.

Системы с прерывистым входным сигналом. Математическое описание дискретных систем

Язык: русский
Формат: реферат
Тип документа: Word Doc
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11

БЕЛОРУССКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ ИНФОРМАТИКИ И РАДИОЭЛЕКТРОНИКИ

Кафедра РТС

РЕФЕРАТ

На тему:

“Системы с прерывистым входным сигналом. Математическое описание
дискретных систем”

МИНСК, 2008

Системы с прерывистым входным сигналом. Функциональные схемы

В радиотехнических системах часто в качестве носителя информации
используют импульсный сигнал (импульсные РЛС, сканирование диаграммы
направленности или переключение процесса слежения с одного объекта на
другой и т.д.). В этом случае на вход дискриминатора поступает
периодический импульсный сигнал (рис.1).

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2701ffff030000000000

Рис.1. Импульсный сигнал на входе дискриминатора.

Функциональные схемы следящих систем при наличии прерываний входного
сигнала приведены на рис.2, 3. Схема (рис.2) отличается от обобщенной
функциональной схемы радиоэлектронной следящей системы наличием ключа
Кл, размыкаемого во время пауз. На рис.3 представлена схема с
фиксатором, который препятствует пропаданию напряжения на входе фильтра
в промежутке между импульсами.

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2701ffff030000000000

Рис.2. Функциональная схема следящей системы с прерывистым входным
сигналом: Дис – дискриминатор; ОГ – опорный генератор.

Фиксатор (экстраполятор нулевого порядка) состоит из сумматора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, линии
задержки на время
picscalex1000100090000032101000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c026002e0041200000026060f001a00ffffffff000010000000c0ffffff
b7ffffffa0040000170200000b00000026060f000c004d61746854797065000060001c00
0000fb0280fe0000000000009001010000cc0402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000008000000320a1002c603
01000000e8791c000000fb0240fe0000000000009001010000000402001054696d657320
4e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d0101000400
0000f001000008000000320aa0011d000100000054791c000000fb0240fe000000000000
9001010000020402001053796d626f6c00774000000052040ab25bd4f47764d4f4770100
000000003000040000002d01000004000000f001010008000000320aa001d40201000000
74791c000000fb0240fe0000000000009001000000020402001053796d626f6c00774000
0000ad030a5f5bd4f47764d4f4770100000000003000040000002d01010004000000f001
000008000000320aa001ad01010000002d790a00000026060f000a00ffffffff01000000
00001c000000fb021000070000000000bc02000000cc0102022253797374656d00000000
0a000000040000000000000000000100000000003000040000002d01000004000000f001
0100030000000000 и интегратора Инт. В фиксаторе во время действия
импульса полезного сигнала на входе интегратор заряжается до некоторого
уровня, который сохраняется до прихода очередного импульса. Перед
приходом очередного импульса интегратор разряжается задержанным на время
picscalex1000100090000032101000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c026002e0041200000026060f001a00ffffffff000010000000c0ffffff
b7ffffffa0040000170200000b00000026060f000c004d61746854797065000060001c00
0000fb0280fe0000000000009001010000cc0402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000008000000320a1002c603
01000000e8791c000000fb0240fe0000000000009001010000000402001054696d657320
4e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d0101000400
0000f001000008000000320aa0011d000100000054791c000000fb0240fe000000000000
9001010000020402001053796d626f6c00774000000096020a7a5bd4f47764d4f4770100
000000003000040000002d01000004000000f001010008000000320aa001d40201000000
74791c000000fb0240fe0000000000009001000000020402001053796d626f6c00774000
00006f030a825bd4f47764d4f4770100000000003000040000002d01010004000000f001
000008000000320aa001ad01010000002d790a00000026060f000a00ffffffff01000000
00001c000000fb021000070000000000bc02000000cc0102022253797374656d00000000
0a000000040000000000000000000100000000003000040000002d01000004000000f001
0100030000000000 отрицательным импульсом, поступающим через линию
задержки.
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Рис.4. Временные диаграммы, поясняющие принцип работы фиксатора.

Использование фиксатора позволяет обеспечить необходимый коэффициент
усиления контура.

Передаточная функция фиксатора:
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000320abd01640c01000000737908000000320a0e026a060100000075791c000000fb024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(1)

Если
picscalex1000100090000032101000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c026002e0051200000026060f001a00ffffffff000010000000c0ffffff
b7ffffffa0050000170200000b00000026060f000c004d61746854797065000060001c00
0000fb0280fe0000000000009001010000cc0402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000008000000320a1002c504
01000000e8791c000000fb0240fe0000000000009001010000000402001054696d657320
4e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d0101000400
0000f001000008000000320aa0011d000100000054791c000000fb0240fe000000000000
9001010000020402001053796d626f6c00774000000072040a9c5bd4f47764d4f4770100
000000003000040000002d01000004000000f001010008000000320aa001d20301000000
74791c000000fb0240fe0000000000009001000000020402001053796d626f6c00774000
0000d3030a765bd4f47764d4f4770100000000003000040000002d01010004000000f001
000008000000320aa001b201020000003e3e0a00000026060f000a00ffffffff01000000
00001c000000fb021000070000000000bc02000000cc0102022253797374656d00000000
0a000000040000000000000000000100000000003000040000002d01000004000000f001
0100030000000000,
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, (2)

где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 ? коэффициент передачи интегратора (величина
обратная постоянной времени).

Структурные схемы систем

Структурная схема системы с прерывистым входным сигналом без фиксатора
отличается от схемы системы с непрерывным входным сигналом наличием
ключа перед звеном с передаточной функцией Wф(р) (рис.5). При
использовании фиксатора схема дополняется звеном с передаточной
функцией, определяемой выражениями (1) или (2).

picscalex100010009000003f29400000000cd9400000000040000000301080005000000
0b0200000000050000000c029600f901030000001e000400000007010400cd940000410b
2000cc009500f801000000009500f8010000000028000000f80100009500000001000800
00000000000000000000000000000000000000000000000000000000ffffff00fefefe00
d0d0d0007c7c7c00a7a7a700e9e9e9004d4d4d00b2b2b2008c8c8c00d9d9d900bdbdbd00
e1e1e100f0f0f00068686800c7c7c7009a9a9a0000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
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000000000000000000000000000000000000000000000000000000000000000000000000
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000000000000000000000000000000000000000000000000000000000000000000000000
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000000000000000000000000000000000000000000000000000000000000000000000000
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000000000202020202020202020202020202020202020202020202020202020202020202
020202020202020202020202020202020202020202020202020202020202020202020202
020202020202020202020202020202020202020202020202020202020202020202020202
020202020202020202020202020202020202020202020202020202020202020202020202
020202020202020202020202020202020202020202020202020202020202020202020202
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Рис.6. Коэффициент передачи ключа.

Наличие ключа делает процесс регулирования прерывистым, а системы –
системами с переменными во времени параметрами.

Анализ таких систем определяется соотношениями между длительностью
импульса, полосой пропускания следящей системы и частотой повторения
импульсов.

Если частота повторения импульсов много больше полосы системы, то анализ
может быть осуществлен методами анализа непрерывных систем.

Если же это условие не выполняется и за время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 происходит значительное изменение ошибки
слежения, то такие системы называют системами с конечным временем съема
данных, или импульсными системами. Анализ их осуществляется отдельно в
момент отсутствия и наличия сигнала на входе, затем решения сшиваются.

Если же за время
picscalex98010009000003c900000002001c00000000000500000009020000000005000
000020101000000050000000102ffffff00050000002e0118000000050000000b0200000
000050000000c02600200021200000026060f001a00ffffffff000010000000c0ffffffb
7ffffffc0010000170200000b00000026060f000c004d61746854797065000060001c000
000fb0280fe0000000000009001010000cc0402001054696d6573204e657720526f6d616
e005bd4f47764d4f4770100000000003000040000002d01000008000000320a1002f9000
1000000e8791c000000fb0240fe0000000000009001010000020402001053796d626f6c0
0774000000023020ae85bd4f47764d4f4770100000000003000040000002d01010004000
000f001000008000000320aa00108000100000074790a00000026060f000a00ffffffff0
100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d0
00000000a000000040000000000000000000100000000003000040000002d01000004000
000f0010100030000000000 ошибка меняется незначительно, анализ системы
можно существенно упростить, представив систему прерывистого
регулирования как дискретную. Дискретными называют системы, в которых
сигналы подвергаются дискретизации по времени.

Рассмотрим методику перехода к дискретной системе на примере системы
прерывистого регулирования без фиксатора.

Чтобы получить структурную схему дискретной системы, вместо ключа вводят
импульсный элемент (рис.7), коэффициент передачи которого является
последовательностью дельта-функций

picscalex1000100090000031102000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02a005800d1200000026060f001a00ffffffff000010000000c0ffffff
a4ffffff400d0000440500000b00000026060f000c004d61746854797065000030011c00
0000fb02c0fd0000000000009001000000020402001053796d626f6c0077400000000904
0ad35bd4f47764d4f4770100000000003000040000002d01000008000000320a89032605
01000000e5791c000000fb0280fe0000000000009001000000020402001053796d626f6c
00774000000044030acc5bd4f47764d4f4770100000000003000040000002d0101000400
0000f001000008000000320a8201660501000000a57908000000320a3f05930501000000
3d791c000000fb0240fe0000000000009001000000020402001053796d626f6c00774000
000009040ad45bd4f47764d4f4770100000000003000040000002d01000004000000f001
010008000000320a40037c09010000002d7908000000320a40034f03010000003d791c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01010004000000f00100000800
0000320a3f057f060100000030791c000000fb0240fe0000000000009001000000000402
001054696d6573204e657720526f6d616e005bd4f47764d4f47701000000000030000400
00002d01000004000000f001010008000000320a4003b80c01000000297908000000320a
4003070801000000287908000000320a4003540201000000297908000000320a40032701
0100000028791c000000fb0280fe0000000000009001010000000402001054696d657320
4e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d0101000400
0000f001000008000000320a3f05ad04010000006b791c000000fb0240fe000000000000
9001010000000402001054696d6573204e657720526f6d616e005bd4f47764d4f4770100
000000003000040000002d01000004000000f001010008000000320a4003c00a02000000
6b5408000000320a40039a0801000000745408000000320a4003ba010100000074540800
0000320a40033900010000006b541c000000fb0240fe0000000000009001010000020402
001053796d626f6c00774000000044030acf5bd4f47764d4f47701000000000030000400
00002d01010004000000f001000008000000320a4003da060100000064540a0000002606
0f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000cc0102
022253797374656d000000000a0000000400000000000000000001000000000030000400
00002d01000004000000f0010100030000000000.

picscalex100010009000003a410000000007f1000000000040000000301080005000000
0b0200000000050000000c0240000401030000001e0004000000070104007f100000410b
2000cc003f000301000000003f0003010000000028000000030100003f00000001000400
00000000000000000000000000000000000000000000000000000000ffffff00fefefe00
1d2124000000000000000000000000000000000000000000000000000000000000000000
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Рис.7. Изображение импульсного элемента на структурной схеме

Импульсный элемент преобразует непрерывную функцию в последовательность
модулированных по площади дельта-функций:

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где
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модулированная по площади дельта-функция (рис.8);

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0100030000000000 ? дискретная функция (рис.9).

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