Файл: Лабораторная работа 3 по дисциплине Программные средства для анализа и синтеза систем управления Создание объектов типа lti.docx

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y5 0 0 0 0 0 0 0y6 0 0 0 0 0 0 0y7 0 0 0 0 0 0 0D = u1 u2 u3 u4 u5 u6 u7 u8 u9 u10y1 0 0 0 0 0 0 0 0 0 0y2 0 0 0 0 0 0 0 0 0 0y3 0 0 0 0 0 0 0 0 0 0y4 0 0 0 0 0 0 0 0 0 0y5 0 0 0 0 0 0 0 1 0 0y6 0 0 0 0 0 0 0 0 1 0y7 0 0 0 0 0 0 0 0 0 1Пункт 1.4SS4 = ss(app4)SS4 =A = x1 x2 x3 x4 x5 x6 x7 x8 x9x1 -3 4 0 0 0 0 0 0 0x2 -4 -3 0 0 0 0 0 0 0x3 0 0 -2 4 0 0 0 0 0x4 0 0 -4 -2 0 0 0 0 0x5 0 0 0 0 -4 2 0 0 0x6 0 0 0 0 -2 -4 0 0 0x7 0 0 0 0 0 0 -3 3 0x8 0 0 0 0 0 0 -3 -3 0x9 0 0 0 0 0 0 0 0 -2x10 0 0 0 0 0 0 0 0 -4x11 0 0 0 0 0 0 0 0 0x12 0 0 0 0 0 0 0 0 0x13 0 0 0 0 0 0 0 0 0x14 0 0 0 0 0 0 0 0 0x15 0 0 0 0 0 0 0 0 0x16 0 0 0 0 0 0 0 0 0x17 0 0 0 0 0 0 0 0 0x18 0 0 0 0 0 0 0 0 0x19 0 0 0 0 0 0 0 0 0x20 0 0 0 0 0 0 0 0 0x21 0 0 0 0 0 0 0 0 0x22 0 0 0 0 0 0 0 0 0x23 0 0 0 0 0 0 0 0 0x24 0 0 0 0 0 0 0 0 0x25 0 0 0 0 0 0 0 0 0x26 0 0 0 0 0 0 0 0 0x27 0 0 0 0 0 0 0 0 0x28 0 0 0 0 0 0 0 0 0x10 x11 x12 x13 x14 x15 x16 x17 x18x1 0 0 0 0 0 0 0 0 0x2 0 0 0 0 0 0 0 0 0x3 0 0 0 0 0 0 0 0 0x4 0 0 0 0 0 0 0 0 0x5 0 0 0 0 0 0 0 0 0x6 0 0 0 0 0 0 0 0 0x7 0 0 0 0 0 0 0 0 0x8 0 0 0 0 0 0 0 0 0x9 4 0 0 0 0 0 0 0 0x10 -2 0 0 0 0 0 0 0 0x11 0 -5 2 0 0 0 0 0 0x12 0 -2 -5 0 0 0 0 0 0x13 0 0 0 -4 5 0 0 0 0x14 0 0 0 -5 -4 0 0 0 0x15 0 0 0 0 0 -3 2 0 0x16 0 0 0 0 0 -2 -3 0 0x17 0 0 0 0 0 0 0 -3 2x18 0 0 0 0 0 0 0 -2 -3x19 0 0 0 0 0 0 0 0 0x20 0 0 0 0 0 0 0 0 0x21 0 0 0 0 0 0 0 0 0x22 0 0 0 0 0 0 0 0 0x23 0 0 0 0 0 0 0 0 0x24 0 0 0 0 0 0 0 0 0x25 0 0 0 0 0 0 0 0 0x26 0 0 0 0 0 0 0 0 0x27 0 0 0 0 0 0 0 0 0x28 0 0 0 0 0 0 0 0 0x19 x20 x21 x22 x23 x24 x25 x26 x27x1 0 0 0 0 0 0 0 0 0x2 0 0 0 0 0 0 0 0 0x3 0 0 0 0 0 0 0 0 0x4 0 0 0 0 0 0 0 0 0x5 0 0 0 0 0 0 0 0 0x6 0 0 0 0 0 0 0 0 0x7 0 0 0 0 0 0 0 0 0x8 0 0 0 0 0 0 0 0 0x9 0 0 0 0 0 0 0 0 0x10 0 0 0 0 0 0 0 0 0x11 0 0 0 0 0 0 0 0 0x12 0 0 0 0 0 0 0 0 0x13 0 0 0 0 0 0 0 0 0x14 0 0 0 0 0 0 0 0 0x15 0 0 0 0 0 0 0 0 0x16 0 0 0 0 0 0 0 0 0x17 0 0 0 0 0 0 0 0 0x18 0 0 0 0 0 0 0 0 0x19 -1 3 0 0 0 0 0 0 0x20 -3 -1 0 0 0 0 0 0 0x21 0 0 -3 3 0 0 0 0 0x22 0 0 -3 -3 0 0 0 0 0x23 0 0 0 0 -4 4 0 0 0x24 0 0 0 0 -4 -4 0 0 0x25 0 0 0 0 0 0 -1 1 0x26 0 0 0 0 0 0 -1 -1 0x27 0 0 0 0 0 0 0 0 -1x28 0 0 0 0 0 0 0 0 -2x28x1 0x2 0x3 0x4 0x5 0x6 0x7 0x8 0x9 0x10 0x11 0x12 0x13 0x14 0x15 0x16 0x17 0x18 0x19 0x20 0x21 0x22 0x23 0x24 0x25 0x26 0x27 2x28 -1B = u1 u2 u3 u4 u5x1 0 0 0 0 0x2 2.991 0 0 0 0x3 0 0 0 0 0x4 2.991 0 0 0 0x5 0 0 0 0 0x6 3.557 0 0 0 0x7 0 0 0 0 0x8 2.582 0 0 0 0x9 0 0 0 0 0x10 0 3.138 0 0 0x11 0 0 0 0 0x12 0 3.557 0 0 0x13 0 0 0 0 0x14 0 3.449 0 0 0x15 0 0 0 0 0x16 0 5.318 0 0 0x17 0 0 0 0 0x18 0 0 5.851 0 0x19 0 0 0 0 0x20 0 0 2.659 0 0x21 0 0 0 0 0x22 0 0 0 3.187 0x23 0 0 0 0 0x24 0 0 0 2.115 0x25 0 0 0 0 0x26 0 0 0 0 4.516x27 0 0 0 0 0x28 0 0 0 0 4.061C = x1 x2 x3 x4 x5 x6y1 1.337 0.6687 0 0 0 0y2 0 0 1.337 0.6687 0 0y3 0 0 0 0 1.687 0.5623y4 0 0 0 0 0 0y5 0 0 0 0 0 0y6 0 0 0 0 0 0x7 x8 x9 x10 x11 x12y1 0 0 2.151 0.9559 0 0y2 0 0 0 0 5.061 1.687y3 0 0 0 0 0 0y4 1.549 1.162 0 0 0 0y5 0 0 0 0 0 0y6 0 0 0 0 0 0x13 x14 x15 x16 x17 x18y1 0 0 0 0 0 0y2 0 0 0 0 0 0y3 2.436 0.8699 0 0 0 0
y4 0 0 2.632 0.3761 0 0y5 0 0 0 0 7.264 0.8546y6 0 0 0 0 0 0x19 x20 x21 x22 x23 x24y1 0 0 0 0 0 0y2 0 0 0 0 0 0y3 0 0 0 0 0 0y4 0 0 0 0 0 0y5 0 0 4.393 1.883 0 0y6 2.632 0.3761 0 0 -1.182 2.364x25 x26 x27 x28y1 0 0 0 0y2 0 0 0 0y3 0 0 0 0y4 0 0 0 0y5 3.321 0.6643 0 0y6 0 0 3.94 0.985D = u1 u2 u3 u4 u5y1 0 0 0 0 0y2 0 0 0 0 0y3 0 0 0 0 0y4 0 0 0 0 0y5 0 0 0 0 0y6 0 0 0 0 03 Используя команду ss2ss(sys2,T) перейти к альтернативной ss-форме. Матрицы перехода Т сгенерировать генератором случайных чисел rand.3 ВыполнениеSYS2 = ss(sys2)С помощью SYS2.A определили размерность матрицы SYS2 для перехода ТT=rand(12);sysT = ss2ss(SYS2,T)sysT =A = x1 x2 x3 x4x1 -17.9 6.928 11.62 -5.625x2 -21.83 11.63 10.33 -11.23x3 -30.4 17.74 15.02 -12.06x4 -21.19 15.99 9.839 -7.433x5 -8.48 9.999 0.1764 3.18x6 -31.55 22 13.97 -13.17x7 -3.273 5.755 1.791 4.063x8 -28.06 20.91 13.27 -10.29x9 -26.44 25.49 6.815 -5.005x10 -20.9 17.08 8.573 -9.648x11 2.613 4.498 -5.871 8.127x12 -20.5 14.23 7.867 -5.357x5 x6 x7 x8x1 -8.339 0.1829 7.059 11.45x2 -13.4 2.137 9.705 27.81x3 -17.46 2.499 12.46 32x4 -13.87 0.5645 9.24 22.79x5 -6.555 -2.341 4.255 10.31x6 -23.6 0.4077 13.89 40.54x7 -3.704 -4.82 1.538 0.9841x8 -19.47 2.037 12.96 33.1x9 -18.1 -0.02729 11.34 35.79x10 -15.86 1.619 10.41 30.16x11 1.683 -6.43 3.441 -3.512x12 -11.42 -0.4247 8.796 25.37x9 x10 x11 x12x1 0.8096 -22.14 5.416 -0.5673x2 3.547 -40.4 7.616 -4.385x3 3.344 -52.08 11.02 -5.4x4 2.275 -37.93 6.869 -4.267x5 -0.00525 -19.12 1.464 -0.139x6 7.001 -60.99 9.42 -4.973x7 1.135 -8.015 -1.431 1.198x8 5.453 -56.07 9.218 -6.938x9 2.937 -56.86 7.526 -5.706x10 5.896 -47.08 6.424 -6.598x11 -0.3199 3.85 -5.776 0.2528x12 2.828 -37.2 6.241 -5.897B = u1 u2 u3x1 1.077 0.9164 7.389x2 2.266 2.772 4.19x3 2.652 3.807 7.512x4 5.21 3.45 3.001x5 3.766 2.48 3.199x6 6.074 2.723 2.02x7 6.366 2.077 5.965x8 1.533 4.407 5.062x9 6.928 4.852 0.9273x10 1.991 3.73 2.536x11 4.749 1.518 3.478x12 4.92 2.117 3.795C = x1 x2 x3 x4 x5 x6y1 54.68 -26.94 -25.5 28.96 38.59 -6.867y2 -25.34 17.35 8.016 -14.94 -24.89 5.26x7 x8 x9 x10 x11 x12y1 -23.22 -66.66 -7.334 93.1 -16.69 3.061y2 12.49 44.63 8.353 -58.46 8.167 -4.243D = u1 u2 u3y1 0 0 0y2 0 0 04 Преобразовать полученные в задании 3 системы в zpk-форму. Сравнить передаточные функции систем с передаточными функциями систем, полученных в пп. 1.4 и 1.5.4 ВыполнениеSYSt = zpk(sysT) SYSt =From input 1 to output...5 (s+20) (s^2 + 2s + 2) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)1: -----------------------------------------------(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)(s+22) (s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 8s + 32)2: -----------------------------------------------(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)From input 2 to output...6 (s+10) (s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 2s + 10) (s^2 + 8s + 32)1: -----------------------------------------------(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)5 (s+2) (s^2 + 2s + 2) (s^2 + 2s + 5) (s^2 + 6s + 13) (s^2 + 2s + 10)

(s^2 + 6s + 18)

2: -----------------------------------------------

(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5)

(s^2 + 6s + 18) (s^2 + 2s + 10)

(s^2 + 8s + 32)

From input 3 to output...

3 (s+6) (s^2 + 2s + 5) (s^2 + 6s + 13)

(s^2 + 2s + 10) (s^2 + 6s + 18)

(s^2 + 8s + 32)

1: -----------------------------------------------

(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5)

(s^2 + 6s + 18) (s^2 + 2s + 10)

(s^2 + 8s + 32)

4 (s+9) (s^2 + 2s + 2) (s^2 + 6s + 13)

(s^2 + 2s + 10) (s^2 + 6s + 18)

(s^2 + 8s + 32)

2: -----------------------------------------------

(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5)

(s^2 + 6s + 18) (s^2 + 2s + 10)

(s^2 + 8s + 32)

>>QC41 = zpk(qc41);

>> bode(QC41,SYSt)

>> sys2=ss(sys2);

>> sys2.A

ans =

-3 2 0 0 0 0 0 0 0 0 0 0

-2 -3 0 0 0 0 0 0 0 0 0 0

0 0 -1 3 0 0 0 0 0 0 0 0

0 0 -3 -1 0 0 0 0 0 0 0 0

0 0 0 0 -3 3 0 0 0 0 0 0

0 0 0 0 -3 -3 0 0 0 0 0 0

0 0 0 0 0 0 -4 4 0 0 0 0

0 0 0 0 0 0 -4 -4 0 0 0 0

0 0 0 0 0 0 0 0 -1 1 0 0

0 0 0 0 0 0 0 0 -1 -1 0 0

0 0 0 0 0 0 0 0 0 0 -1 2

0 0 0 0 0 0 0 0 0 0 -2 -1

>> T = rand(12);

>> sysT = ss2ss(sys2,T);

>> bode(sys2,sysT)

>> zpk(sys2)

ans =

From input 1 to output...

5 (s+20)

1: ---------------

(s^2 + 6s + 13)

(s+22)

2: ---------------

(s^2 + 2s + 10)

From input 2 to output...

6 (s+10)

1: ---------------

(s^2 + 6s + 18)

5 (s+2)

2: ---------------

(s^2 + 8s + 32)

From input 3 to output...

3 (s+6)

1: --------------

(s^2 + 2s + 2)

4 (s+9)

2: --------------

(s^2 + 2s + 5)

Continuous-time zero/pole/gain model.

>> zpk(sysT)

ans =

From input 1 to output...

5 (s+20) (s^2 + 2s + 2) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)

1: ---------------------------------------------------------------------------------------------

(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)

(s+22) (s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 8s + 32)

2: ---------------------------------------------------------------------------------------------

(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)

From input 2 to output...

6 (s+10) (s^2 + 2s + 2) (s^2 + 2s + 5) (s^2 + 6s + 13) (s^2 + 2s + 10) (s^2 + 8s + 32)

1: ---------------------------------------------------------------------------------------------

(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)

5 (s+2) (s^2 + 2s + 2) (s^2 + 2s + 5) (s^2 + 6s + 13) (s^2 + 2s + 10) (s^2 + 6s + 18)

2: ---------------------------------------------------------------------------------------------

(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)

From input 3 to output...

3 (s+6) (s^2 + 2s + 5) (s^2 + 6s + 13) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)

1: ---------------------------------------------------------------------------------------------

(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)

4 (s+9) (s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)

2: ---------------------------------------------------------------------------------------------

(s^2 + 2s + 2) (s^2 + 6s + 13) (s^2 + 2s + 5) (s^2 + 6s + 18) (s^2 + 2s + 10) (s^2 + 8s + 32)



>> minreal(zpk(sysT))

ans =

From input 1 to output...

5 (s+20)

1: ---------------

(s^2 + 6s + 13)

(s+22)

2: ---------------

(s^2 + 2s + 10)

From input 2 to output...

6 (s+10)

1: ---------------

(s^2 + 6s + 18)

5 (s+2)

2: ---------------

(s^2 + 8s + 32)

From input 3 to output...

3 (s+6)

1: --------------

(s^2 + 2s + 2)

4 (s+9)

2: --------------

(s^2 + 2s + 5)

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