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solve nonlinear system of equations issue.

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Hugo Hamilton
Hugo Hamilton 2015-6-18
关闭： MATLAB Answer Bot 2021-8-20
I`m trying to make this code bellow to work but, seems like i've got some error and I don't know how to solve. This code should give me the solution of a 6x6 nonlinear system of equations. I'm using the "solve" function, should I use another one? It would be usefull too if I can get the symbolic solution of the R's and C's parameters, in function of the the a's.
if true
A = -0.0084;
B = 12.4815;
C = -0.15931;
D = 56.4282;
E = -0.37668;
F = 2.23716;
G = 4.56831;
syms R1 R2 R3 C1 C2 C3
a0 = C/B+E/B+G/B+A/D+E/D+G/D+A/F+C/F+G/F;
a1 = E/(B*D)+G/(B*D)+C/(B*F)+G/(B*F)+A/(D*F)+G/(D*F);
a2 = G/(B*D*F);
a3 = 1/B+1/D+1/F;
a4 = 1/(B*D)+1/(B*F)+1/(D*F);
a5 = 1/(B*D*F);
S = solve('1/(20000*C1) + 1/(20000*C2) + 1/(20000*C3)=a0','(C1*R1*R2 + C2*R1*R2 + C2*R1*R3 + C2*R2*R3 + C3*R1*R3 + C3*R2*R3)/(20000*C1*C2*C3*R1*R2*R3) = a1','(R1 + R2 + R3)/(20000*C1*C2*C3*R1*R2*R3) = a2','1/(100000*C1) + 1/(100000*C2) + 1/(100000*C3) + 1/(C1*R1) + 1/(C2*R2) + 1/(C3*R3) = a3','(C3 + (C1*R1)/100000 + (C2*R2)/100000 + (C3*R1)/100000 + (C3*R2)/100000)/(C1*C2*C3*R1*R2) + (C1*R1 + C2*R2 + (C1*R1*R2)/100000 + (C2*R1*R2)/100000)/(C1*C2*C3*R1*R2*R3) = a4','(R1 + R2 + R3 + 100000)/(100000*C1*C2*C3*R1*R2*R3) = a5','R1','R2','R3','C1','C2','C3');
end
  1 个评论
Star Strider
Star Strider 2015-6-18
When I attempted to solve your system (using solve with the lower-case ‘s’), it just gave up (in R2015a).
What is your original network? (It is always possible that you may not have analysed or characterised it correctly.)

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回答（2 个）

Azzi Abdelmalek
Azzi Abdelmalek 2015-6-18
Use solve not Solve
Walter Roberson
Walter Roberson 2015-6-18 
A = -0.0084;
B = 12.4815;
C = -0.15931;
D = 56.4282;
E = -0.37668;
F = 2.23716;
G = 4.56831;

syms R1 R2 R3 C1 C2 C3
a0 = C/B+E/B+G/B+A/D+E/D+G/D+A/F+C/F+G/F;
a1 = E/(B*D)+G/(B*D)+C/(B*F)+G/(B*F)+A/(D*F)+G/(D*F);
a2 = G/(B*D*F);
a3 = 1/B+1/D+1/F;
a4 = 1/(B*D)+1/(B*F)+1/(D*F);
a5 = 1/(B*D*F);
S = solve(1/(20000*C1) + 1/(20000*C2) + 1/(20000*C3) - a0, (C1*R1*R2 + C2*R1*R2 + C2*R1*R3 + C2*R2*R3 + C3*R1*R3 + C3*R2*R3)/(20000*C1*C2*C3*R1*R2*R3) - a1, (R1 + R2 + R3)/(20000*C1*C2*C3*R1*R2*R3) - a2, 1/(100000*C1) + 1/(100000*C2) + 1/(100000*C3) + 1/(C1*R1) + 1/(C2*R2) + 1/(C3*R3) - a3, (C3 + (C1*R1)/100000 + (C2*R2)/100000 + (C3*R1)/100000 + (C3*R2)/100000)/(C1*C2*C3*R1*R2) + (C1*R1 + C2*R2 + (C1*R1*R2)/100000 + (C2*R1*R2)/100000)/(C1*C2*C3*R1*R2*R3) - a4, (R1 + R2 + R3 + 100000)/(100000*C1*C2*C3*R1*R2*R3) - a5, R1, R2 , R3, C1, C2, C3);
  1 个评论
Walter Roberson
Walter Roberson 2015-6-19
编辑：Walter Roberson 2015-6-19

The solutions are:

[C1 = -0.4461646544e-2, C2 = -0.1784004227e-3, C3 = 0.1882728654e-4, R1 = 1.174062707*10^6, R2 = -9781.547493, R3 = -1.060426096*10^5]
[C1 = -0.3389681642e-2, C2 = -0.3913004980e-3, C3 = 0.1994594956e-4, R1 = 1.179017807*10^6, R2 = -5055.827149, R3 = -1.157234305*10^5]
[C1 = 0.2119389587e-4, C2 = 0.1945650375e-2, C3 = -0.2424439526e-2, R1 = -1.301221986*10^5, R2 = 1181.689443, R3 = 1.187179066*10^6]
[C1 = 0.2352974075e-4, C2 = 0.1208655909e-3, C3 = -0.2883195751e-3, R1 = -3.687309804*10^5, R2 = 43614.63767, R3 = 1.383356769*10^6]
[C1 = 0.1487214168e-3, C2 = 0.1412855522e-4, C3 = -0.3309343282e-4, R1 = 54482.22349, R2 = -1.749572795*10^6, R3 = 2.753329868*10^6],
[C1 = 0.2495289258e-4-0.1993032731e-4*I, C2 = 0.2304846111e-4+0.2178925031e-4*I, C3 = -0.9106413699e-4-0.6114544012e-3*I, R1 = 5.293758021*10^5-2.330764531*10^5*I, R2 = 5.457018310*10^5+1.484636723*10^5*I, R3 = -19142.11257+83314.07280*I]
[C1 = 0.2495289258e-4+0.1993032731e-4*I, C2 = 0.2304846111e-4-0.2178925031e-4*I, C3 = -0.9106413699e-4+0.6114544012e-3*I, R1 = 5.293758021*10^5+2.330764531*10^5*I, R2 = 5.457018310*10^5-1.484636723*10^5*I, R3 = -19142.11257-83314.07280*I]
[C1 = 0.2589774071e-4-0.1494241798e-4*I, C2 = 0.2441752825e-4-0.2269921972e-4*I, C3 = -0.2355944763e-5+0.2649938508e-4*I, R1 = 5.408541893*10^5-5.177244909*10^5*I, R2 = 1.594864338*10^5+1.193413097*10^6*I, R3 = 3.560509102*10^5-6.782605561*10^5*I]
[C1 = 0.2589774071e-4+0.1494241798e-4*I, C2 = 0.2441752825e-4+0.2269921972e-4*I, C3 = -0.2355944763e-5-0.2649938508e-4*I, R1 = 5.408541893*10^5+5.177244909*10^5*I, R2 = 1.594864338*10^5-1.193413097*10^6*I, R3 = 3.560509102*10^5+6.782605561*10^5*I]
[C1 = 0.2629006112e-4-0.1271208704e-3*I, C2 = 0.4656771904e-4-0.2584409754e-4*I, C3 = 0.2572753326e-4+0.1462101062e-4*I, R1 = 49938.56523+86025.15396*I, R2 = 6.993322548*10^5-8.451832209*10^5*I, R3 = 3.102562631*10^5+7.589662188*10^5*I]
[C1 = 0.2629006112e-4+0.1271208704e-3*I, C2 = 0.4656771904e-4+0.2584409754e-4*I, C3 = 0.2572753326e-4-0.1462101062e-4*I, R1 = 49938.56523-86025.15396*I, R2 = 6.993322548*10^5+8.451832209*10^5*I, R3 = 3.102562631*10^5-7.589662188*10^5*I]
[C1 = 0.3126409254e-4-0.1130524733e-4*I, C2 = 0.2719003443e-4+0.1343640581e-4*I, C3 = -0.6769445217e-4-0.3992079749e-4*I, R1 = 6.699418194*10^5-8.693515341*10^5*I, R2 = 5.684122552*10^5+7.330220343*10^5*I, R3 = -1.715059477*10^5+1.473101172*10^5*I]
[C1 = 0.3126409254e-4+0.1130524733e-4*I, C2 = 0.2719003443e-4-0.1343640581e-4*I, C3 = -0.6769445217e-4+0.3992079749e-4*I, R1 = 6.699418194*10^5+8.693515341*10^5*I, R2 = 5.684122552*10^5-7.330220343*10^5*I, R3 = -1.715059477*10^5-1.473101172*10^5*I]
[C1 = 0.3268603575e-4-0.2050052106e-4*I, C2 = 0.2601243075e-4-0.1483290392e-4*I, C3 = -0.6409913350e-5+0.3174125142e-4*I, R1 = 3.162201919*10^5+1.098023223*10^6*I, R2 = 5.280644453*10^5-5.322842026*10^5*I, R3 = 2.160466849*10^5-5.599731990*10^5*I]
[C1 = 0.3268603575e-4+0.2050052106e-4*I, C2 = 0.2601243075e-4+0.1483290392e-4*I, C3 = -0.6409913350e-5-0.3174125142e-4*I, R1 = 3.162201919*10^5-1.098023223*10^6*I, R2 = 5.280644453*10^5+5.322842026*10^5*I, R3 = 2.160466849*10^5+5.599731990*10^5*I]
[C1 = 0.3626803089e-4-0.1531205361e-4*I, C2 = 0.4303851920e-4+0.2121447799e-4*I, C3 = 0.2149151458e-3+0.2596669209e-4*I, R1 = 1.646432179*10^5-2.379573937*10^5*I, R2 = 1.754620505*10^5+1.267408248*10^5*I, R3 = 7.166551907*10^5+1.114847563*10^5*I]
[C1 = 0.3626803089e-4+0.1531205361e-4*I, C2 = 0.4303851920e-4-0.2121447799e-4*I, C3 = 0.2149151458e-3-0.2596669209e-4*I, R1 = 1.646432179*10^5+2.379573937*10^5*I, R2 = 1.754620505*10^5-1.267408248*10^5*I, R3 = 7.166551907*10^5-1.114847563*10^5*I]
[C1 = 0.4061952768e-4-0.1439124973e-4*I, C2 = 0.2455921515e-3+0.4192753332e-5*I, C3 = 0.4148528628e-4+0.1492861648e-4*I, R1 = 1.391654638*10^5-1.802886574*10^5*I, R2 = 7.781320811*10^5+10537.29881*I, R3 = 1.409404199*10^5+1.697533909*10^5*I]
[C1 = 0.4061952768e-4+0.1439124973e-4*I, C2 = 0.2455921515e-3-0.4192753332e-5*I, C3 = 0.4148528628e-4-0.1492861648e-4*I, R1 = 1.391654638*10^5+1.802886574*10^5*I, R2 = 7.781320811*10^5-10537.29881*I, R3 = 1.409404199*10^5-1.697533909*10^5*I]
[C1 = 0.7960958164e-4-0.5732134278e-4*I, C2 = 0.6294576649e-4-0.6131454147e-4*I, C3 = 0.2693945078e-4+0.1213272754e-4*I, R1 = 8.187046281*10^5-5.991012132*10^5*I, R2 = 1.176185691*10^5+29404.68843*I, R3 = 1.219147323*10^5+5.697014313*10^5*I]
[C1 = 0.7960958164e-4+0.5732134278e-4*I, C2 = 0.6294576649e-4+0.6131454147e-4*I, C3 = 0.2693945078e-4-0.1213272754e-4*I, R1 = 8.187046281*10^5+5.991012132*10^5*I, R2 = 1.176185691*10^5-29404.68843*I, R3 = 1.219147323*10^5-5.697014313*10^5*I]

where I is sqrt(-1).

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