2
БЕЛОРУССКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ ИНФОРМАТИКИ И РАДИОЭЛЕКТРОНИКИ
Кафедра РТС
РЕФЕРАТ
На тему:
“Метод статистической и гармонической линеаризации. Расчет автоколебаний
по критерию Найквиста”
МИНСК, 2008
Метод статистической линеаризации
Метод основан на замене нелинейного преобразования процессов
статистически эквивалентными им линейным преобразованиями. Нелинейный
элемент заменяется линейным эквивалентом (рис.1). В результате замены
система линеаризуется, что позволяет использовать методы исследования
линейных систем.
Замена нелинейного преобразования линейным является приближенной и
справедливой лишь в некоторых отношениях. Поэтому не существует
однозначной эквивалентности при использовании различных критериев.
В частности, если нелинейность определяется безинерционной зависимостью
вида
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01000000297908000000320a8001e2030100000028791c000000fb0240fe000000000000
9001010000000402001054696d6573204e657720526f6d616e005bd4f47764d4f4770100
000000003000040000002d01010004000000f001000008000000320a8001980401000000
787908000000320a8001090301000000797908000000320a800132000100000076791c00
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0a6b5bd4f47764d4f4770100000000003000040000002d01000004000000f00101000800
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0000fb021000070000000000bc02000000cc0102022253797374656d000000000a000000
040000000000010000000100000000003000040000002d01010004000000f00100000300
00000000, (1)
используется два критерия эквивалентности.
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040000002701ffff030000000000
Рис.1.
Первый критерий предполагает равенство на выходе нелинейного элемента и
его линейного эквивалента математических ожиданий и дисперсий процессов.
Второй критерий – минимум среднего квадрата разности процессов на выходе
нелинейного элемента и его линейного эквивалента.
Процесс на входе и выходе нелинейного элемента представим в виде:
picscalex100010009000003a501000002001c0000000000050000000902000000000500
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0f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000cc0102
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00002d01010004000000f0010000030000000000; (2)
picscalex100010009000003a501000002001c0000000000050000000902000000000500
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526f6d616e005bd4f47764d4f4770100000000003000040000002d01000004000000f001
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3000040000002d01010004000000f001000008000000320a7701fa0a010000006f791c00
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0a2e5bd4f47764d4f4770100000000003000040000002d01000004000000f00101000800
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0f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000cc0102
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00002d01010004000000f0010000030000000000, (3)
гдеpicscalex1000100090000030501000002001c0000000000050000000902000000000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? математическое
ожидание процесса на выходе НЭ;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 ? центрированная
случайная составляющая.
Процесс на выходе линейного эквивалента представляется в следующем виде: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, (4)
где
picscalex100010009000003c900000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02600220021200000026060f001a00ffffffff000010000000c0ffffff
b7ffffffe0010000170200000b00000026060f000c004d61746854797065000060001c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000008000000320a10021801
0100000030791c000000fb0240fe0000000000009001010000000402001054696d657320
4e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d0101000400
0000f001000008000000320aa0013900010000006b790a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d
000000000a000000040000000000000000000100000000003000040000002d0100000400
0000f0010100030000000000 ? коэффициент передачи линейного эквивалента по
математическому ожиданию;
picscalex100010009000003c900000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02200280011200000026060f001a00ffffffff000010000000c0ffffff
a6ffffff40010000c60100000b00000026060f000c004d61746854797065000050001c00
0000fb0220ff0000000000009001000000000402001054696d6573204e657720526f6d61
6e001643c7771f43c77720c0c97700003000040000002d01000008000000320ae001da00
0100000031791c000000fb0280fe0000000000009001010000000402001054696d657320
4e657720526f6d616e001643c7771f43c77720c0c97700003000040000002d0101000400
0000f001000008000000320a80013a00010000006b790a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d
000000000a0021008a01000000000000000080e412002942c777040000002d0100000400
0000f0010100030000000000 ? коэффициент передачи по центрированной
случайной составляющей.
Воспользуемся первым критерием эквивалентности: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. (5)
Из этих уравнений находим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;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,
где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 ? плотность вероятности процесса на входе нелинейного
элемента.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 – коэффициент передачи линейного эквивалента по
центрированной случайной составляющей (по первому критерию).
По второму критерию эквивалентности: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;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;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;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;
Для определения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 и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, при которых выполняется условие
эквивалентности, найдем частные производные и приравняем их нулю: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;
picscalex1000100090000035902000003001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02e00420111200000026060f001a00ffffffff000010000000c0ffffff
afffffffe01000008f0400000b00000026060f000c004d61746854797065000010010800
0000fa0200001000000000000000040000002d0100000500000014025002400005000000
13025002fd020500000014029100fc0b05000000130291004e0e1c000000fb0240fe0000
000000009001000000000402001054696d6573204e657720526f6d616e005bd4f47764d4
f4770100000000003000040000002d01010008000000320ac00210100100000030790800
0000320ac0020e0b01000000327908000000320ac002c60401000000327908000000320a
a8016d02010000005d7908000000320aa8012401010000005b791c000000fb0280fe0000
000000009001000000000402001054696d6573204e657720526f6d616e005bd4f47764d4
f4770100000000003000040000002d01020004000000f001010008000000320a30038508
01000000317908000000320af701fd0601000000327908000000320a8c04fc0101000000
31791c000000fb0240fe0000000000009001000000020402001053796d626f6c00774000
0000b2030a305bd4f47764d4f4770100000000003000040000002d01010004000000f001
020008000000320ac002bf0e010000003d7908000000320ac002b609010000002d790800
0000320ac0026e03010000003d7908000000320a1c04720001000000b67908000000320a
a801520001000000b6791c000000fb0240fe000000000000900101000000040200105469
6d6573204e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d01
020004000000f001010008000000320ac002910d01000000767908000000320ac0020a0c
01000000787908000000320ac002d407010000006b7908000000320a1c044b0101000000
6b791c000000fb0280fe0000000000009001010000000402001054696d6573204e657720
526f6d616e005bd4f47764d4f4770100000000003000040000002d01010004000000f001
020008000000320a3003ee060100000078791c000000fb0280fe00000000000090010000
0002040200104d54204578747261000000002b040ab85bd4f47764d4f477010000000000
3000040000002d01020004000000f001010008000000320af701e50c010000006f791c00
0000fb0240fe000000000000900100000002040200104d5420457874726100000000b203
0a325bd4f47764d4f4770100000000003000040000002d01010004000000f00102000800
0000320aa801b701010000006f791c000000fb0240fe0000000000009001010000020402
001053796d626f6c0077400000002b040ab95bd4f47764d4f47701000000000030000400
00002d01020004000000f001010008000000320ac0028a050100000073790a0000002606
0f000a00ffffffff0100000000001c000000fb021000070000000000bc02000000cc0102
022253797374656d000000000a0000000400000000000100000001000000000030000400
00002d01010004000000f0010200030000000000;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;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.
При расчете этих коэффициентов полагают, что распределение на входе
нормальное: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;
Определив величины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;
picscalex100010009000003b101000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c020003800b1200000026060f001a00ffffffff000010000000c0ffffff
afffffff400b0000af0200000b00000026060f000c004d61746854797065000060001c00
0000fb0240fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000008000000320a4002b00a
01000000297908000000320a4002d107010000002c7908000000320a4002f90401000000
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Рис.2. Характеристика релейного типа:
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3000040000002d01010004000000f0010000030000000000;
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коэффициенты равны:
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Метод гармонической линеаризации
Основы метода.
Метод используется для исследования нелинейных систем, описываемых
дифференциальными уравнениями различного порядка. Эффективен для расчета
параметров собственных колебаний в системе, используется также для
анализа точности при гармоническом задающем воздействии.
Рассмотрим метод применительно к расчету параметров собственных
колебаний в нелинейной системе.
Разделим систему на линейную часть и нелинейное звено (рис.3).
picscalex92010009000003a659000000008159000000000400000003010800050000000
b0200000000050000000c02cd00c101030000001e00040000000701040081590000410b2
000cc00cc00c00100000000cc00c0010000000028000000c0010000cc000000010004000
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222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
222222222222222222222222222222222222222222222222222222222222222222222222
2222222222222222222222222222222222222222222222222222222040000002701ffff0
30000000000
Рис.3. Модель нелинейной системы.
Уравнение линейной части:
picscalex1000100090000034101000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c026002c0081200000026060f001a00ffffffff000010000000c0ffffff
b7ffffff80080000170200000b00000026060f000c004d61746854797065000060001c00
0000fb0240fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000008000000320aa001a507
01000000797908000000320aa001ec0501000000707908000000320aa001aa0201000000
577908000000320aa0014e000100000078791c000000fb0280fe00000000000090010100
00cc0402001054696d6573204e657720526f6d616e005bd4f47764d4f477010000000000
3000040000002d01010004000000f001000008000000320a1002320401000000eb791c00
0000fb0240fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000004000000f00101000800
0000320aa001da0601000000297908000000320aa00113050100000028791c000000fb02
40fe0000000000009001000000020402001053796d626f6c007740000000d5060a395bd4
f47764d4f4770100000000003000040000002d01010004000000f001000008000000320a
a0017c01010000003d790a00000026060f000a00ffffffff0100000000001c000000fb02
1000070000000000bc02000000cc0102022253797374656d000000000a00000004000000
0000000000000100000000003000040000002d01000004000000f0010100030000000000
,(6)
При возникновении автоколебаний процесс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 на
выходе линейной части не является строго гармоническим, но мы будем
полагать, что линейное звено является фильтром нижних частот и подавляет
все гармоники, за исключением первой. Это предположение называется
гипотезой фильтра. Если она не подтверждается, то ошибки при применении
гармонической линеаризации могут быть значительными.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.
Пусть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;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. (7)
Представим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 в виде
ряда Фурье: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;
(8)
Полагаем, что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.
Это справедливо, если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 симметрична относительно начала координат и отсутствует
внешнее воздействие. Полагая, что высшие гармоники подавляются, будем
искать только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 и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Из уравнения (7) находим: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;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. (9)
Подставив (8. 20) в (8. 19) и ограничив ряд слагаемыми первой гармоники,
получим: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(10)
где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 (11)
Таким образом, нелинейное уравнение для
picscalex1000100090000039d00000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02e00180011200000026060f001a00ffffffff000010000000c0ffffff
3700000040010000170200000b00000026060f000c004d61746854797065000060001c00
0000fb0240fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000008000000320a20016300
0100000079790a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d000000000a000000040000000000ffff
ffff0100000000003000040000002d01010004000000f0010000030000000000
заменили приближенным линейным уравнением (11) для первой гармоники.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 и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 называют гармоническими коэффициентами передачи
нелинейного звена. Коэффициенты
picscalex100010009000003c900000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02600220021200000026060f001a00ffffffff000010000000c0ffffff
b7ffffffe0010000170200000b00000026060f000c004d61746854797065000060001c00
0000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000008000000320a10022301
0100000030791c000000fb0240fe0000000000009001010000000402001054696d657320
4e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d0101000400
0000f001000008000000320aa00139000100000071790a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d
000000000a000000040000000000000000000100000000003000040000002d0100000400
0000f0010100030000000000 и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 в рассматриваемом случае зависят от амплитуды,
при более сложной нелинейной зависимости зависят еще и от частоты.
Рассчитанные значения коэффициентов гармонической линеаризации для
типовых нелинейностей можно найти в учебниках и справочной литературе.
Передаточная функция разомкнутой системы может быть представлена в
следующем виде: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;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;
где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 ? эквивалентная передаточная функция
нелинейно – го звена.
Частотная передаточная функция разомкнутой системы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.
Характеристическое уравнение
picscalex100010009000003fb01000003001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02e004e0131200000026060f001a00ffffffff000010000000c0ffffff
b1ffffffa0130000910400000b00000026060f000c004d61746854797065000000010800
0000fa0200001000000000000000040000002d0100000500000014027002a10e05000000
1302700200101c000000fb0240fe0000000000009001000000000402001054696d657320
4e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d0101000800
0000320ae002b71201000000307908000000320ae002bc0701000000297908000000320a
e002570601000000287908000000320ae002df0201000000297908000000320ae0027a01
0100000028791c000000fb0280fe0000000000009001000000000402001054696d657320
4e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d0102000400
0000f001010008000000320a5003800d01000000317908000000320a5003080a01000000
30791c000000fb0240fe0000000000009001000000020402001053796d626f6c00774000
0000d9050ac35bd4f47764d4f4770100000000003000040000002d01010004000000f001
020008000000320ae0024e11010000003d7908000000320a9c031c1001000000fa790800
0000320a6e041c1001000000fb7908000000320aec011c1001000000f97908000000320a
9c03640801000000ea7908000000320a6e04640801000000eb7908000000320aec016408
01000000e97908000000320ae0025c0b010000002b7908000000320ae002d10301000000
2b791c000000fb0240fe0000000000009001010000020402001053796d626f6c00774000
000042030a335bd4f47764d4f4770100000000003000040000002d01020004000000f001
010008000000320a3f04970e0100000077791c000000fb0240fe00000000000090010100
00000402001054696d6573204e657720526f6d616e005bd4f47764d4f477010000000000
3000040000002d01010004000000f001020008000000320ac601d60e0100000053790800
0000320ae002b60c01000000717908000000320ae0021a0901000000717908000000320a
e002ff0601000000737908000000320ae002390501000000527908000000320ae0022202
01000000737908000000320ae0022b000100000051790a00000026060f000a00ffffffff
0100000000001c000000fb021000070000000000bc02000000cc0102022253797374656d
000000000a000000040000000000020000000100000000003000040000002d0102000400
0000f0010100030000000000.
Модуль частотной передаточной функции нелинейного звена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.
Фазочастотная характеристика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;
(picscalex1000100090000038101000002001c000000000005000000090200000000050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)
Модуль определяет отношение амплитуд, а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 фазовый сдвиг на выходе относительно входного сигнала.
Если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 симметрична относительно начала координат, однозначна и
не имеет гистерезиса, то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 и тогда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.
Часто при анализе используется величина обратная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. Она называется
гармоническим импедансом нелинейного звена: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.
Расчет автоколебаний по критерию Найквиста
В соответствии с критерием Найквиста строится годограф частотной
передаточной функции разомкнутой системы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Условием возникновения в системе колебаний является прохождение
амплитудно-фазовой характеристики через точку (-1,j0) комплексной
плоскости. Для определения условий прохождения годографа через эту точку
приравняем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.
Чтобы решить это уравнение можно, задавая значение амплитуды, строить
амплитудно-фазовую характеристику(рис.8.18) Значение амплитуды а=А, при
которой АФХ пройдет через точку (-1,j0) будет соответствовать амплитуде
собственных колебаний. Значение частоты определяют по частоте в точке
(-1,j0).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Рис.4. Амплитудно-фазовая характеристика нелинейной системы.
Тогда искомое колебание
picscalex1000100090000030e01000002001c0000000000050000000902000000000500
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0000050000000c02e001c0081200000026060f001a00ffffffff000010000000c0ffffff
d7ffffff80080000b70100000b00000026060f000c004d61746854797065000030001c00
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6e005bd4f47764d4f4770100000000003000040000002d01000008000000320a8001fa07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.
При нелинейной зависимости вида
picscalex1000100090000030d01000002001c0000000000050000000902000000000500
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0000050000000c024002c0061200000026060f001a00ffffffff000010000000c0ffffff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0000fb021000070000000000bc02000000cc0102022253797374656d000000000a000000
040000000000010000000100000000003000040000002d01010004000000f00100000300
00000000 передаточную функцию разомкнутой системы можно представить в
виде
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0000fa0200001000000000000000040000002d0100000500000014025002c60805000000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. (12)
Это уравнение решается графическим методом (рис.5).
Строим амплитудно-фазовую характеристику линейного звена и кривую
импеданса нелинейного звена. Определяем точку пересечения. Частоту
picscalex1000100090000039d00000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02a001a0011200000026060f001a00ffffffff000010000000c0ffffff
c6ffffff60010000660100000b00000026060f000c004d61746854797065000020001c00
0000fb0280fe0000000000009001000000020002001053796d626f6c0077400000006405
0a231643c7771f43c77720c0c97700003000040000002d01000008000000320a60013400
0100000057790a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d000000000a0021008a0100000000ffff
fffffcf312002942c777040000002d01010004000000f0010000030000000000
определим по АФХ линейного звена в точке пересечения. Амплитуду А
определим по кривой импеданса нелинейного звена.
Чтобы определить являются ли колебания устойчивыми автоколебаниями,
нужно задать приращение амплитуды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; при этом точка на импедансе смещается влево
вниз. Это будет соответствовать
уменьшениюpicscalex1000100090000032901000002001c000000000005000000090200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,
следовательно, кривая годографа ПФ разомкнутой системы не будет
охватывать точку с координатами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. Поэтому амплитуда колебаний
начнет уменьшаться, и система вернется в исходное состояние. То же будет
и при отрицательном приращении.
Критерий устойчивости периодического режима сводится к тому, чтобы часть
кривой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соответствующая меньшим амплитудам, охватывалась
амплитудно-фазовой характеристикой линейной части.
При отсутствии в системе периодических режимов (решения уравнения
(8.23)) можно предположить, что система будет устойчива.
Условие устойчивости равновесного состояния (отсутствия автоколебаний):
при устойчивой или нейтральной в разомкнутом состоянии линейной части её
АФХ не охватывает годограф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.
ЛИТЕРАТУРА
1. Коновалов. Г.Ф. Радиоавтоматика: Учебник для вузов. – М.: Высш. шк.,
2000.
2. Радиоавтоматика: Учеб. пособие для вузов. / Под ред. А. Бесекерского.
– М.: Высш. шк., 2005.
3. Первачев С.В. Радиоавтоматика: Учебник для вузов. – М.: Радио и
связь, 2002.
4. Цифровые системы фазовой синхронизации Под ред. И. Жодзишского – М.:
Радио, 2000.
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