7e26afe5-9748-4331-bd12-109d2829bf4e 106 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

A general purpose, simple ODE solver to simulate (possibly non-linear) dynamic systems.

CONTINUOUS TIME

2 f 2 g x.0 NumIt dt dynSys ξ x.0 : x ξ : k 1 NumIt range ξ ξ dt ξ ξ r g f * + eval : x x ξ augment : 21 line for x 41 line :

DISCRETE TIME

2 f 2 g x.0 NumIt dynSysDiscr ξ x.0 : x ξ : k 1 NumIt range ξ ξ ξ r g f eval : x x ξ augment : 21 line for x 41 line :

EXAMPLE 1 - Mass-Spring-Damper

Linear system with 2 states and 1 input: unit step response.

x u MasSprDmp 1 M / u 1 el η x 1 el * - K x 2 el * - (* x 1 el 21 mat :

M 1 :

η 0.7 :

K 1 :

system parameters

x r Ctrl1 111 mat :

Constant input, i.e. no state feedback in this case

initial condition x0 0021 mat :

Sol1 any1 any2 MasSprDmp any1 any2 Ctrl1 x0 150 0.1 dynSys :

Sol1 0 0.1 0.193 0.2785 0.3561 0.4254 0.4864 0.5388 0.5827 0.6181 0.6452 0.6643 0.6755 0.6794 0.6762 0.6664 0.6506 0.6292 0.6028 0.5719 0.5372 0.4992 0.4585 0.4156 0.3712 0.3257 0.2797 0.2336 0.188 0.1432 0.0997 0.0578 0.0178 0.0199 - 0.0552 - 0.0878 - 0.1176 - 0.1444 - 0.1682 - 0.1888 - 0.2063 - 0.2207 - 0.2321 - 0.2404 - 0.2459 - 0.2485 - 0.2485 - 0.246 - 0.2412 - 0.2343 - 0.2255 - 0.2149 - 0.2028 - 0.1894 - 0.175 - 0.1596 - 0.1436 - 0.1271 - 0.1103 - 0.0934 - 0.0766 - 0.06 - 0.0439 - 0.0282 - 0.0132 - 0.001 0.0143 0.0267 0.0381 0.0485 0.0577 0.0658 0.0727 0.0785 0.0832 0.0868 0.0893 0.0907 0.0911 0.0906 0.0893 0.0871 0.0842 0.0806 0.0764 0.0717 0.0666 0.0611 0.0553 0.0494 0.0433 0.0371 0.0309 0.0248 0.0188 0.013 0.0074 0.002 0.003 - 0.0077 - 0.0121 - 0.016 - 0.0196 - 0.0228 - 0.0255 - 0.0278 - 0.0297 - 0.0312 - 0.0323 - 0.033 - 0.0333 - 0.0333 - 0.033 - 0.0323 - 0.0314 - 0.0302 - 0.0287 - 0.0271 - 0.0253 - 0.0233 - 0.0213 - 0.0191 - 0.0169 - 0.0146 - 0.0124 - 0.0101 - 0.0079 - 0.0057 - 0.0036 - 0.0016 - 0.0003 0.002 0.0037 0.0052 0.0066 0.0078 0.0089 0.0098 0.0106 0.0112 0.0117 0.012 0.0122 0.0122 0.0122 0.012 0.0117 0.0113 0.0108 0.0102 0.0096 00 0.01 0.0293 0.0571 0.0928 0.1353 0.1839 0.2378 0.2961 0.3579 0.4224 0.4888 0.5564 0.6243 0.692 0.7586 0.8237 0.8866 0.9468 1.004 1.0578 1.1077 1.1535 1.1951 1.2322 1.2648 1.2927 1.3161 1.3349 1.3492 1.3592 1.365 1.3667 1.3647 1.3592 1.3504 1.3387 1.3243 1.3074 1.2886 1.2679 1.2458 1.2226 1.1986 1.174 1.1492 1.1243 1.0997 1.0756 1.0521 1.0296 1.0081 0.9878 0.9689 0.9514 0.9354 0.9211 0.9084 0.8973 0.888 0.8803 0.8743 0.8699 0.8671 0.8658 0.8659 0.8673 0.87 0.8738 0.8787 0.8844 0.891 0.8983 0.9061 0.9145 0.9231 0.9321 0.9411 0.9502 0.9593 0.9682 0.9769 0.9854 0.9934 1.0011 1.0082 1.0149 1.021 1.0265 1.0315 1.0358 1.0395 1.0426 1.0451 1.047 1.0483 1.049 1.0492 1.0489 1.0481 1.0469 1.0453 1.0434 1.0411 1.0385 1.0357 1.0328 1.0296 1.0264 1.0231 1.0198 1.0164 1.0131 1.0099 1.0068 1.0038 1.0009 0.9982 0.9957 0.9933 0.9912 0.9893 0.9876 0.9861 0.9849 0.9839 0.9831 0.9825 0.9822 0.982 0.982 0.9822 0.9826 0.9831 0.9838 0.9846 0.9854 0.9864 0.9875 0.9886 0.9898 0.991 0.9922 0.9934 0.9946 0.9958 0.997 0.9981 0.9992 1.0002 2151 mat

v Sol1 1 row transpose :

s Sol1 2 row transpose :

v x el s x el 2 1 sys

7

Note: subscript "x" forces vectors elements to be plotted.

EXAMPLE 2 - Linear Feedback Stabilization

Linear system with 3 states and 2 inputs

x u LinSys1 0.5 x 1 el * x 2 el + u 2 el + 0.5 x 1 el * x 3 el + 2 x 1 el * - u 1 el + u 2 el + 31 mat :

x r Ctrl2 1 0.5 21 mat :

Constant input

x0 00031 mat :

Sol2 any1 any2 LinSys1 any1 any2 Ctrl2 x0 50 0.1 dynSys :

Sol2 0 0.05 0.1025 0.1594 0.2225 0.2938 0.3751 0.4684 0.5756 0.6986 0.8392 0.9994 1.1809 1.3855 1.6145 1.8695 2.1517 2.4618 2.8006 3.1681 3.5642 3.9878 4.4377 4.9115 5.4062 5.9179 6.4416 6.9711 7.4991 8.0166 8.5133 8.9774 9.3951 9.751 10.0274 10.205 10.2623 10.1754 9.9186 9.464 8.7814 7.839 6.6028 5.0375 3.1061 0.7709 2.0067 - 5.2649 - 9.042 - 13.3745 - 18.297 - 00 0.0175 0.0516 0.1015 0.1664 0.2454 0.3376 0.442 0.5573 0.6823 0.8154 0.9546 1.098 1.2429 1.3866 1.5258 1.6567 1.7751 1.8761 1.9545 2.0044 2.0192 1.9917 1.9141 1.778 1.5744 1.2937 0.9255 0.4594 0.1159 - 0.8116 - 1.6394 - 2.6109 - 3.7375 - 5.0303 - 6.4997 - 8.1554 - 10.0057 - 12.0573 - 14.3151 - 16.7812 - 19.4551 - 22.3326 - 25.4054 - 28.6605 - 32.0795 - 35.6378 - 39.3039 - 43.0385 - 46.7939 - 0 0.15 0.29 0.4195 0.5376 0.6431 0.7344 0.8093 0.8657 0.9005 0.9108 0.893 0.8431 0.7569 0.6298 0.4569 0.233 0.0473 - 0.3897 - 0.7998 - 1.2835 - 1.8463 - 2.4939 - 3.2314 - 4.0637 - 4.9949 - 6.0285 - 7.1668 - 8.4111 - 9.7609 - 11.2142 - 12.7669 - 14.4123 - 16.1414 - 17.9416 - 19.797 - 21.6881 - 23.5905 - 25.4756 - 27.3093 - 29.0521 - 30.6584 - 32.0762 - 33.2468 - 34.1043 - 34.5755 - 34.5796 - 34.0283 - 32.8253 - 30.8669 - 28.042 - 351 mat

x1 Sol2 1 row transpose :

x2 Sol2 2 row transpose :

x3 Sol2 3 row transpose :

x1 x el x2 x el x3 x el 3 1 sys

K 1.4 0.5 - 1.4 - 3.3 - 1.9 - 023 mat :

The state grows indefinitely, i.e. the system is unstable.

Try to stabilize with proportional state feedback matrix:

x r Ctrl3 K x 1 el x 2 el x 3 el 31 mat * 1 0.5 21 mat + :

Sol3 any1 any2 LinSys1 any1 any2 Ctrl3 x0 50 0.1 dynSys :

x1 Sol3 1 row transpose :

x2 Sol3 2 row transpose :

x3 Sol3 3 row transpose :

x1 x el x2 x el x3 x el 3 1 sys

Sol3 0 0.05 0.086 0.1103 0.1252 0.1323 0.1334 0.1299 0.1231 0.1138 0.1029 0.0911 0.079 0.0669 0.0551 0.0439 0.0334 0.0237 0.0149 0.007 0.0001 - 0.0064 - 0.0118 - 0.0165 - 0.0206 - 0.0241 - 0.027 - 0.0294 - 0.0315 - 0.0331 - 0.0345 - 0.0356 - 0.0365 - 0.0372 - 0.0377 - 0.0381 - 0.0384 - 0.0386 - 0.0388 - 0.0389 - 0.039 - 0.039 - 0.0391 - 0.0391 - 0.0391 - 0.0391 - 0.039 - 0.039 - 0.039 - 0.039 - 0.039 - 00 0.0175 0.0478 0.0868 0.1315 0.1791 0.2278 0.2759 0.3223 0.3662 0.407 0.4445 0.4784 0.5087 0.5356 0.5592 0.5797 0.5974 0.6125 0.6252 0.6359 0.6448 0.6521 0.6581 0.6629 0.6667 0.6697 0.672 0.6738 0.6751 0.676 0.6767 0.6771 0.6774 0.6775 0.6776 0.6776 0.6775 0.6774 0.6773 0.6772 0.6772 0.6771 0.677 0.6769 0.6769 0.6768 0.6768 0.6768 0.6768 0 0.15 0.2595 0.3354 0.384 0.4106 0.4199 0.4161 0.4025 0.382 0.3568 0.3288 0.2995 0.2701 0.2414 0.214 0.1884 0.1648 0.1434 0.1241 0.107 0.092 0.079 0.0678 0.0582 0.0502 0.0434 0.0379 0.0333 0.0297 0.0267 0.0244 0.0226 0.0213 0.0203 0.0196 0.0191 0.0188 0.0186 0.0185 0.0185 0.0186 0.0187 0.0188 0.0189 0.019 0.0191 0.0192 0.0193 0.0194 0.0195 351 mat

EXAMPLE 3 - Nonlinear Equations (Lorentz Model)

x u Lorentz 5 x 2 el x 1 el - (* x 1 el x 3 el * - 15 x 1 el * + x 2 el - x 1 el x 2 el * 1 x 3 el * - 31 mat :

x r Ctrl4 0 :

x0 0.1 0.2 0.3 13 mat transpose :

Sol4 any1 any2 Lorentz any1 any2 Ctrl4 x0 500 0.02 dynSys :

Sol4 0.1 0.11 0.1215 0.1347 0.1496 0.1665 0.1854 0.2066 0.2303 0.2569 0.2867 0.3199 0.357 0.3984 0.4447 0.4964 0.5541 0.6185 0.6904 0.7707 0.8603 0.9602 1.0717 1.196 1.3346 1.4891 1.6611 1.8526 2.0655 2.302 2.5644 2.8551 3.1763 3.5304 3.9194 4.3451 4.8084 5.3094 5.8466 6.4166 7.0131 7.6263 8.2422 8.8416 9.3999 9.8869 10.2685 10.5082 10.5716 10.4305 10.0686 9.4859 8.7 7.7454 6.6685 5.5208 4.352 3.2047 2.1118 1.0957 0.1697 0.66 - 1.3923 - 2.0291 - 2.5743 - 3.0326 - 3.4092 - 3.7092 - 3.9377 - 4.0997 - 4.2004 - 4.2449 - 4.2387 - 4.1873 - 4.0965 - 3.9723 - 3.8204 - 3.6467 - 3.4567 - 3.2557 - 3.0485 - 2.8393 - 2.6318 - 2.4291 - 2.2337 - 2.0476 - 1.8722 - 1.7085 - 1.557 - 1.418 - 1.2914 - 1.1771 - 1.0745 - 0.9831 - 0.9023 - 0.8314 - 0.7696 - 0.7164 - 0.6709 - 0.6326 - 0.6007 - 0.5748 - 0.5543 - 0.5387 - 0.5276 - 0.5207 - 0.5175 - 0.518 - 0.5217 - 0.5286 - 0.5385 - 0.5513 - 0.567 - 0.5855 - 0.6068 - 0.631 - 0.6581 - 0.6882 - 0.7215 - 0.7582 - 0.7983 - 0.8422 - 0.89 - 0.9421 - 0.9987 - 1.0603 - 1.127 - 1.1995 - 1.278 - 1.3631 - 1.4553 - 1.5551 - 1.6632 - 1.78 - 1.9064 - 2.0429 - 2.1903 - 2.3492 - 2.5203 - 2.7043 - 2.9019 - 3.1135 - 3.3397 - 3.5805 - 3.8361 - 4.1061 - 4.3898 - 4.6861 - 4.9931 - 5.3082 - 5.6279 - 5.9479 - 6.2626 - 6.5653 - 6.8482 - 7.1026 - 7.319 - 7.4874 - 7.5983 - 7.6429 - 7.6142 - 7.5075 - 7.3213 - 7.0574 - 6.7212 - 6.3216 - 5.8697 - 5.3786 - 4.862 - 4.3335 - 3.8053 - 3.2882 - 2.7909 - 2.32 - 1.8801 - 1.4741 - 1.1032 - 0.7673 - 0.4657 - 0.1965 - 0.0422 0.253 0.4384 0.6009 0.7433 0.868 0.9774 1.0737 1.159 1.2351 1.3038 1.3666 1.4249 1.48 1.533 1.5848 1.6364 1.6885 1.7419 1.7973 1.8551 1.9159 1.9802 2.0484 2.1209 2.1982 2.2804 2.368 2.4612 2.5603 2.6655 2.777 2.8949 3.0193 3.1502 3.2875 3.4312 3.5809 3.7361 3.8965 4.0612 4.2293 4.3996 4.5709 4.7413 4.9091 5.072 5.2277 5.3735 5.5065 5.6239 5.7226 5.7998 5.8527 5.879 5.8769 5.8449 5.7826 5.6899 5.568 5.4185 5.2439 5.0474 4.8325 4.6033 4.3637 4.1179 3.8698 3.6229 3.3805 3.1454 2.9198 2.7057 2.5043 2.3166 2.1431 1.984 1.8393 1.7088 1.5919 1.4881 1.3968 1.3172 1.2486 1.1902 1.1414 1.1015 1.0697 1.0456 1.0286 1.0182 1.014 1.0156 1.0227 1.0351 1.0526 1.0751 1.1025 1.1347 1.1717 1.2137 1.2607 1.3129 1.3704 1.4334 1.5022 1.5771 1.6585 1.7465 1.8417 1.9444 2.055 2.174 2.3018 2.4388 2.5854 2.7421 2.9091 3.0867 3.2751 3.4743 3.6842 3.9044 4.1343 4.3729 4.6188 4.8703 5.1248 5.3796 5.6309 5.8746 6.1057 6.3187 6.5076 6.6663 6.7883 6.8677 6.8992 6.8786 6.8031 6.6718 6.4858 6.248 5.9636 5.6391 5.2824 4.9022 4.5071 4.1056 3.7056 3.3137 2.9357 2.5759 2.2375 1.9227 1.6326 1.3675 1.1271 0.9106 0.7168 0.5441 0.391 0.2557 0.1365 0.0316 0.0605 - 0.1416 - 0.2131 - 0.2763 - 0.3325 - 0.3829 - 0.4286 - 0.4704 - 0.5092 - 0.5458 - 0.581 - 0.6152 - 0.6491 - 0.6831 - 0.7179 - 0.7537 - 0.791 - 0.8302 - 0.8717 - 0.9157 - 0.9628 - 1.0132 - 1.0673 - 1.1254 - 1.188 - 1.2555 - 1.3282 - 1.4066 - 1.4912 - 1.5824 - 1.6808 - 1.7868 - 1.9011 - 2.0241 - 2.1565 - 2.2988 - 2.4516 - 2.6154 - 2.7908 - 2.9782 - 3.1779 - 3.3903 - 3.6153 - 3.8527 - 4.1022 - 4.3629 - 4.6335 - 4.9122 - 5.1966 - 5.4835 - 5.769 - 6.0482 - 6.3154 - 6.5641 - 6.787 - 6.9764 - 7.1244 - 7.2232 - 7.266 - 7.2469 - 7.1624 - 7.0109 - 6.7936 - 6.5144 - 6.1798 - 5.7983 - 5.3801 - 4.936 - 4.477 - 4.0136 - 3.5551 - 3.1095 - 2.683 - 2.2805 - 1.9051 - 1.5587 - 1.2421 - 0.9551 - 0.6968 - 0.4658 - 0.2603 - 0.0783 - 0.0824 0.2239 0.3483 0.4578 0.5543 0.6397 0.7157 0.7838 0.8455 0.9021 0.9548 1.0046 1.0526 1.0995 1.1461 1.1932 1.2414 1.2912 1.3433 1.3981 1.456 1.5177 1.5833 1.6535 1.7287 1.8091 1.8953 1.9876 2.0864 2.1922 2.3053 2.4261 2.5549 2.692 2.8377 2.9923 3.1558 3.3283 3.5097 3.6998 3.8979 4.1036 4.3158 4.5331 4.754 4.9763 5.1975 5.4146 5.624 5.8218 6.0036 6.1648 6.3006 6.4061 6.4767 6.5085 6.4983 6.4437 6.344 6.1997 6.0127 5.7864 5.5256 5.2359 4.9237 4.5956 4.2583 3.9182 3.581 3.2517 2.9345 2.6325 2.3483 2.0834 0.2 0.2254 0.2532 0.2839 0.3179 0.3556 0.3975 0.4442 0.4962 0.5541 0.6188 0.691 0.7715 0.8613 0.9616 1.0735 1.1983 1.3376 1.4931 1.6664 1.8597 2.075 2.315 2.5821 2.8792 3.2093 3.5758 3.9818 4.4308 4.9261 5.4708 6.0672 6.7172 7.4208 8.1762 8.9784 9.8184 10.6816 11.5462 12.3812 13.1453 13.7853 14.2363 14.4241 14.2705 13.7024 12.6659 11.1417 9.1606 6.8123 4.2411 1.6271 0.8457 - 3.0237 - 4.8089 - 6.1675 - 7.1206 - 7.7243 - 8.0493 - 8.1644 - 8.1275 - 7.9825 - 7.7603 - 7.4811 - 7.1579 - 6.7987 - 6.4091 - 5.9939 - 5.5578 - 5.1063 - 4.6456 - 4.1827 - 3.7249 - 3.2797 - 2.8538 - 2.4534 - 2.0834 - 1.7472 - 1.447 - 1.1836 - 0.9565 - 0.7644 - 0.6049 - 0.4753 - 0.3725 - 0.2934 - 0.2347 - 0.1935 - 0.167 - 0.1525 - 0.1479 - 0.1511 - 0.1607 - 0.175 - 0.1931 - 0.214 - 0.2371 - 0.2617 - 0.2874 - 0.3141 - 0.3415 - 0.3696 - 0.3984 - 0.4279 - 0.4582 - 0.4894 - 0.5218 - 0.5555 - 0.5907 - 0.6276 - 0.6666 - 0.7079 - 0.7518 - 0.7986 - 0.8486 - 0.9021 - 0.9596 - 1.0214 - 1.0879 - 1.1596 - 1.237 - 1.3206 - 1.4108 - 1.5084 - 1.6139 - 1.7279 - 1.8513 - 1.9847 - 2.129 - 2.285 - 2.4536 - 2.6356 - 2.8319 - 3.0436 - 3.2715 - 3.5165 - 3.7793 - 4.0605 - 4.3607 - 4.68 - 5.0183 - 5.3747 - 5.7481 - 6.1363 - 6.5362 - 6.9435 - 7.3525 - 7.7558 - 8.144 - 8.5058 - 8.8278 - 9.0947 - 9.2896 - 9.3947 - 9.3922 - 9.2661 - 9.0034 - 8.5964 - 8.0445 - 7.3557 - 6.5472 - 5.645 - 4.6822 - 3.6961 - 2.7247 - 1.8028 - 0.9588 - 0.2129 - 0.4237 0.9486 1.3659 1.6849 1.9179 2.0784 2.18 2.2352 2.2552 2.2494 2.2259 2.191 2.1499 2.1066 2.0641 2.0248 1.9904 1.962 1.9405 1.9265 1.9203 1.9221 1.9319 1.9498 1.9757 2.0095 2.0512 2.1007 2.1578 2.2227 2.2952 2.3753 2.4632 2.5589 2.6624 2.7738 2.8932 3.0207 3.1564 3.3002 3.4522 3.6123 3.7803 3.9559 4.1388 4.3283 4.5237 4.724 4.9279 5.1337 5.3397 5.5434 5.7421 5.9328 6.1119 6.2755 6.4192 6.5385 6.6288 6.6854 6.7038 6.6801 6.611 6.4943 6.3292 6.1162 5.8575 5.5573 5.2211 4.8561 4.4704 4.0729 3.6728 3.2788 2.8989 2.5401 2.2077 1.9056 1.6364 1.401 1.199 1.0294 0.89 0.7783 0.6917 0.627 0.5815 0.5525 0.5374 0.5339 0.54 0.5542 0.5748 0.6008 0.6311 0.6651 0.7022 0.7419 0.7841 0.8286 0.8754 0.9244 0.9759 1.0299 1.0868 1.1468 1.2103 1.2774 1.3487 1.4246 1.5054 1.5916 1.6837 1.7823 1.8877 2.0007 2.1217 2.2514 2.3903 2.5391 2.6983 2.8686 3.0506 3.2448 3.4517 3.6717 3.9051 4.1519 4.4122 4.6854 4.9708 5.2674 5.5733 5.8863 6.2033 6.5202 6.8321 7.1331 7.416 7.6724 7.893 8.0676 8.1855 8.2358 8.2082 8.0939 7.8864 7.5825 7.1829 6.6932 6.1239 5.4902 4.8111 4.1081 3.4035 2.7187 2.0725 1.4799 0.9513 0.4926 0.1052 0.213 - 0.4667 - 0.6625 - 0.8079 - 0.9107 - 0.9785 - 1.0183 - 1.0362 - 1.0379 - 1.0278 - 1.0097 - 0.9869 - 0.9618 - 0.9364 - 0.9121 - 0.8901 - 0.8713 - 0.8562 - 0.8452 - 0.8387 - 0.8367 - 0.8393 - 0.8467 - 0.8587 - 0.8755 - 0.897 - 0.9231 - 0.9541 - 0.9898 - 1.0304 - 1.0761 - 1.1269 - 1.183 - 1.2448 - 1.3124 - 1.3863 - 1.4667 - 1.554 - 1.6488 - 1.7515 - 1.8626 - 1.9827 - 2.1124 - 2.2525 - 2.4034 - 2.5661 - 2.7412 - 2.9293 - 3.1313 - 3.3478 - 3.5794 - 3.8267 - 4.0899 - 4.3693 - 4.6647 - 4.9757 - 5.3014 - 5.6402 - 5.99 - 6.3476 - 6.7091 - 7.069 - 7.4207 - 7.7562 - 8.0657 - 8.3381 - 8.5608 - 8.7202 - 8.8023 - 8.7934 - 8.6812 - 8.4562 - 8.1126 - 7.6505 - 7.0758 - 6.4017 - 5.6474 - 4.838 - 4.0018 - 3.1682 - 2.3648 - 1.6157 - 0.9389 - 0.3463 - 0.157 0.5712 0.9013 1.1551 1.3424 1.4735 1.5586 1.6072 1.6279 1.6278 1.6133 1.5893 1.5599 1.5284 1.4973 1.4684 1.4433 1.4229 1.4081 1.3993 1.3968 1.4009 1.4116 1.429 1.4532 1.484 1.5216 1.5659 1.617 1.675 1.7399 1.8118 1.8911 1.9778 2.0722 2.1746 2.2853 2.4047 2.5331 2.6709 2.8184 2.9761 3.1442 3.3231 3.5129 3.714 3.9262 4.1494 4.3834 4.6275 4.8809 5.1423 5.41 5.6817 5.9546 6.2253 6.4894 6.742 6.9771 7.1882 7.368 7.5087 7.6021 7.6402 7.6157 7.5223 7.3554 7.1127 6.7949 6.4059 5.9529 5.4467 4.9004 4.3295 3.7501 3.1782 2.6286 2.1136 1.643 1.2231 0.8573 0.5462 0.288 0.0791 0.085 - 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x1 Sol4 1 row transpose :

x2 Sol4 2 row transpose :

x3 Sol4 3 row transpose :

xyPlot x3 x2 augment :

x3 x2 augment x3 x1 augment x2 x1 augment 3 1 sys Sol4 transpose