10
БЕЛОРУССКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ ИНФОРМАТИКИ И РАДИОЭЛЕКТРОНИКИ
Кафедра РТС
РЕФЕРАТ
На тему:
“Дискретные системы радиоавтоматики”
МИНСК, 2008
Передаточные функции дискретных систем
Передаточная функция дискретной системы определяется как отношение
z-изображений выходной и входной величин при нулевых начальных условиях: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;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.
Передаточные функции дискретной системы при нулевом значении
флюктуационной составляющей определяются выражениями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; (1)
picscalex100010009000003f301000003001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02e00400121200000026060f001a00ffffffff000010000000c0ffffff
c0ffffffc0110000a00400000b00000026060f000c004d61746854797065000010010800
0000fa0200001000000000000000040000002d0100000500000014025002680705000000
13025002a4111c000000fb0240fe0000000000009001000000000402001054696d657320
4e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d0101000800
0000320a1e04ff1001000000297908000000320a1e04850f01000000287908000000320a
1e04500701000000317908000000320a9701e80f01000000297908000000320a97016e0e
01000000287908000000320ac002f60401000000297908000000320ac0027c0301000000
28791c000000fb0240fe0000000000009001010000000402001054696d6573204e657720
526f6d616e005bd4f47764d4f4770100000000003000040000002d01020004000000f001
010008000000320a1e043b10010000007a7908000000320a1e04670b0100000057790800
0000320a1e04b60901000000537908000000320a9701240f010000007a7908000000320a
9701500a01000000577908000000320a97019f0801000000537908000000320ac0023204
010000007a7908000000320ac00247000100000048791c000000fb0280fe000000000000
9001010000cc0402001054696d6573204e657720526f6d616e005bd4f47764d4f4770100
000000003000040000002d01010004000000f001020008000000320a8e04ef0c02000000
cfcd08000000320a8e04ae0a01000000e4cd08000000320a0702d80b02000000cfcd0800
0000320a0702970901000000e4cd08000000320a3003890201000000f3cd1c000000fb02
40fe0000000000009001000000020402001053796d626f6c0077400000003c030ab35bd4
f47764d4f4770100000000003000040000002d01020004000000f001010008000000320a
1e045d08010000002bcd08000000320ac002fb05010000003dcd1c000000fb0280fe0000
000000009001010000020402001053796d626f6c007740000000e1030aca5bd4f47764d4
f4770100000000003000040000002d01010004000000f001020008000000320a3003b701
010000006ccd0a00000026060f000a00ffffffff0100000000001c000000fb0210000700
00000000bc02000000cc0102022253797374656d000000000a0000000400000000000200
00000100000000003000040000002d01020004000000f0010100030000000000. (2)
Если в системе используется фиксатор, то передаточная функция
приведенной непрерывной части системы определяется выражением
picscalex990100090000030b02000003001c00000000000500000009020000000005000
000020101000000050000000102ffffff00050000002e0118000000050000000b0200000
000050000000c022005e0121200000026060f001a00ffffffff000010000000c0ffffffa
7ffffffa0120000c70400000b00000026060f000c004d617468547970650000e00008000
000fa0200001000000000000000040000002d010000050000001402f002dc07050000001
302f002e00d1c000000fb0240fe0000000000009001000000000402001054696d6573204
e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d01010008000
000320a60030d1201000000297908000000320a6003a81001000000287908000000320a4
802c40701000000317908000000320a6003870501000000297908000000320a600322040
100000028791c000000fb0240fe0000000000009001010000000402001054696d6573204
e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d01020004000
000f001010008000000320a6003501101000000737908000000320a6003f70d010000005
77908000000320abc048a0a01000000737908000000320a48022e0a01000000657908000
000320a6003ca0401000000737908000000320a60030f000100000057791c000000fb028
0fe0000000000009001010000cc0402001054696d6573204e657720526f6d616e005bd4f
47764d4f4770100000000003000040000002d01010004000000f001020008000000320ad
003610f01000000f4791c000000fb0280fe0000000000009001010000000402001054696
d6573204e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d010
20004000000f001010008000000320a7f01040c0200000073541c000000fb0280fe00000
00000009001010000cc0402001054696d6573204e657720526f6d616e005bd4f47764d4f
4770100000000003000040000002d01010004000000f001020008000000320ad00391010
2000000cfcd1c000000fb0280fe0000000000009001000000020402001053796d626f6c0
0774000000078030a115bd4f47764d4f4770100000000003000040000002d01020004000
000f001010008000000320a7f010e0b010000002dcd1c000000fb0240fe0000000000009
001000000020402001053796d626f6c00774000000018040ab85bd4f47764d4f47701000
00000003000040000002d01010004000000f001020008000000320a4802dd08010000002
dcd08000000320a60037d06010000003dcd0a00000026060f000a00ffffffff010000000
0001c000000fb021000070000000000bc02000000cc0102022253797374656d000000000
a000000040000000000020000000100000000003000040000002d01020004000000f0010
100030000000000,
где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 ? передаточная функция последовательного
соединения фиксатора и формирующего фильтра.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;
picscalex100010009000003cd02000003001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02a006e01c1200000026060f001a00ffffffff000010000000c0ffffff
bfffffffa01c00005f0600000b00000026060f000c004d61746854797065000070010800
0000fa0200001000000000000000040000002d01000005000000140250030c0a05000000
13025003b60e050000001402500381130500000013025003af1b1c000000fb0240fe0000
000000009001000000020402001053796d626f6c00774000000007040a4d5bd4f47764d4
f4770100000000003000040000002d01010008000000320aba05cb1b01000000ef790800
0000320a3c06cb1b01000000fe7908000000320abd02cb1b01000000ef7908000000320a
0d04cb1b01000000fd7908000000320ade01cb1b01000000fc7908000000320aba059a12
01000000ef7908000000320a3c069a1201000000ee7908000000320abd029a1201000000
ef7908000000320a0d049a1201000000ed7908000000320ade019a1201000000ec790800
0000320ac0030710010000002d7908000000320aa405d20e01000000fe7908000000320a
0d04d20e01000000fd7908000000320a7602d20e01000000fc7908000000320aa4052509
01000000ee7908000000320a0d04250901000000ed7908000000320a7602250901000000
ec7908000000320ac0039206010000003d791c000000fb0280fe00000000000090010000
00020402001053796d626f6c00774000000044030a235bd4f47764d4f477010000000000
3000040000002d01020004000000f001010008000000320a87017314010000002d791c00
0000fb0240fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01010004000000f00102000800
0000320a1c05441701000000737908000000320a50024d1a01000000737908000000320a
5002f41601000000577908000000320a5002931301000000657908000000320ac0036611
010000005a7908000000320a1c050d0c01000000737908000000320a5002540d01000000
737908000000320a5002fb0901000000577908000000320ac003f107010000005a790800
0000320ac003d804010000007a7908000000320ac0030f000100000057791c000000fb02
80fe0000000000009001010000cc0402001054696d6573204e657720526f6d616e005bd4
f47764d4f4770100000000003000040000002d01020004000000f001010008000000320a
c0025e1801000000f4791c000000fb0280fe000000000000900101000000040200105469
6d6573204e657720526f6d616e005bd4f47764d4f4770100000000003000040000002d01
010004000000f001020008000000320a870169150200000073541c000000fb0280fe0000
000000009001010000cc0402001054696d6573204e657720526f6d616e005bd4f47764d4
f4770100000000003000040000002d01020004000000f001010008000000320ac002650b
01000000f45408000000320a3004910102000000cfcd1c000000fb0240fe000000000000
9001000000000402001054696d6573204e657720526f6d616e005bd4f47764d4f4770100
000000003000040000002d01010004000000f001020008000000320a50020a1b01000000
29cd08000000320a5002a5190100000028cd08000000320a5002110e0100000029cd0800
0000320a5002ac0c0100000028cd08000000320ac0039c050100000029cd08000000320a
c00322040100000028cd0a00000026060f000a00ffffffff0100000000001c000000fb02
1000070000000000bc02000000cc0102022253797374656d000000000a00000004000000
0000020000000100000000003000040000002d01020004000000f0010100030000000000
.
Умножение изображения по Лапласу на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соответствует
задержке оригинала на величину Т. С учетом теоремы сдвига и обозначения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 (3)
получим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 (4)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 ? определяется по
таблицам z – изображений.
Разностные уравнения
Разностные уравнения определяют связь между дискретными значениями
выходной и входной величин в тактовых точках.
Чтобы составить разностное уравнение, надо представить дискретную
передаточную функцию в следующем виде: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. (5)
Если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? значение выходной величины, а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? входной в виде
z-изображения, то связь между ними определяется выражением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. (6)
Подставим (5) в (6):
picscalex990100090000034b03000002001c00000000000500000009020000000005000
000020101000000050000000102ffffff00050000002e0118000000050000000b0200000
000050000000c02000380381200000026060f001a00ffffffff000010000000c0ffffffa
fffffff40380000af0200000b00000026060f000c004d61746854797065000060001c000
000fb0240fe0000000000009001000000000402001054696d6573204e657720526f6d616
e005bd4f47764d4f4770100000000003000040000002d01000008000000320a40025c370
2000000292e08000000320a4002e23501000000282e1c000000fb0240fe0000000000009
001000000a10402001054696d6573204e657720526f6d616e005bd4f47764d4f47701000
00000003000040000002d01010004000000f001000008000000320a4002923401000000c
b2e1c000000fb0240fe0000000000009001000000000402001054696d6573204e6577205
26f6d616e005bd4f47764d4f4770100000000003000040000002d01000004000000f0010
10008000000320a4002f13301000000292e09000000320a4002d92b030000002e2e2e650
8000000320a4002241c01000000282e08000000320a4002dd1901000000292e090000003
20a40024912030000002e2e2e6508000000320a4002e30301000000312e08000000320a4
002e00202000000292808000000320a400266010100000028281c000000fb0280fe00000
00000009001000000000402001054696d6573204e657720526f6d616e005bd4f47764d4f
4770100000000003000040000002d01010004000000f001000008000000320a770147290
1000000322808000000320ab002922601000000322808000000320a77013c23010000003
12808000000320ab002cf2001000000312808000000320ab002851d01000000302808000
000320a7701b70f01000000322808000000320ab002020d01000000322808000000320a7
701880901000000312808000000320ab0021b070100000031281c000000fb0240fe00000
00000009001010000000402001054696d6573204e657720526f6d616e005bd4f47764d4f
4770100000000003000040000002d01000004000000f001010008000000320a400298360
10000007a2808000000320a4002db30010000007a2808000000320a4002c12e010000006
22808000000320a40027e27010000007a2808000000320a4002be2501000000622808000
000320a40029d21010000007a2808000000320a4002252001000000622808000000320a4
002b71c01000000622808000000320a40021b17010000007a2808000000320a40023f150
1000000612808000000320a4002ee0d010000007a2808000000320a4002180c010000006
12808000000320a4002e907010000007a2808000000320a40025b0601000000612808000
000320a40021c02010000007a2808000000320a40020f000100000056281c000000fb028
0fe0000000000009001010000000402001054696d6573204e657720526f6d616e005bd4f
47764d4f4770100000000003000040000002d01010004000000f001000008000000320a7
701a432010000006d2808000000320ab002952f010000006d2808000000320a7701e4180
10000006e2808000000320ab0022916010000006e281c000000fb0280fe0000000000009
001000000020402001053796d626f6c0077400000004c030a355bd4f47764d4f47701000
00000003000040000002d01000004000000f001010008000000320a7701b431010000002
d2808000000320a77015728010000002d2808000000320a77017622010000002d2808000
000320a7701f417010000002d2808000000320a7701c70e010000002d2808000000320a7
701c208010000002d281c000000fb0240fe0000000000009001000000020402001053796
d626f6c007740000000ec030af65bd4f47764d4f4770100000000003000040000002d010
10004000000f001000008000000320a4002702d010000002b2808000000320a4002962a0
10000002b2808000000320a40026d24010000002b2808000000320a4002d41e010000002
b2808000000320a4002d31a010000003d2808000000320a4002e013010000002b2808000
000320a40020611010000002b2808000000320a4002b90a010000002b2808000000320a4
002fc04010000002b280a00000026060f000a00ffffffff0100000000001c000000fb021
000070000000000bc02000000cc0102022253797374656d000000000a000000040000000
000000000000100000000003000040000002d01000004000000f0010100030000000000
(7)
Применим к левой и правой частям уравнения (7) теорему обращения. С
учетом теоремы запаздывания оригинала можно записать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, (8)
где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;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.
Из уравнения (8) можно определить значения оригинала в тактовых точках: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. (9)
Уравнение (9) является разностным уравнением, определяющим связь между
входной и выходной величинами в тактовых точках.
Операторный коэффициент передачи дискретной системы
Для составления операторного коэффициента передачи вводится оператор
запаздывания – с.
Действие его на временную функцию приводит ее к сдвигу по времени на
величину Т: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;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;
…………………………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.
При использовании оператора с разностное уравнение записывается в виде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,
где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.
Чтобы перейти от дискретной ПФ к операторному коэффициенту передачи,
необходимо сделать замену:
picscalex1000100090000032901000002001c0000000000050000000902000000000500
0000020101000000050000000102ffffff00050000002e0118000000050000000b020000
0000050000000c02a002a0051200000026060f001a00ffffffff000010000000c0ffffff
afffffff600500004f0200000b00000026060f000c004d61746854797065000030001c00
0000fb0240fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e005bd4f47764d4f4770100000000003000040000002d01000008000000320a40028f04
01000000637908000000320a40024e00010000007a791c000000fb0240fe000000000000
9001000000020402001053796d626f6c0077400000006e040a015bd4f47764d4f4770100
000000003000040000002d01010004000000f001000008000000320a4002340301000000
3d791c000000fb0280fe0000000000009001000000020402001053796d626f6c00774000
000064040a5f5bd4f47764d4f4770100000000003000040000002d01000004000000f001
010008000000320a77012b01010000002d791c000000fb0280fe00000000000090010000
00000402001054696d6573204e657720526f6d616e005bd4f47764d4f477010000000000
3000040000002d01010004000000f001000008000000320a7701f5010100000031790a00
000026060f000a00ffffffff0100000000001c000000fb021000070000000000bc020000
00cc0102022253797374656d000000000a00000004000000000000000000010000000000
3000040000002d01000004000000f0010100030000000000.
Комплексный коэффициент передачи дискретной системы
Комплексный коэффициент передачи дискретной системы (частотную
передаточную функцию) можно получить из передаточной функции дискретной
системы путем замены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: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.
Комплексный коэффициент передачи дискретной системы определяется как
отношение комплексных амплитуд управляемой величины Y(kT) и задающего
воздействия в тактовых точках kT. По формированию значений выходного
процесса в тактовых точках дискретная система эквивалентна непрерывной с
комплексным коэффициентом передачи Hд(jw).
Комплексный коэффициент передачи является периодической функцией
переменной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 с
периодом изменения, равным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.
Устойчивость дискретных систем
Устойчивость дискретной системы связана с расположением полюсов ее
передаточной функции на комплексной плоскости. Если все полюса
расположены в левой полуплоскости, система устойчива. Таким образом,
заменив в передаточной функции H(z) z на esT и решив характеристическое
уравнение, можно определить устойчивость.
При переходе от s-плоскости к z-плоскости левая полуплоскость плоскости
s трансформируется в круг единичного радиуса. Поэтому дискретная система
устойчива, если полюсы ее передаточной функции H(z) расположены внутри
окружности единичного радиуса, т.е. удовлетворяют условию
|zi|
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