7 equation non linear system converge too slow

2 Ansichten (letzte 30 Tage)
Nicolo' Nicolo'
Nicolo' Nicolo' am 18 Jun. 2022
Beantwortet: Walter Roberson am 19 Jun. 2022
Ran in:
I try to solve this non linear system with voltage points obtained from laboratory measurments.
% voltage value
Eoc=18.09;
v2=13.69;
v3=12.73;
v4= 11.31;
v5=10.22;
v6=9.71;
v7=8.91;
v8=8.41;
% current value
Ifc2=1;
Ifc3=2;
Ifc4=4;
Ifc5=6;
Ifc6=7;
Ifc7=9;
Ifc8=10;
% point 1
E1 = @(x)[Eoc - x(1)*log(Ifc2/x(2))-x(3)*exp(x(4)*Ifc2)-x(5)- x(6)*log(Ifc2/x(2))-x(7)*Ifc2-v2;
%% point 2
Eoc - x(1)*log(Ifc3/x(2))-x(3)*exp(x(4)*Ifc3)-x(5)- x(6)*log(Ifc3/x(2))-x(7)*Ifc3-v3;
%% point 3
Eoc - x(1)*log(Ifc4/x(2))-x(3)*exp(x(4)*Ifc4)-x(5)- x(6)*log(Ifc4/x(2))-x(7)*Ifc4-v4;
%% point 4
Eoc - x(1)*log(Ifc5/x(2))-x(3)*exp(x(4)*Ifc5)-x(5)- x(6)*log(Ifc5/x(2))-x(7)*Ifc5-v5;
%% point 5
Eoc - x(1)*log(Ifc6/x(2))-x(3)*exp(x(4)*Ifc6)-x(5)- x(6)*log(Ifc6/x(2))-x(7)*Ifc6-v6;
%% point 6
Eoc - x(1)*log(Ifc7/x(2))-x(3)*exp(x(4)*Ifc7)-x(5)- x(6)*log(Ifc7/x(2))-x(7)*Ifc7-v7;
%% point 7
Eoc - x(1)*log(Ifc8/x(2))-x(3)*exp(x(4)*Ifc8)-x(5)- x(6)*log(Ifc8/x(2))-x(7)*Ifc8-v8];
% x(1) A
% x(2) Io
% x(3) M
% x(4) N
% x(5) C
% x(6) D
% x(7) Rohm
x0 = [ 0.5 0.5 0.5 0.5 0.5 0.5 0.5];
options = optimoptions('fsolve','Display','iter','StepTolerance',1e-9);
options.MaxFunctionEvaluations = 16000000;
options.MaxIterations = 500000;
[x,fval,exitflag] = fsolve(E1,x0,options)
Norm of First-order Trust-region Iteration Func-count f(x) step optimality radius 0 8 7536.71 7.41e+04 1 1 16 1031.27 1 1.03e+04 1 2 24 227.732 1 2.96e+03 1 3 32 71.3023 1 760 1 4 33 71.3023 2.5 760 2.5 5 41 21.3747 0.625 118 0.625 6 42 21.3747 1.5625 118 1.56 7 43 21.3747 0.390625 118 0.391 8 44 21.3747 0.0976563 118 0.0977 9 52 14.6733 0.0244141 122 0.0244 10 60 11.96 0.0610352 163 0.061 11 68 10.2985 0.152588 114 0.153 12 76 9.71052 0.152588 67.4 0.153 13 84 8.93493 0.38147 140 0.381 14 92 8.87528 0.953674 82.4 0.954 15 100 6.9487 0.953674 70 0.954 16 108 6.69045 2.38419 51.4 2.38 17 109 6.69045 5.96046 51.4 5.96 18 117 5.27646 1.49012 40.9 1.49 19 118 5.27646 3.72529 40.9 3.73 20 126 3.63694 0.931323 28 0.931 21 127 3.63694 2.32831 28 2.33 22 135 2.15387 0.582077 13.4 0.582 23 143 1.84128 1.45519 34.7 1.46 24 144 1.84128 1.45519 34.7 1.46 25 152 1.33448 0.363798 8.85 0.364 26 153 1.33448 0.909495 8.85 0.909 27 161 1.04473 0.227374 40 0.227 28 169 0.779429 0.227374 6.58 0.227 29 170 0.779429 0.568434 6.58 0.568 30 171 0.779429 0.142109 6.58 0.142 31 179 0.744596 0.0355271 68.1 0.0355 32 187 0.478181 0.0355271 6.32 0.0355 33 195 0.46088 0.0888178 9.22 0.0888 34 196 0.46088 0.222045 9.22 0.222 35 204 0.448007 0.0555112 7.54 0.0555 36 212 0.436195 0.0555112 6.63 0.0555 37 220 0.426734 0.138778 7.97 0.139 38 228 0.411175 0.138778 5.08 0.139 39 236 0.0659658 0.346945 19.1 0.347 40 244 0.0290188 0.867362 1.06 0.867 41 245 0.0290188 2.1684 1.06 2.17 42 246 0.0290188 0.542101 1.06 0.542 43 254 0.0283883 0.135525 1.1 0.136 44 255 0.0283883 0.338813 1.1 0.339 45 263 0.0277058 0.0847033 0.878 0.0847 46 271 0.0249458 0.211758 5.65 0.212 47 272 0.0249458 0.211758 5.65 0.212 48 280 0.0219848 0.0529396 0.757 0.0529 49 288 0.0218098 0.132349 1.18 0.132 50 296 0.0216618 0.132349 1.73 0.132 51 304 0.0216008 0.132349 2.38 0.132 52 312 0.021558 0.132349 2.28 0.132 53 320 0.0212921 0.132349 2.4 0.132 54 328 0.0212058 0.132349 2.91 0.132 55 336 0.0211371 0.132349 3.45 0.132 56 337 0.0211371 0.132349 3.45 0.132 57 345 0.0205764 0.0330872 0.625 0.0331 58 353 0.0201497 0.0827181 0.79 0.0827 59 354 0.0201497 0.206795 0.79 0.207 60 362 0.0201133 0.0516988 1.03 0.0517 61 370 0.0200177 7.23749e-05 0.533 0.0517 62 378 0.0199727 0.0516988 1.42 0.0517 63 386 0.0198181 0.0516988 0.579 0.0517 64 394 0.0195865 0.129247 2.14 0.129 65 395 0.0195865 0.323117 2.14 0.323 66 403 0.0194586 0.0807794 1.39 0.0808 67 411 0.019438 0.0807794 1.39 0.0808 68 419 0.0194004 0.0807794 1.26 0.0808 69 427 0.019352 0.0807794 1.11 0.0808 70 435 0.019286 0.0807794 1.05 0.0808 71 443 0.0192459 0.0807794 1.19 0.0808 72 451 0.0192173 0.0807794 1.4 0.0808 73 459 0.0191947 0.0807794 1.61 0.0808 74 467 0.0191761 0.0807794 1.82 0.0808 75 475 0.0191607 0.0807794 2.05 0.0808 76 483 0.019155 0.0807794 2.02 0.0808 77 491 0.0191264 0.0807794 2.05 0.0808 78 499 0.0191207 0.0807794 2.02 0.0808 79 507 0.0190922 0.0807794 2.05 0.0808 80 515 0.0190867 0.0807794 2.02 0.0808 81 523 0.0190673 0.0807794 1.84 0.0808 82 531 0.0190423 0.0807794 1.66 0.0808 83 539 0.0190036 0.0807794 1.64 0.0808 84 547 0.0189913 0.0807794 1.62 0.0808 85 555 0.0189639 0.0807794 1.47 0.0808 86 563 0.0189286 0.0807794 1.31 0.0808 87 571 0.0188787 0.0807794 1.29 0.0808 88 579 0.0188568 0.0807794 1.28 0.0808 89 587 0.0188182 0.0807794 1.15 0.0808 90 595 0.0187622 0.0807794 1.13 0.0808 91 603 0.0187341 0.0807794 1.12 0.0808 92 611 0.0186827 0.0807794 1.13 0.0808 93 619 0.0186564 0.0807794 1.13 0.0808 94 627 0.018606 0.0807794 1.14 0.0808 95 635 0.0185754 0.0807794 1.3 0.0808 96 643 0.0185526 0.0807794 1.48 0.0808 97 651 0.0185403 0.0807794 1.48 0.0808 98 659 0.0185039 0.0807794 1.5 0.0808 99 667 0.0184848 0.0807794 1.69 0.0808 100 675 0.0184694 0.0807794 1.89 0.0808 101 683 0.0184572 0.0807794 2.11 0.0808 102 684 0.0184572 0.0807794 2.11 0.0808 103 692 0.0183764 0.0201948 0.47 0.0202 104 700 0.0179044 0.0504871 3.27 0.0505 105 701 0.0179044 0.126218 3.27 0.126 106 709 0.0177134 0.0315544 0.523 0.0316 107 710 0.0177134 0.0788861 0.523 0.0789 108 718 0.0176956 0.0197215 0.397 0.0197 109 719 0.0176956 0.0493038 0.397 0.0493 110 727 0.0176743 0.012326 0.96 0.0123 111 735 0.0176478 0.0308149 0.413 0.0308 112 743 0.0173592 0.0770372 0.97 0.077 113 744 0.0173592 0.192593 0.97 0.193 114 752 0.0173545 0.0481482 0.955 0.0481 115 760 0.0173381 0.0481482 0.626 0.0481 116 768 0.017329 0.0481482 0.563 0.0481 117 776 0.0173179 0.0481482 0.511 0.0481 118 784 0.0173084 0.0481482 0.532 0.0481 119 792 0.0173006 0.0481482 0.601 0.0481 120 800 0.0172946 0.0481482 0.696 0.0481 121 808 0.0172901 0.0481482 0.741 0.0481 122 816 0.0172835 0.0481482 0.753 0.0481 123 824 0.0172787 0.0481482 0.76 0.0481 124 832 0.017272 0.0481482 0.76 0.0481 125 840 0.0172668 0.0481482 0.821 0.0481 126 848 0.017263 0.0481482 0.84 0.0481 127 856 0.0172577 0.0481482 0.793 0.0481 128 864 0.0172508 0.0481482 0.773 0.0481 129 872 0.0172461 0.0481482 0.774 0.0481 130 880 0.01724 0.0481482 0.725 0.0481 131 888 0.0172323 0.0481482 0.699 0.0481 132 896 0.0172268 0.0481482 0.701 0.0481 133 904 0.0172198 0.0481482 0.654 0.0481 134 912 0.0172111 0.0481482 0.624 0.0481 135 920 0.0172042 0.0481482 0.667 0.0481 136 928 0.017199 0.0481482 0.692 0.0481 137 936 0.0171923 0.0481482 0.655 0.0481 138 944 0.0171843 0.0481482 0.596 0.0481 139 952 0.0171744 0.0481482 0.555 0.0481 140 960 0.0171663 0.0481482 0.585 0.0481 141 968 0.0171597 0.0481482 0.657 0.0481 142 976 0.0171545 0.0481482 0.746 0.0481 143 984 0.0171505 0.0481482 0.777 0.0481 144 992 0.0171449 0.0481482 0.737 0.0481 145 1000 0.0171377 0.0481482 0.717 0.0481 146 1008 0.0171324 0.0481482 0.707 0.0481 147 1016 0.0171255 0.0481482 0.711 0.0481 148 1024 0.0171202 0.0481482 0.77 0.0481 149 1032 0.0171158 0.0481482 0.847 0.0481 150 1040 0.017112 0.0481482 0.929 0.0481 151 1048 0.0171092 0.0481482 0.941 0.0481 152 1056 0.017105 0.0481482 0.889 0.0481 153 1064 0.0170993 0.0481482 0.873 0.0481 154 1072 0.0170958 0.0481482 0.874 0.0481 155 1080 0.0170904 0.0481482 0.874 0.0481 156 1088 0.017087 0.0481482 0.875 0.0481 157 1096 0.0170822 0.0481482 0.823 0.0481 158 1104 0.0170759 0.0481482 0.798 0.0481 159 1112 0.0170719 0.0481482 0.803 0.0481 160 1120 0.0170665 0.0481482 0.754 0.0481 161 1128 0.0170602 0.0481482 0.693 0.0481 162 1136 0.0170528 0.0481482 0.626 0.0481 163 1144 0.0170444 0.0481482 0.562 0.0481 164 1152 0.0170346 0.0481482 0.493 0.0481 165 1160 0.0170229 0.0481482 0.419 0.0481 166 1161 0.0170229 0.120371 0.419 0.12 167 1169 0.0170063 0.0300927 0.346 0.0301 168 1170 0.0170063 0.0752316 0.346 0.0752 169 1178 0.0168328 0.0188079 2.66 0.0188 170 1186 0.0166736 0.0470198 0.506 0.047 171 1187 0.0166736 0.117549 0.506 0.118 172 1195 0.0166597 0.0293874 0.314 0.0294 173 1203 0.0152434 0.0734684 1.55 0.0735 174 1204 0.0152434 0.183671 1.55 0.184 175 1212 0.0152104 0.0459177 0.714 0.0459 176 1213 0.0152104 0.0459177 0.714 0.0459 177 1221 0.0152026 0.0114794 0.0386 0.0115 178 1222 0.0152026 0.0286986 0.0386 0.0287 179 1230 0.0152022 0.00717465 0.0848 0.00717 180 1231 0.0152022 0.0179366 0.0848 0.0179 181 1239 0.015202 0.00448416 0.0534 0.00448 182 1247 0.0152017 0.0112104 0.0413 0.0112 183 1248 0.0152017 0.028026 0.0413 0.028 184 1256 0.0152014 0.00700649 0.138 0.00701 185 1264 0.015201 0.00700649 0.0399 0.00701 186 1272 0.0152006 0.0175162 0.455 0.0175 187 1280 0.0151977 0.0175162 0.104 0.0175 188 1281 0.0151977 0.0437906 0.104 0.0438 189 1289 0.0151974 0.0109476 0.0386 0.0109 190 1297 0.0151921 0.0273691 0.134 0.0274 191 1298 0.0151921 0.0684228 0.134 0.0684 192 1306 0.015192 0.0171057 0.144 0.0171 193 1314 0.0151917 0.0171057 0.0853 0.0171 194 1322 0.0151915 0.0171057 0.0638 0.0171 195 1330 0.0151912 0.0171057 0.0488 0.0171 196 1331 0.0151912 0.0427642 0.0488 0.0428 197 1339 0.0151909 0.0106911 0.0419 0.0107 198 1340 0.0151909 0.0267276 0.0419 0.0267 199 1348 0.0151907 0.00668191 0.112 0.00668 200 1356 0.0151904 0.00668191 0.0404 0.00668 201 1357 0.0151904 0.0167048 0.0404 0.0167 202 1365 0.0151898 0.00417619 0.212 0.00418 203 1373 0.0151891 0.0104405 0.038 0.0104 204 1381 0.0151884 0.0261012 0.0996 0.0261 205 1382 0.0151884 0.065253 0.0996 0.0653 206 1390 0.0151882 0.0163133 0.0656 0.0163 207 1398 0.015188 0.0163133 0.0461 0.0163 208 1399 0.015188 0.0407832 0.0461 0.0408 209 1407 0.0151876 0.0101958 0.0445 0.0102 210 1408 0.0151876 0.0254895 0.0445 0.0255 211 1416 0.0151874 0.00637237 0.0999 0.00637 212 1424 0.0151872 0.00637237 0.0407 0.00637 213 1425 0.0151872 0.0159309 0.0407 0.0159 214 1433 0.0151867 0.00398273 0.177 0.00398 215 1441 0.0151862 0.00995682 0.0385 0.00996 216 1449 0.0151841 0.0248921 0.0409 0.0249 217 1450 0.0151841 0.0622302 0.0409 0.0622 218 1451 0.0151841 0.0155575 0.0409 0.0156 219 1459 0.0151837 0.00388938 0.158 0.00389 220 1467 0.0151832 0.00972346 0.0388 0.00972 221 1475 0.0151788 0.0243087 0.202 0.0243 222 1476 0.0151788 0.0607716 0.202 0.0608 223 1484 0.0151783 0.0151929 0.118 0.0152 224 1492 0.015178 0.0151929 0.0607 0.0152 225 1500 0.0151778 0.0151929 0.0379 0.0152 226 1501 0.0151778 0.0379823 0.0379 0.038 227 1509 0.0151773 0.00949557 0.107 0.0095 228 1510 0.0151773 0.0237389 0.107 0.0237 229 1518 0.015177 0.00593473 0.0509 0.00593 230 1526 0.0151767 0.0148368 0.039 0.0148 231 1534 0.0151693 0.0370921 0.0378 0.0371 232 1535 0.0151693 0.0927302 0.0378 0.0927 233 1543 0.0151688 0.0231825 0.0757 0.0232 234 1544 0.0151688 0.0579563 0.0757 0.058 235 1552 0.0151686 0.0144891 0.0376 0.0145 236 1553 0.0151686 0.0362227 0.0376 0.0362 237 1561 0.0151682 0.00905568 0.0859 0.00906 238 1562 0.0151682 0.0226392 0.0859 0.0226 239 1570 0.015168 0.0056598 0.0575 0.00566 240 1578 0.0151677 0.0141495 0.0389 0.0141 241 1586 0.0151638 0.0353737 0.107 0.0354 242 1587 0.0151638 0.0884344 0.107 0.0884 243 1588 0.0151638 0.0221086 0.107 0.0221 244 1596 0.0151635 0.00552715 0.041 0.00553 245 1604 0.0151634 0.0138179 0.237 0.0138 246 1612 0.0151626 0.0138179 0.0576 0.0138 247 1613 0.0151626 0.0345447 0.0576 0.0345 248 1621 0.0151623 0.00863617 0.0421 0.00864 249 1622 0.0151623 0.0215904 0.0421 0.0216 250 1630 0.0151621 0.00539761 0.105 0.0054 251 1638 0.0151619 0.00539761 0.041 0.0054 252 1646 0.0151615 6.26998e-06 0.154 0.0135 253 1654 0.015161 0.013494 0.0387 0.0135 254 1662 0.0151595 0.033735 0.171 0.0337 255 1663 0.0151595 0.0843376 0.171 0.0843 256 1671 0.0151593 0.0210844 0.147 0.0211 257 1679 0.0151591 0.0210844 0.143 0.0211 258 1687 0.015159 0.0210844 0.143 0.0211 259 1695 0.0151589 0.0210844 0.138 0.0211 260 1703 0.0151588 0.0210844 0.134 0.0211 261 1711 0.0151586 0.0210844 0.134 0.0211 262 1719 0.0151585 0.0210844 0.133 0.0211 263 1727 0.0151584 0.0210844 0.133 0.0211 264 1735 0.0151583 0.0210844 0.133 0.0211 265 1743 0.0151581 0.0210844 0.133 0.0211 266 1751 0.015158 0.0210844 0.137 0.0211 267 1759 0.0151579 0.0210844 0.138 0.0211 268 1767 0.0151578 0.0210844 0.138 0.0211 269 1775 0.0151576 0.0210844 0.138 0.0211 270 1783 0.0151575 0.0210844 0.138 0.0211 271 1791 0.0151574 0.0210844 0.138 0.0211 272 1799 0.0151573 0.0210844 0.138 0.0211 273 1807 0.0151572 0.0210844 0.138 0.0211 274 1815 0.015157 0.0210844 0.138 0.0211 275 1823 0.0151569 0.0210844 0.142 0.0211 276 1831 0.0151568 0.0210844 0.146 0.0211 277 1839 0.0151567 0.0210844 0.147 0.0211 278 1847 0.0151566 0.0210844 0.147 0.0211 279 1855 0.0151565 0.0210844 0.147 0.0211 280 1863 0.0151564 0.0210844 0.142 0.0211 281 1871 0.0151563 0.0210844 0.139 0.0211 282 1879 0.0151561 0.0210844 0.138 0.0211 283 1887 0.015156 0.0210844 0.142 0.0211 284 1895 0.0151559 0.0210844 0.142 0.0211 285 1903 0.0151558 0.0210844 0.142 0.0211 286 1911 0.0151557 0.0210844 0.146 0.0211 287 1919 0.0151556 0.0210844 0.147 0.0211 288 1927 0.0151555 0.0210844 0.143 0.0211 289 1935 0.0151554 0.0210844 0.139 0.0211 290 1943 0.0151552 0.0210844 0.135 0.0211 291 1951 0.0151551 0.0210844 0.13 0.0211 292 1959 0.0151549 0.0210844 0.129 0.0211 293 1967 0.0151548 0.0210844 0.129 0.0211 294 1975 0.0151547 0.0210844 0.126 0.0211 295 1983 0.0151545 0.0210844 0.125 0.0211 296 1991 0.0151544 0.0210844 0.128 0.0211 297 1999 0.0151543 0.0210844 0.129 0.0211 298 2007 0.0151541 0.0210844 0.129 0.0211 299 2015 0.015154 0.0210844 0.129 0.0211 300 2023 0.0151538 0.0210844 0.126 0.0211 301 2031 0.0151537 0.0210844 0.125 0.0211 302 2039 0.0151536 0.0210844 0.124 0.0211 303 2047 0.0151534 0.0210844 0.121 0.0211 304 2055 0.0151532 0.0210844 0.12 0.0211 305 2063 0.0151531 0.0210844 0.123 0.0211 306 2071 0.015153 0.0210844 0.124 0.0211 307 2079 0.0151528 0.0210844 0.121 0.0211 308 2087 0.0151526 0.0210844 0.117 0.0211 309 2095 0.0151524 0.0210844 0.106 0.0211 310 2103 0.0151523 0.0210844 0.106 0.0211 311 2111 0.0151521 0.0210844 0.106 0.0211 312 2119 0.0151519 0.0210844 0.106 0.0211 313 2127 0.0151517 0.0210844 0.103 0.0211 314 2135 0.0151515 0.0210844 0.102 0.0211 315 2143 0.0151513 0.0210844 0.104 0.0211 316 2151 0.0151511 0.0210844 0.108 0.0211 317 2159 0.0151509 0.0210844 0.109 0.0211 318 2167 0.0151508 0.0210844 0.107 0.0211 319 2175 0.0151506 0.0210844 0.103 0.0211 320 2183 0.0151503 0.0210844 0.0992 0.0211 321 2191 0.0151501 0.0210844 0.0948 0.0211 322 2199 0.0151499 0.0210844 0.0894 0.0211 323 2207 0.0151496 0.0210844 0.0866 0.0211 324 2215 0.0151493 0.0210844 0.0833 0.0211 325 2223 0.015149 0.0210844 0.0826 0.0211 326 2231 0.0151488 0.0210844 0.0838 0.0211 327 2239 0.0151485 0.0210844 0.0809 0.0211 328 2247 0.0151482 0.0210844 0.0784 0.0211 329 2255 0.0151479 0.0210844 0.0785 0.0211 330 2263 0.0151476 0.0210844 0.0759 0.0211 331 2271 0.0151472 0.0210844 0.0715 0.0211 332 2279 0.0151468 0.0210844 0.0654 0.0211 333 2287 0.0151464 0.0210844 0.0564 0.0211 334 2288 0.0151464 0.052711 0.0564 0.0527 335 2296 0.0151458 0.0131777 0.0421 0.0132 336 2297 0.0151458 0.0329444 0.0421 0.0329 337 2305 0.015145 0.00823609 0.162 0.00824 338 2313 0.015144 0.00823609 0.0405 0.00824 339 2321 0.0151409 0.0205902 0.517 0.0206 340 2329 0.0151318 0.0205902 0.0931 0.0206 341 2330 0.0151318 0.0514756 0.0931 0.0515 342 2338 0.0151312 0.0128689 0.0396 0.0129 343 2346 0.0120393 0.0321722 0.102 0.0322 344 2347 0.0120393 0.0804306 0.102 0.0804 345 2355 0.0120391 0.0201076 0.103 0.0201 346 2363 0.0120388 0.0201076 0.0737 0.0201 347 2371 0.0120387 0.0201076 0.0697 0.0201 348 2379 0.0120386 0.0201076 0.0668 0.0201 349 2387 0.0120384 0.0201076 0.0634 0.0201 350 2395 0.0120383 0.0201076 0.0617 0.0201 351 2403 0.0120381 0.0201076 0.0563 0.0201 352 2411 0.012038 0.0201076 0.0561 0.0201 353 2419 0.0120378 0.0201076 0.0571 0.0201 354 2427 0.0120377 0.0201076 0.0562 0.0201 355 2435 0.0120375 0.0201076 0.0553 0.0201 356 2443 0.0120373 0.0201076 0.0534 0.0201 357 2451 0.0120371 0.0201076 0.0581 0.0201 358 2459 0.012037 0.0201076 0.0562 0.0201 359 2467 0.0120368 0.0201076 0.0562 0.0201 360 2475 0.0120367 0.0201076 0.0581 0.0201 361 2483 0.0120365 0.0201076 0.0595 0.0201 362 2491 0.0120364 0.0201076 0.0628 0.0201 363 2499 0.0120363 0.0201076 0.0629 0.0201 364 2507 0.0120361 0.0201076 0.0596 0.0201 365 2515 0.012036 0.0201076 0.0606 0.0201 366 2523 0.0120359 0.0201076 0.0612 0.0201 367 2531 0.0120357 0.0201076 0.0593 0.0201 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0.00725209 0.00981 0.00725 644 4138 0.010343 0.0181302 0.00981 0.0181 645 4146 0.0103429 0.00453256 0.0164 0.00453 646 4154 0.0103429 0.00453256 0.00838 0.00453 647 4155 0.0103429 0.0113314 0.00838 0.0113 648 4163 0.0103429 0.00283285 0.0285 0.00283 649 4171 0.0103428 0.00708212 0.00765 0.00708 650 4179 0.0103428 0.0177053 0.0302 0.0177 651 4180 0.0103428 0.0177053 0.0302 0.0177 652 4188 0.0103427 0.00442632 0.00796 0.00443 653 4196 0.0103421 0.0110658 0.164 0.0111 654 4204 0.0103408 0.0110658 0.0219 0.0111 655 4205 0.0103408 0.0276645 0.0219 0.0277 656 4213 0.0103408 0.00691613 0.00752 0.00692 657 4221 0.0103405 0.0172903 0.00779 0.0173 658 4222 0.0103405 0.0432258 0.00779 0.0432 659 4230 0.010339 0.0108065 0.22 0.0108 660 4238 0.0103366 0.0108065 0.023 0.0108 661 4239 0.0103366 0.0270161 0.023 0.027 662 4247 0.0103365 0.00675403 0.00734 0.00675 663 4255 0.0103362 0.0168851 0.00779 0.0169 664 4256 0.0103362 0.0422127 0.00779 0.0422 665 4264 0.0103362 0.0105532 0.082 0.0106 666 4272 0.0103359 0.0105532 0.0213 0.0106 667 4273 0.0103359 0.0263829 0.0213 0.0264 668 4281 0.0103358 0.00659574 0.00743 0.0066 669 4289 0.0103351 0.0164893 0.0381 0.0165 670 4290 0.0103351 0.0412234 0.0381 0.0412 671 4298 0.010335 0.0103058 0.0228 0.0103 672 4306 0.010335 0.0103058 0.00832 0.0103 673 4307 0.010335 0.0257646 0.00832 0.0258 674 4315 0.0103349 0.00644115 0.0112 0.00644 675 4316 0.0103349 0.0161029 0.0112 0.0161 676 4324 0.0103349 0.00402572 0.0137 0.00403 677 4332 0.0103349 0.00402572 0.00829 0.00403 678 4333 0.0103349 0.0100643 0.00829 0.0101 679 4341 0.0103349 0.00251607 0.0201 0.00252 680 4349 0.0103348 0.00629018 0.0075 0.00629 681 4357 0.0103303 0.0157255 0.18 0.0157 682 4358 0.0103303 0.0393137 0.18 0.0393 683 4366 0.0103283 0.00982841 0.017 0.00983 684 4367 0.0103283 0.024571 0.017 0.0246 685 4375 0.0103283 0.00614276 0.00754 0.00614 686 4376 0.0103283 0.0153569 0.00754 0.0154 687 4384 0.0103278 0.00383922 0.0999 0.00384 688 4392 0.0103272 0.00959806 0.0151 0.0096 689 4393 0.0103272 0.0239951 0.0151 0.024 690 4401 0.0103271 0.00599879 0.00769 0.006 691 4402 0.0103271 0.014997 0.00769 0.015 692 4410 0.010327 0.00374924 0.047 0.00375 693 4418 0.0103269 0.00374924 0.00741 0.00375 694 4426 0.0103043 0.00937311 0.587 0.00937 695 4434 0.0102849 0.0234328 0.0976 0.0234 696 4435 0.0102849 0.0585819 0.0976 0.0586 697 4443 0.0102844 0.0146455 0.031 0.0146 698 4444 0.0102844 0.0146455 0.031 0.0146 699 4452 0.0102844 0.00366137 0.00658 0.00366 700 4460 0.0102839 0.00915342 0.128 0.00915 701 4468 0.010283 0.00915342 0.0134 0.00915 702 4469 0.010283 0.0228836 0.0134 0.0229 703 4477 0.010283 0.00572089 0.00643 0.00572 704 4485 0.0102792 0.0143022 0.197 0.0143 705 4486 0.0102792 0.0357556 0.197 0.0358 706 4494 0.0102772 0.00893889 0.0159 0.00894 707 4495 0.0102772 0.0223472 0.0159 0.0223 708 4503 0.0102772 0.00558681 0.00642 0.00559 709 4511 0.0102771 0.013967 0.135 0.014 710 4519 0.0102762 0.013967 0.0355 0.014 711 4520 0.0102762 0.0349175 0.0355 0.0349 712 4528 0.0102762 0.00872938 0.0119 0.00873 713 4536 0.0102761 0.00872938 0.0075 0.00873 714 4537 0.0102761 0.0218235 0.0075 0.0218 715 4545 0.0102761 0.00545587 0.00711 0.00546 716 4546 0.0102761 0.0136397 0.00711 0.0136 717 4554 0.0102761 0.00340992 0.0133 0.00341 718 4562 0.0102761 0.00852479 0.00722 0.00852 719 4563 0.0102761 0.021312 0.00722 0.0213 720 4571 0.0102761 0.00532799 0.00784 0.00533 721 4572 0.0102761 0.01332 0.00784 0.0133 722 4580 0.010276 0.00333 0.0129 0.00333 723 4588 0.010276 0.00333 0.00688 0.00333 724 4589 0.010276 0.00832499 0.00688 0.00832 725 4597 0.010276 0.00208125 0.0172 0.00208 726 4605 0.010276 0.00520312 0.00626 0.0052 727 4613 0.0102748 0.0130078 0.108 0.013 728 4614 0.0102748 0.0325195 0.108 0.0325 729 4622 0.0102742 0.00812987 0.0187 0.00813 730 4630 0.0102742 0.0203247 0.0152 0.0203 731 4631 0.0102742 0.0203247 0.0152 0.0203 732 4639 0.0102742 0.00508117 0.00642 0.00508 733 4640 0.0102742 0.0127029 0.00642 0.0127 734 4648 0.010274 0.00317573 0.0627 0.00318 735 4656 0.0102738 0.00793933 0.0115 0.00794 736 4657 0.0102738 0.0198483 0.0115 0.0198 737 4665 0.0102738 0.00496208 0.00662 0.00496 738 4666 0.0102738 0.0124052 0.00662 0.0124 739 4674 0.0102738 0.0031013 0.0266 0.0031 740 4682 0.0102737 0.00775325 0.00912 0.00775 741 4683 0.0102737 0.0193831 0.00912 0.0194 742 4691 0.0102737 0.00484578 0.00687 0.00485 743 4692 0.0102737 0.0121145 0.00687 0.0121 744 4700 0.0102737 0.00302861 0.0165 0.00303 745 4708 0.0102737 0.00302861 0.00678 0.00303 746 4709 0.0102737 0.00757153 0.00678 0.00757 747 4717 0.0102737 0.00189288 0.018 0.00189 ...
x = 1×7
-0.2307 0.0163 0.3180 -0.0003 -0.5394 1.2682 0.3232
fval = 7×1
0.0278 -0.0545 0.0001 0.0231 0.0500 -0.0570 0.0105
exitflag = -2
I work with 500000 iterations but the f(x) converge to 0 too slow, I try to change xO values but the improvements are negiglible.
I am grateful for any help solving the issue.
Thanks!
  1 Kommentar
Walter Roberson
Walter Roberson am 18 Jun. 2022
If you have the Symbolic Toolbox, you can solve the equations 1, 2, 3, 4, 6,for x(1), x(2), x(3), x(7), x(5) as closed form, leaving two equations in x(4), x(6)
However going further for symbolic solutions is difficult. You could try more, or you could switch to numeric at that point, using matlabFunction to generate a function handle (hint: use the 'vars' option) that you could fsolve. The equations are notably messier than what you started with but there would be only two variables.

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Walter Roberson
Walter Roberson am 19 Jun. 2022
Ran in:
% voltage value
Eoc=18.09;
v2=13.69;
v3=12.73;
v4= 11.31;
v5=10.22;
v6=9.71;
v7=8.91;
v8=8.41;
% current value
Ifc2=1;
Ifc3=2;
Ifc4=4;
Ifc5=6;
Ifc6=7;
Ifc7=9;
Ifc8=10;
% point 1
E1 = @(x)[Eoc - x(1)*log(Ifc2/x(2))-x(3)*exp(x(4)*Ifc2)-x(5)- x(6)*log(Ifc2/x(2))-x(7)*Ifc2-v2;
%% point 2
Eoc - x(1)*log(Ifc3/x(2))-x(3)*exp(x(4)*Ifc3)-x(5)- x(6)*log(Ifc3/x(2))-x(7)*Ifc3-v3;
%% point 3
Eoc - x(1)*log(Ifc4/x(2))-x(3)*exp(x(4)*Ifc4)-x(5)- x(6)*log(Ifc4/x(2))-x(7)*Ifc4-v4;
%% point 4
Eoc - x(1)*log(Ifc5/x(2))-x(3)*exp(x(4)*Ifc5)-x(5)- x(6)*log(Ifc5/x(2))-x(7)*Ifc5-v5;
%% point 5
Eoc - x(1)*log(Ifc6/x(2))-x(3)*exp(x(4)*Ifc6)-x(5)- x(6)*log(Ifc6/x(2))-x(7)*Ifc6-v6;
%% point 6
Eoc - x(1)*log(Ifc7/x(2))-x(3)*exp(x(4)*Ifc7)-x(5)- x(6)*log(Ifc7/x(2))-x(7)*Ifc7-v7;
%% point 7
Eoc - x(1)*log(Ifc8/x(2))-x(3)*exp(x(4)*Ifc8)-x(5)- x(6)*log(Ifc8/x(2))-x(7)*Ifc8-v8];
syms X [1 7]
E = E1(X);
sol1 = solve(E(1:4), X([1 2 3 7]))
Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.
sol1 = struct with fields:
X1: -(3*X5 + 4*X6*log(exp((1576*log(2) - 788*log(3) - 400*X5*log(2) + 200*X5*log(3) - 2624*exp(X4)*log(2) + 1082*exp(X4)*log(3) + 1509*exp(3*X4)*log(2) - 344*exp(3*X4)*log(3) - 394*exp(5*X4)*log(2) - 400*X5*exp(3*X4)*log(2) + 100*X5*exp(3*X4)*log(… X2: exp(-(1576*log(2) - 788*log(3) - 400*X5*log(2) + 200*X5*log(3) - 2624*exp(X4)*log(2) + 1082*exp(X4)*log(3) + 1509*exp(3*X4)*log(2) - 344*exp(3*X4)*log(3) - 394*exp(5*X4)*log(2) - 400*X5*exp(3*X4)*log(2) + 100*X5*exp(3*X4)*log(3) + 100*X5*exp(5… X3: (X5 + 2*X6*log(exp((1576*log(2) - 788*log(3) - 400*X5*log(2) + 200*X5*log(3) - 2624*exp(X4)*log(2) + 1082*exp(X4)*log(3) + 1509*exp(3*X4)*log(2) - 344*exp(3*X4)*log(3) - 394*exp(5*X4)*log(2) - 400*X5*exp(3*X4)*log(2) + 100*X5*exp(3*X4)*log(3) … X7: (log(exp((1576*log(2) - 788*log(3) - 400*X5*log(2) + 200*X5*log(3) - 2624*exp(X4)*log(2) + 1082*exp(X4)*log(3) + 1509*exp(3*X4)*log(2) - 344*exp(3*X4)*log(3) - 394*exp(5*X4)*log(2) - 400*X5*exp(3*X4)*log(2) + 100*X5*exp(3*X4)*log(3) + 100*X5*e…
E2 = subs(E(5:end), sol1)
E2 = 
sol5 = solve(E2(2), X(5))
E5 = subs(E2([1 3:end]), X(5), sol5)
%at this point E5 should be a system of two equations in X(4) and X(6), and
%you should be able to solve from there
%I do not show it because this demonstration system times out trying to
%compute sol5

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