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Нелинейные элементы

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11

Предмет: Теория автоматического управления

Тема: НЕЛИНЕЙНЫЕ ЭЛЕМЕНТЫ

1. Классификация нелинейных элементов

Нелинейные зависимости z = f(x) можно классифицировать по различным
признакам:

1. По гладкости характеристик: гладкая – если в любой точке
характеристики существует производная dz/dx, т. е. функция
дифференцируема (рис. 1а, б); кусочно-линейная – характеристика, в
которой производные имеют разрыв первого (рис.2а) или второго рода (рис.
2б).

Рис. 1

Рис.2

По однозначности: однозначные – в которых каждому значению вхо-дной
величины соответствует одно значение выходной величины (рис. 3a);
многозначные – в которых каждому значению входной величины х
соответствует несколько значений выходной величины z (рис.3б, в, г).

Р?. 3

По симметрии: четно-симметричные – симметричные относительно оси
ординат, т. е. z(х) = z (- х) (рис. 4а); нечетно-симметричные –
сим-метричные относительно начала координат, при этом z (х) = – z ( – х
) (рис. 4б); не симметричные (рис. 4в).

Р?. 4

2. Нелинейные цепи

Нелинейными называются цепи, в состав которых входит хотя бы один
нелинейный элемент. Нелинейные элементы описываются нелинейными
характеристиками, которые не имеют строгого аналитического выражения,
определяются экспериментально и задаются таблично или графиками.

Нелинейные элементы можно разделить на двух – и многополюсные. Последние
содержат три (различные полупроводниковые и электронные триоды) и более
(магнитные усилители, многообмоточные трансформаторы, тетроды, пентоды и
др.) полюсов, с помощью которых они подсоединяются к электрической цепи.
Характерной особенностью многополюсных элементов является то, что в
общем случае их свойства определяются семейством характеристик,
представляющих зависимости выходных характеристик от входных переменных
и наоборот: входные характеристики строят для ряда фиксированных
значений одного из выходных параметров, выходные – для ряда
фиксированных значений одного из входных.

По другому признаку классификации нелинейные элементы можно разделить на
инерционные и безынерционные. Инерционными называются элементы,
характеристики которых зависят от скорости изменения переменных. Для
таких элементов статические характеристики, определяющие зависимость
между действующими значениями переменных, отличаются от динамических
характеристик, устанавливающих взаимосвязь между мгновенными значениями
переменных. Безынерционными называются элементы, характеристики которых
не зависят от скорости изменения переменных. Для таких элементов
статические и динамические характеристики совпадают.

Понятия инерционных и безынерционных элементов относительны: элемент
может рассматриваться как безынерционный в допустимом (ограниченном
сверху) диапазоне частот, при выходе за пределы которого он переходит в
разряд инерционных.

В зависимости от вида характеристик различают нелинейные элементы с
симметричными и несимметричными характеристиками. Симметричной
называется характеристика, не зависящая от направления определяющих ее
величин, т.е. имеющая симметрию относительно начала системы координат.
Для несимметричной характеристики это условие не выполняется, т.е.
Наличие у нелинейного элемента симметричной характеристики позволяет в
целом ряде случаев упростить анализ схемы, осуществляя его в пределах
одного квадранта.

По типу характеристики можно также разделить все нелинейные элементы на
элементы с однозначной и неоднозначной характеристиками. Однозначной
называется характеристика, у которой каждому значению х соответствует
единственное значение y и наоборот. В случае неоднозначной
характеристики каким-то значениям х может соответствовать два или более
значения y или наоборот. У нелинейных резисторов неоднозначность
характеристики обычно связана с наличием падающего участка, а у
нелинейных индуктивных и емкостных элементов – с гистерезисом.

Наконец, все нелинейные элементы можно разделить на управляемые и
неуправляемые. В отличие от неуправляемых управляемые нелинейные
элементы (обычно трех- и многополюсники) содержат управляющие каналы,
изменяя напряжение, ток, световой поток и др. в которых, изменяют их
основные характеристики: вольт-амперную, вебер-амперную или
кулон-вольтную.

В зависимости от вида составляющих нелинейных элементов, называют
нелинейные цепи.

3. Коэффициент усиления нелинейного элемента

Рассмотрим нелинейный элемент (рис. 5). Подадим на вход нелинейного
элемента гармонический сигнал с амплитудой – А0 и определим первую
гармонику выходного сигнала.

Рис. 5

При этом для входного и выходного сигналов можно записать следующие
соотношения
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 (1)

где: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 – модуль вектора;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 – аргумент
вектора.

Рассмотрим характеристику нелинейного элемента
-wmetafile80100090000031001000002001700000000000500000009020000000004000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, которая называется комплексным коэффициентом передачи
нелинейного элемента. Эту характеристику можно строить в комплексной
плоскости также, как и комплексный коэффициент передачи линейной части.
При этом характеристика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- зависит от частоты сигнала и не зависит от его амплитуды.
Характеристика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- зависит от амплитуды входного сигнала и не зависит от
частоты, так как нелинейный элемент является безинерционным. Для
однозначных характеристик его значения является действительными
величинами, а для многозначных – комплексными.

Рассмотрим примеры построения комплексных коэффициентов передачи для
наиболее характерных нелинейных элементов –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.

1. Нелинейный элемент типа “усилитель с ограничением”. Характеристики
звена показаны на рис. 6. Подобными характеристиками обладают различного
типа усилительные и исполнительные элементы автоматики (электронные,
магнитные, пневматические, гидравлические и др.) в области больших
входных сигналов.
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fffffffff7ffffffffffffffffffbffffffffff7fffffff83ffffffffffffffffffe001f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Рис. 6

Если амплитуда входного воздействия меньше а, то это обычное линейное
безинерционное звено, при этом коэффициент усиления к является
постоянной величиной. Фазовый сдвиг между входом и выходом равен нулю,
поскольку характеристика нелинейного элемента является симметричной. По
мере увеличения амплитуды
-wmetafile8010009000003b200000002001700000000000500000009020000000004000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 коэффициент
усиления уменьшается. В некоторых методах исследования нелинейных систем
используется характеристика обратного комплексного коэффициента передачи
нелинейного элемента
(-1/wmetafile80100090000031001000002001700000000000500000009020000000004
00000002010100050000000102ffffff00040000002e0118000500000031020100000005
0000000b0200000000050000000c02a002e0060e00000026060f001200ffffffff000008
000000c0ffb0ffa00650020b00000026060f000c004d6174685479706500006000150000
00fb0200fe0000000000009001010000000002001054696d6573204e657720526f6d616e
000000040000002d01000009000000320ae0014000010000004b00590109000000320ae0
01e703010000004100320115000000fb02c0fe0000000000009001010000000002001054
696d6573204e657720526f6d616e004379040000002d01010004000000f0010000090000
00320a6002a801010000004800e70015000000fb0200fe00000000000090010000000000
02001054696d6573204e657720526f6d616e000000040000002d01000004000000f00101
0009000000320ae0010003010000002800a60009000000320ae001ec05010000002900a6
0017000000fb02c0fe0000000000009001000000cc0002001054696d6573204e65772052
6f6d616e20437972000000040000002d01010004000000f001000009000000320a6002ff
04010000003000a0000a00000026060f000a00ffffffff01000000000010000000fb0210
00080000000000bc02000000000102022253797374656d0006040000002d010000040000
00f0010100030000000000555501165555320055553b053fff80006aaa87056aaa80006a
aa86133fff8000). Эта характеристика приведена на рис. 6.

Так как фазового сдвига между гармониками входного и выходного сигнала
нет, то характеристика совпадает с вещественной осью.

Нелинейный элемент типа ” зона нечувствительности “. Характеристики
звена показаны на рис. 7. Подобными характеристиками обладают различного
типа усилители в области малых входных сигналов.

picscalex60010009000003665c000000006526000000001610000026060f002220574d4
64301000000000001004e55000000000400000000200000e84a0000e86a0000010000006
c0000000000000000000000ea010000310100000000000000000000eb4a0000b02e00002
0454d4600000100e86a00000c00000001000000000000000000000000000000000400000
0030000900100002c010000000000000000000000000000801a0600e0930400460000002
c00000020000000454d462b014001001c000000100000000210c0db01000000600000006
000000046000000841c0000781c0000454d462b224004000c000000000000001e4009000
c00000000000000244001000c000000000000003040020010000000040000000000803f2
14007000c0000000000000008400005d01b0000c41b00000210c0db01000000000000000
000000000000000000000000100000089504e470d0a1a0a0000000d49484452000001eb0
0000132080200000055a06f11000000017352474200aece1ce9000000097048597300000
ec400000ec401952b0e1b00001b4a49444154785eed9ded9ae4a6ae46f79cfbbfe7393d2
12104db7c4a20c1ea1f792a3d20a425f9b54c51d5bf7efffefd3f7e2000010840c02181f
f73e8332e4300021080c01f0228387500010840c02b0114dc6be6f01b021080000a4e0d4
0000210f04a0005f79a39fc860004208082530310800004bc1240c1bd660ebf21000108a
0e0d40004200001af045070af99c36f0840000228383500010840c02b0114dc6be6f01b0
21080000a4e0d40000210f04a0005f79a39fc860004208082530310800004bc1240c1bd6
60ebf21000108a0e0d40004200001af045070af99c36f0840000228383500010840c02b0
114dc6be6f01b021080000a4e0d40000210f04a0005f79a39fc86c025047efdfa7549a40
361a2e003d09802010840c0040114dc441a7002024a04b206967e5689f32eb328f82ef2a
c0b0108406096000a3e4b90f910b89cc07c5f3f6fe1da14fcfafdfbf761c1bf56c379611
e9635c25122f07339a4c59ffeeff34a0923b3df97af9dcc7e1645f95fd3c18591ed46941
85a367b660ffe5373e127a0bf56bebf5a1b5a1ecbd7e432dfb26be479bda4035ebdaaca7
77b2c3f6b5196edb8e2c80315fc5abd6e6f7fb85a062e957ba6045dae5e478d82db382ce
0ed1a7c4f460a911ea8e031da500dd5423cb20e9ecdd1f3d198abe5c8d44f0625b565216
567329ce3a79fa3e0afa7a6ae95efc6c245c41b415d32ac5776abd7d7ebc6fa17ccaab54
bb2d015e6390a9e867d73f7fdb55fd955160cbe8dc0cf25d325dfe57b7f97a9e7eedf6df
067e23d53c1678878991b2eb9ec273a9f1d3f889b8ce98547cbe325d70bfc2c34cbb1c6c
23e75f8997749d0d4bc337e2d1ca8e0cf065ca4e00ce6f8f5c8cd33d8f48cc153b54f856
3305fc65dfa12f1f0fbe77fbfc2c91af057b3614cf8a102670ae334058fd59036a73380e
ccccd0a9d0eda4e6a8ef1a46bdbba10f5d7a3e131a0ec04729a82c71b7bf6c20e71714f9
ecf1ce24b60f01e025f22deb8e99136d7e935187660eec1b82cd2d3147c1938230b21df4
61271921baf229e6dd99d14afeb585070c7e943be1d27cfb6ebd5ed94d74dbc42975d351
879b03dd8551a2878172e0643e01c02e9a99296d7cfc853c94edf82ca4666c6bf08b2cd3
2505be77cb355f60ef8000be353b2005f8fdcc44e276b64e2e0a7115a1ee3799f746f3ee
35158d37323f1f570fda466438c5fcf94c75fda3329a6079fa1b76d6ef5c8cd6b3bf37a0
fd816030b3b2190ee8067afa3ec0e84f2bab13e7c3f1870e08c2928b8cb3cf61eb9e16d2
8976936efb4a0e0d2688f651b051fe3667a16ef1a994ecf59ce897c2407f91e2e0a147c1
89de989d5e6886bc674fe5c39572db66a34f316aa4b9c3a00053f35b37f3e06fdf5e63ef
27d6cd609ec320228f8c909ff6a6d68794ecefa71b151ae8594a2e0c7d53b0141e09b006
a785875a0e0872594702e22907e52e6a2b00935218082530e107049804f30ba4c9bb4d32
8b83451ec41600901f6439660b6be080a6e3d43f807010840e08b000a4e6d40000210f04
a0005f79a39fc86404a20fe0506f6c7af2a0c14fcaa7413ecb104c2b678f8029c638324b
00701149ca280c00904f89ced0959ec8f0105ef67c60c081823807c1b4bc83a7750f075a
c5909021a04d8f8d6a0eac5260aee2553f809817702ed5f260cc1f308a0e0e7e59488ae2
380885f97f27f0246c1af4d3d811f4500113f2a9dcdc1a0e0cda81808014b04befe363cd
be296b2a4ee0b7fab5e1db1d4029c37902279951dcae6ec74d3839f9d5fa28300044e268
0829f9c5d62830004ce2680820be7975d4861a098830004be09a0e092d5817c4bd2c4160
42050238082d70835ff7b90eff017e291f2666c0c840004c6097016659c5d3a3395eff07
bf1af88e350814caa2eb312cb2696e80f80d861c42acd7e93b620cf31597997076707d5b
f566cf12a8e492faed7d5ef49320a2e90ebf4da782d328135febaeac4ef0a228e61c4328
1dbcae6f5f1f7e00b875d94d9ab2f93ef5973cc8700047a08a47fdae2c2dd4b14bca7581
e6391ef297c4c86c0288128dc9981f0372eb29fd1451ccc43c1c793d422df698330be123
3210081bf083c85fb1eb17e2d8173b65617eff715e4fbb92d2eb20db720c0ec2154c4ed5
dca73522c330c1794cd8c7bed7349280ade5e2d9591e5ee3b7bd35f4a07b52fc5a77ded1
5c5f2f1b6bb9561f71bcb24a50302bffcb449b900d845e9be405a364f82514717cfababe
16c7b37a0dd134e8a6537cbcdeb873d93e0047fc4f9351928785f8d76c9779fe97da30b7
71a77227e522cfb2a62ffca6877630e50f04650ddc3f8c6fd6e644c80c03f0faf9184d42
6e4a96851f08eccb637e0f1b92feca574acb17c6875abc7511b7e522ccb0bc1ca826c9b7
46502056fc53526c474e2ad7c19773d816ce7e47a1e4d0050f03aa65858e1bd94b294c77
fcd868ddd00eacecd8da836adf161c2a6ff69f427c532975597b369bdc7d2b6f93cb87d5
d78dd8f6b148bb1947ccdd258b4dd66fb48d9a8dbadb57bd83eb27d75b3235d049bcab75
992361deb537047826b0ab7c8bb31c03795d3aa332249afae521d605fc191ef6a120b03f
a147c66a5ec81f7e77f654bdc7ea54ed27b0dd04bd4ed7eb68f9ce4d93bddac63e5408cb
b8d7cf7d661367ec33e78c899ac7c4f52603a0420b09e00f23dcf7cb58223dff3398b168
cb75769a4d57780c360cb1135862098dfb34d21df22f95daae065f9fef9d7f44724bc192
363fe6421ac8c68e55a33608f9fcb3b16ed29e659bc9dd5ebc8750a5e95efb0b512bffd6
0ef6510bdedf52756647811ff2b5ea959bb9a3a1c9ad9c9ca109f5eed612d37e08146350
47168a71ae4595c2ab38b14fcaa84a59fe259a94ad9cd43aa44b0d345c0e0bdb3cbff058
341240879858267f2fdba3b917ef19885044ffa13455cbcf57edd2f7e2566016356a9851
e76e5ad6ee6fa29b7e1917928f299858e9fab74691ccf2d0b505dc1dbbbefa8ec46522be
28fc665ec45ec5eafa55705f4155141c4d3c72023656c4dd1da05c19ae736fdd155f0d76
cc5cdee679f9bfe662faf6c5b79cc19f16b38dc54c4cd8e45373c2b2860fae32ea234846
10e174ed468682ec49886aca8e037df6c539d15ac5a3b77b8c9cbe6f52e3e6973f1f418c
2e2750f58cedd0ddb32732d059f91ef54f204e56f380dbdfea4f29dbeab39ec001321700
081194d38207ca51054147c205551e9b2ee75d7ed7ad89f107b14fde70ba54462160210b
89080fca6ea807c8b703f6083b8cca110e093f9ae2c88a4d2b5116be48d5c17b195d9d59
3b92eaa82f3c23db8b5f23d356d595caf570597cadeec5bd800dc4be0b93a35299e11490
547bec5d3d365901d9b2e5caa838d74beaa3162dc0201310547bef7a633ddb8fff184666
7573a38a3f2248f38e855a38c829321bd0cb55b4e8fe8b5cf62240420e097808c82d3f4f
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701ffff030000000000

Рис. 7

Если амплитуда входного
сигналаwmetafile8010009000003b200000002001700000000000500000009020000000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расположена в пределах диапазона а, то выходной сигнал равен нулю в
противном случае выходной сигнал равен не нулю, так как появляются
вершины входной гармоники. Фазового сдвига нет. При больших амплитудах
входного сигнала коэффициент усиления имеет постоянное значение, т. е.
нелинейность не оказывает существенного влияния на выходной сигнал.

3. Нелинейный элемент типа ” трехпозиционное реле без гистерезиса”.
Характеристики звена показаны на рис.8. Эта характеристика присуща
релейным системам с обратной связью.

Так как характеристика однозначная, то фазового сдвига нет. Если
амплитуда входного
сигналаwmetafile8010009000003b200000002001700000000000500000009020000000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, то
выходной сигнал превращается в последовательность импульсов. При малых и
больших амплитудах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 коэффициент k
– мал.
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108400002010820d60192848b10800004106b6a0002108040000288758024e1220420000
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ffffffffffffffffffff9fffefffffffffffffffffffffffffffffffffffffffffffffff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Рис. 8

4. Нелинейный элемент типа “релейная характеристика”. Характеристики
звена показаны на (рис. 9).

Рис. 9

Первая гармоника будет сдвинута в сторону запаздывания. Величина
фазового сдвига зависит от амплитуды входного сигнала и величины а.

Отношение амплитуд А1/А0 при больших значениях амплитуды входного
сигнала стремится к 0 , при этом фазовый сдвиг уменьшается. При малых
амплитудах фазовый сдвиг равен 90.

Если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 – вектор, то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 –
обратный вектор.

5. Нелинейный элемент типа “люфт, зазор”. Характеристики данного

Рис. 10

нелинейного элемента приведены на рис. 10.

Модели нелинейных элементов. Модели нелинейных элементов могут быть
реализованы путем включения в цепь операционного усилителя (на вход или
в обратную связь) нелинейных двухполюсников. В зависимости от
характеристик двухполюсника и способа его подключения можно реализовать
любую нелинейную зависимость (рис. 11а, б, в).

Р?. 11

Модели нелинейных звеньев широко используются при моделировании систем
автоматического управления на ЭВМ.

Литература

1. Атабеков Г.И., Тимофеев А.Б., Купалян С.Д., Хухриков С.С.
Теоретические основы электротехники (ТОЭ). Нелинейные электрические
цепи. Электромагнитное поле. 5-е изд. Изд-во: ЛАНЬ, 2005. – 432с.

2. Бесекерский В.А., Попов Е.П. “Теория систем автоматического
управления”. Профессия, 2003 г. – 752с.

3. Гаврилов Нелинейные цепи в программах схемотехнического
моделирования. Изд-во: СОЛОН-ПРЕСС, 2002. – 368с.

4. Дорф Р., Бишоп Р. Автоматика. Современные системы управления. 2002г.
– 832с.

5. Сборник задач по теории автоматического регулирования и управления/
Под редакцией В. А. Бесекерского. — M.: Наука, 1978.

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