D? tP + tT =3D J W 2
=3D
=3D
=3D
.
Найдем велич=
ину
перемещения при отработке за весь цикл
q =3D q 3 =3D
=3D
=3D
=3D
=3D
=3D
=3D
.
Перейдем к относительн=
ым
единицам
=3D Т/ М .
J W H /Мн =3D Т/ М – время разгона до W H с Mн .
,
где Мдин
=3D J <=
v:shape
id=3D"_x0000_i1212" type=3D"#_x0000_t75" style=3D'width:23.25pt;height:36p=
t' o:ole=3D""
fillcolor=3D"window">
.
tP / =
W =3D =
W H =3D
– время разгона
привода до номинальной скорости с номинальным моментом. =
p>
Т/ м =
» 1 сек; =
span>Тм =3D rа <=
span
style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:Symbol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man";
mso-char-type:symbol;mso-symbol-font-family:Symbol'>× Т/ ам=
sub>.
.
В момент времени t2
W =
* С3(2) =3D К * РП ( q / 3 - q * (2) ) =3D W * (2) .
Подставим зн=
ачение W * (2) в выражение
величины перемещения при отработке за весь цикл в относительных единицах
q * 3 =3D Т/ м
Отсюда, коэффициент
регулятора положения
.
.
Чтобы обеспечить отраб=
отку q 3 без перерегулирования=
и
дотягивания, т.е. оптимально, коэффициент регулятора КРП должен быть разным для разных q 3 . При других сигналах
задания q 3 и неизменном коэффици=
енте
регулятора графика и скорости будут отличаться от треугольного. <=
/span>
Диаграмма сигналов при
отработке нового перемещения q 3 */ < =
q 3 * представлена на рисун=
ке
6.12.
.
До точки t2 =
процесс
идет точно так же, как и в предыдущем случае. Сам же момент t2
наступит раньше.
=3D W * ( 2 ) .
В момент времени t3
сигналы заданной и фактической скорости вновь будут равны, и регулятор скор=
ости
сойдет с ограничения. При большом Крп
примерное равенство W 3 и W ФАКТ будет соблюдаться на
протяжении всего оставленного пути. Момент двигателя при этом снижается и
позиционная система доходит до точки t4 с дотягиванием (будет пу=
льсирующий
режим).
В случае
>
, перемещение будет отрабатываться с перерегулированием.<=
o:p>
С дотягиванием система
предпочтительнее, поэтому расчет П-регулятора положения ведут для так
называемого настроечного перемещения, которое является максимальным при
отработке по треугольной тахограмме (рисунок 6.13).
.
Отсюда, настроечный
коэффициент регулятора положения равен
Крп * =3D
.
При таком коэффициенте
регулятора настроечное перемещение будет отработано оптимально, а все перем=
ещения
меньше настроечного будут отрабатываться с дотягиванием. <=
/p>
2.5.1
Сравнительная оценка коэффиц=
иентов
регулятора положения для малого и средних перемещений
&nbs=
p;
Для режима малых перем=
ещений
(РМП) при настройке контуров тока, скорости и положения на модульный оптиму=
м
Тс =3D 2Тт , Тт =3D 2Т =
m , Т m =3D 0,005с.
Пусть максимальный мом=
ент
равен Мм *=
sup>=3D2
и Тм / =
=3D1с,
тогда численное значение коэффициента регулятора положения будет равно=
Крп * =3D 1/2Тс =3D 1/8 Т m =3D
.
Для режима средних
перемещений
Крп * =3D 2М<=
span
style=3D'text-transform:uppercase'>м * /Тм / =3D
.
Таким образом, контур
положения, оптимизированный для режима малых перемещений, имеет коэффициент
значительно больший, чем настроечное значение коэффициента для режима средн=
их
перемещений, поэтому отработка заданий будет, как правило, осуществляться с
перерегулированием.
&nbs=
p;
К большим перемещениям
относят перемещения больше настроечного =
q * з > =
q * з(настр) .
Рисунок 6.14
Рисунок 6.15
Тахограмма отработки =
больших
перемещений показана на рисунке 6.14. Так как в этом случае торможение
начинается при максимальной скорости, равной единице в относительных единиц=
ах,
поэтому коэффициент регулятора должен быть таким же, как и для настроечного
перемещения. Поэтому все перемещения будут происходить оптимально (см. рису=
нок
6.15).
&nbs=
p;
Для того чтобы перемещ=
ения
меньше настроечного, отрабатывались оптимально, регулятор положения должен =
быть
нелинейным. Для подтверждения проанализируем отработку перемещения, меньшего
настроечного, которое будет оптимальным (см. рисунок 6.16).
Крп * =3D2
.
=
В момент
времени t £ t1 Uрп * =3D 1 <=
span
style=3D'mso-ansi-language:RU'>; в момент времени t =
=
> t1 Uрп<=
/span> * =3D
Крп * =
( =
q * з – q * )=
.
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