controle 3 unidade

FACULDADE INDEPENDENTE DO NORDESTE

ENGENHARIA ELÉTRICA

CONTROLE II

VITÓRIA DA CONQUISTA – BAHIA

DEZEMBRO DE 2015

RODRIGO SOUZA DA SILVA

JACQUESON ALVES MONTEIRO NOGUEIRA

ABSON LUZ

SIMULAÇÕES

Trabalho referente a matéria de Controle II referente a nota da a nota integral da terceira unidade. Com a supervisão da professora Nathalia.

VITÓRIA DA CONQUISTA – BAHIA

DEZEMBRO DE 2015

1. OBJETIVOS

1 Encontre uma função transferência para o sistema a ser simulado.

Os dados são referentes a velocidade de referência de um motor, e a velocidade de saída, a partir deste dado encontre, utilizando o bloco de identificação de sistemas do Matlab:

1.1 – A saída utilizando função de transferência;1.2 – A saída utilizando o método arx;1.3 – A saída utilizando o método armax.

OBS: Utilize o workspace vel_ref como entrada e o de saída vel.

Depois, utilizando os seguintes comandos, determine a função transferência para cada saída encontrada acima:

[num,den]=th2tf(arx332)sysd=tf(num,den,1)sysc=d2c(sysd)

2. SIMULAÇÕES

Stepplot do Tf1

P => kp = 143.44PI => kp = 129.1 Ki = 0.6PID => kp = 172.128

Ki = 0.36Kd = 0.09

Stepplot do Amx

P => kp = 18.5PI => kp = 16.65 Ki = 6.66PID => kp = 22.2

Ki = 4Kd = 1

Stepplot do Arx

P => kp = 2.86PI => kp = 2.574 Ki = 70PID => kp = 3.432

Ki = 42Kd = 10.5

Sistema com a função transferencia do tf1

- Para encontrar a função transferência do tf1

>> [num,den]=th2tf (tf1)

sysd=tf(num,den,1)

sysc=d2c(sysd)

num =

Columns 1 through 9

0 0 0 0.0035 3.1212 0.5482 8.9315 1.2020 8.0753

Columns 10 through 17

0.7847 2.8022 0.1701 0.3476 0.0103 0.0111 0.0001 0.0000

den =

Columns 1 through 9

1.0000 3.9258 15.1841 37.7894 65.4515 90.6030 95.9916 82.6671

56.7496


31.0258 13.3894 4.3706 1.0436 0.1657 0.0152 0.0007 0.0000

sysd =

0.003492 z^13 + 3.121 z^12 + 0.5482 z^11 + 8.931 z^10 + 1.202 z^9 + 8.075

z^8 + 0.7847 z^7 + 2.802 z^6 + 0.1701 z^5 + 0.3476 z^4 + 0.0103 z^3 +

0.01108 z^2 + 0.0001442 z + 3.963e-05

--------------------------------------------------------------------------------------

z^16 + 3.926 z^15 + 15.18 z^14 + 37.79 z^13 + 65.45 z^12 + 90.6 z^11 + 95.99

z^10 + 82.67 z^9 + 56.75 z^8 + 31.03 z^7 + 13.39 z^6 + 4.371 z^5 + 1.044 z^4

+ 0.1657 z^3 + 0.01522 z^2 + 0.0006858 z + 3.963e-05

Sample time: 1 seconds

Discrete-time transfer function.

Warning: The model order was increased to handle real negative poles.

> In warning at 25

In ssdata.utInvDiscretize at 73

In ssdata.d2c at 22

In tfdata.d2c at 38

In SystemArray>SystemArray.d2c_ at 446

In tf.tf>tf.d2c_ at 794

In DynamicSystem.d2c at 98

sysc =

-11.31 s^17 - 75.56 s^16 - 532 s^15 - 2422 s^14 - 1.031e04 s^13 - 3.353e04

s^12 - 1.047e05 s^11 - 2.544e05 s^10 - 6.341e05 s^9 - 1.172e06 s^8 - 2.461e06

s^7 - 3.38e06 s^6 - 6.118e06 s^5 - 5.665e06 s^4 - 8.774e06 s^3 - 4.041e06 s^2 -

5.351e06 s + 3.202e05

----------------------------------------------------------------------------------------

s^18 + 10.46 s^17 + 88.56 s^16 + 510.6 s^15 + 2525 s^14 + 1.006e04 s^13 +

3.554e04 s^12 + 1.06e05 s^11 + 2.877e05 s^10 + 6.671e05 s^9 + 1.456e06 s^8

+ 2.676e06 s^7 + 4.819e06 s^6 + 6.901e06 s^5 + 1.023e07 s^4 + 1.05e07 s^3 +

1.235e07 s^2 + 7.063e06 s + 6.148e06

Continuous-time transfer function.

Erro encontrado ao tentar utilizar o controlador

Sistema com a função transferência do amx

- Para encontrar a função transferência do arx401421

>> [num,den]=th2tf(arx401421)

sysd=tf(num,den,1)

sysc=d2c(sysd)

num =

Columns 1 through 9

0 0 0 0 0 0 0 0 0


0 0 0 0 0 0 0 0 0


0 0 0 0.0681 0.0340 -0.0035 0.0600 -0.0411 0.0184


-0.0157 -0.0407 -0.0007 -0.0501 0.0260 0.0359 -0.0250 0.0405

0


0 0 0 0 0

den =

Columns 1 through 9

1.0000 -0.2318 0.0009 -0.1661 0.0173 0.0039 -0.1502 -0.1449 -

0.0982


-0.0250 -0.0154 -0.0591 -0.0323 -0.0184 0.0734 -0.0743 0.0341 -

0.0028


-0.0091 0.0352 -0.0640 0.0681 -0.0520 0.0071 0.0172 -0.0276

0.0102


0.0354 -0.0505 0.0454 -0.0296 0.0194 0.0204 -0.0636 0.0442 -

0.0162


0.0138 -0.0126 -0.0184 0.0376 -0.0150

sysd =

0.06806 z^19 + 0.03402 z^18 - 0.003503 z^17 + 0.05999 z^16 - 0.04113 z^15 +

0.01835 z^14 - 0.01573 z^13 - 0.04068 z^12 - 0.0007436 z^11 - 0.05011 z^10 +

0.02603 z^9 + 0.03592 z^8 - 0.02503 z^7 + 0.04051 z^6

-----------------------------------------------------------------------------------------

z^40 - 0.2318 z^39 + 0.0008586 z^38 - 0.1661 z^37 + 0.01729 z^36 + 0.003881

z^35 - 0.1502 z^34 - 0.1449 z^33 - 0.0982 z^32 - 0.025 z^31 - 0.01543 z^30 -

0.0591 z^29 - 0.03232 z^28 - 0.0184 z^27 + 0.07336 z^26 - 0.07433 z^25 +

0.03408 z^24 - 0.002769 z^23 - 0.009093 z^22 + 0.03516 z^21 - 0.06402 z^20

+ 0.06808 z^19 - 0.05205 z^18 + 0.007147 z^17 + 0.01718 z^16 - 0.02758 z^15

+ 0.01019 z^14 + 0.0354 z^13 - 0.05053 z^12 + 0.04541 z^11 - 0.02961 z^10 +

0.01938 z^9 + 0.02039 z^8 - 0.06362 z^7 + 0.0442 z^6 - 0.01621 z^5 + 0.01378

z^4 - 0.01264 z^3 - 0.01844 z^2 + 0.03758 z - 0.01503




> In warning at 25


In ssdata.d2c at 22

In tfdata.d2c at 38




sysc =

0.07811 s^40 + 0.2943 s^39 + 5.168 s^38 + 17.61 s^37 + 154.7 s^36 + 475.9

s^35 + 2774 s^34 + 7695 s^33 + 3.332e04 s^32 + 8.317e04 s^31 + 2.838e05

s^30 + 6.358e05 s^29 + 1.769e06 s^28 + 3.548e06 s^27 + 8.226e06 s^26 +

1.471e07 s^25 + 2.878e07 s^24 + 4.567e07 s^23 + 7.592e07 s^22 + 1.063e08

s^21 + 1.505e08 s^20 + 1.844e08 s^19 + 2.22e08 s^18 + 2.356e08 s^17 +

2.404e08 s^16 + 2.17e08 s^15 + 1.874e08 s^14 + 1.386e08 s^13 + 1.036e08

s^12 + 5.676e07 s^11 + 4.078e07 s^10 + 1.174e07 s^9 + 1.205e07 s^8 -

4.434e05 s^7 + 2.749e06 s^6 - 6.967e05 s^5 + 3.782e05 s^4 - 8.276e04 s^3 +

1.413e04 s^2 - 1949 s + 753.5

----------------------------------------------------------------------------------------

s^41 + 4.288 s^40 + 78.02 s^39 + 297.2 s^38 + 2753 s^37 + 9356 s^36 +

5.83e04 s^35 + 1.774e05 s^34 + 8.3e05 s^33 + 2.263e06 s^32 + 8.419e06 s^31

+ 2.059e07 s^30 + 6.294e07 s^29 + 1.38e08 s^28 + 3.538e08 s^27 + 6.941e08

s^26 + 1.512e09 s^25 + 2.647e09 s^24 + 4.935e09 s^23 + 7.674e09 s^22 +

1.229e10 s^21 + 1.688e10 s^20+ 2.322e10 s^19 + 2.796e10 s^18 + 3.29e10

s^17 + 3.439e10 s^16 + 3.437e10 s^15 + 3.079e10 s^14 + 2.584e10 s^13 +

1.949e10 s^12 + 1.35e10 s^11 + 8.368e09 s^10 + 4.656e09 s^9 + 2.289e09 s^8

+ 9.81e08 s^7 + 3.611e08 s^6 + 1.108e08 s^5 + 2.747e07 s^4 + 5.175e06 s^3 +

6.723e05 s^2 + 4.802e04 s + 753.5


Sistema com Controlador P

Sistema com Controlador PI

Sistema com Controlador PID

- Para encontrar a função transferência do amx412022

>> [num,den]=th2tf(amx412022)

sysd=tf(num,den,1)

sysc=d2c(sysd)

num =

Columns 1 through 9

0 0 0.0137 -0.0066 -0.0095 0.0180 -0.0150 0.1196 -0.0884


0.0423 0.0244 -0.0679 0.0212 0.0329 -0.0153 0.0536 -0.0405 -

0.0170


0.0032 0.0054 -0.0073 0.0364 0 0 0 0 0


0 0 0 0 0 0 0 0 0


0 0 0 0 0 0

den =

Columns 1 through 9

1.0000 -0.8058 0.0731 -0.1419 0.1138 0.0417 -0.1390 0.0749 -

0.0837


0.0702 0.0122 -0.1138 0.0066 0.0113 0.0404 -0.0672 0.0136 -

0.0513


0.0578 0.0315 -0.0723 0.0774 -0.1057 0.0600 0.0209 -0.0277

0.0045


0.0148 -0.0469 0.0635 -0.0399 0.0218 0.0015 -0.0625 0.0799 -

0.0317


0.0082 -0.0173 -0.0098 0.0470 -0.0345 0.0073

sysd =

0.01368 z^39 - 0.006555 z^38 - 0.009474 z^37 + 0.01796 z^36 - 0.01501 z^35

+ 0.1196 z^34 - 0.08842 z^33 + 0.0423 z^32 + 0.02438 z^31 - 0.06794 z^30 +

0.0212 z^29 + 0.03289 z^28 - 0.01531 z^27 + 0.05355 z^26 - 0.0405 z^25 -

0.01704 z^24 + 0.003172 z^23 + 0.005393 z^22 - 0.007315 z^21 + 0.0364 z^20

-------------------------------------------------------------------------------------

z^41 - 0.8058 z^40 + 0.07313 z^39 - 0.1419 z^38 + 0.1138 z^37 + 0.04169 z^36

- 0.139 z^35 + 0.07494 z^34 - 0.08373 z^33 + 0.07021 z^32 + 0.01225 z^31 -

0.1138 z^30 + 0.006596 z^29 + 0.01131 z^28 + 0.04036 z^27 - 0.06725 z^26 +

0.0136 z^25 - 0.05126 z^24 + 0.05777 z^23 + 0.03148 z^22 - 0.07234 z^21 +

0.07738 z^20 - 0.1057 z^19 + 0.06003 z^18 + 0.02087 z^17 - 0.02769 z^16 +

0.004505 z^15 + 0.01479 z^14 - 0.04685 z^13 + 0.06353 z^12 - 0.03985 z^11 +

0.02182 z^10 + 0.001455 z^9 - 0.06248 z^8 + 0.0799 z^7 - 0.03173 z^6 +

0.008204 z^5 - 0.01727 z^4 - 0.009821 z^3 + 0.047 z^2 - 0.03454 z + 0.007337




> In warning at 25


In ssdata.d2c at 22

In tfdata.d2c at 38




sysc =

0.01224 s^41 + 0.06297 s^40 + 0.8729 s^39 + 3.772 s^38 + 27.63 s^37 + 102.5

s^36 + 520.5 s^35 + 1685 s^34 + 6587 s^33 + 1.883e04 s^32 + 5.994e04 s^31 +

1.527e05 s^30 + 4.092e05 s^29 + 9.337e05 s^28 + 2.154e06 s^27 + 4.412e06

s^26 + 8.88e06 s^25 + 1.631e07 s^24 + 2.883e07 s^23 + 4.722e07 s^22 +

7.342e07 s^21 + 1.064e08 s^20 + 1.45e08 s^19 + 1.843e08 s^18 + 2.185e08

s^17 + 2.41e08 s^16 + 2.466e08 s^15 + 2.34e08 s^14 + 2.053e08 s^13 +

1.667e08 s^12 + 1.25e08 s^11 + 8.665e07 s^10 + 5.533e07 s^9 + 3.24e07 s^8 +

1.722e07 s^7 + 8.163e06 s^6 + 3.372e06 s^5 + 1.178e06 s^4 + 3.339e05 s^3 +

7.126e04 s^2 + 1.015e04 s + 1017

----------------------------------------------------------------------------------------

s^42 + 4.996 s^41 + 80.94 s^40 + 352 s^39 + 2954 s^38 + 1.128e04 s^37 +

6.463e04 s^36 + 2.177e05 s^35 + 9.494e05 s^34 + 2.834e06 s^33 + 9.935e06

s^32 + 2.633e07 s^31+ 7.664e07 s^30 + 1.805e08 s^29 + 4.45e08 s^28 +

9.308e08 s^27 + 1.967e09 s^26 + 3.648e09 s^25 + 6.654e09 s^24 + 1.091e10

s^23 + 1.722e10 s^22 + 2.483e10 s^21 + 3.395e10 s^20 + 4.277e10 s^19 +

5.044e10 s^18 + 5.507e10 s^17 + 5.566e10 s^16 + 5.206e10 s^15 + 4.463e10

s^14 + 3.523e10 s^13 + 2.522e10 s^12 + 1.646e10 s^11 + 9.619e09 s^10 +

5.047e09 s^9 + 2.328e09 s^8 + 9.405e08 s^7 + 3.246e08 s^6+ 9.418e07 s^5 +

2.213e07 s^4 + 4.022e06 s^3 + 5.177e05 s^2 + 3.948e04 s + 1017


Sistema da função transferencia do arx

Sistema com Controlador P

Sistema com Controlador PI

Sistema com Controlador PID

controle 3 unidade

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