how to solve a system of non linear-equations

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steven rijns 2020 年 1 月 13 日

Hello,
The problem I am trying to solve consists of four non-linear equations. First I try to repoduce a known problem to check if my outcomes are correct.
So for this example I know the outcomes:
R1 is around: 0.0068
R2 is around: 0.0140
C1 is around: 7.926*10^6
C2 is around 2.38*10^4
However I am not able to repoduce these numbers with the following script:
syms R1 R2 C1 C2
h = 60;
h=Ts;
b0 = 0.009229;
R0 = b0;
a1 = (Ts/(R1*C1)) + (Ts/(R2*C2)) -2 == -1.817;
a2 = 1 - (Ts/(R1*C1)) - (Ts/(R2*C2)) + ((Ts^2)/(R1*C1*R2*C2)) == 0.8168;
b1 = (Ts/C1) + (Ts/C2) + ((Ts*R0)/(R1*C1)) + ((Ts*R0)/(R2*C2)) - (2*R0) == -0.01419;
b2 = R0 + ((Ts^2)/(R1*C1*C2)) + ((Ts^2)/(R2*C1*C2)) + (((Ts^2)*R0)/(R1*R2*C1*C2)) - (Ts/C1) - (Ts/C2) - ((Ts*R0)/(R1*C1)) - ((Ts*R0)/(R2*C2)) == 0.004967;
sol = solve([a1, a2, b1, b2], [R1 R2 C1 C2], 'Real', true);
R1sol = sol.R1;
R2sol = sol.R2;
C1sol = sol.C1;
C2sol = sol.C2;
R1sol = vpa(R1sol);
R2sol = vpa(R2sol);
C1sol = vpa(C1sol);
C2sol = vpa(C2sol);
Does anyone know how to solve this problem to get the correct results?
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Devineni Aslesha 2020 年 1 月 16 日
Hi Steven,
Could you provide the source from which R1, R2, C1 and C2 values are derived? Or were they solved manually?

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回答 (2 件)

Cameron B 2020 年 1 月 17 日
I ran the code below and some different versions of vpasolve, but I still got the same answer: no solution. So I have to think that part of the problem could be the values of a1, a2, b0, b1, and b2. I don't know where these values of -1.817, 0.8168, 0.009229, -0.01419, and 004967 came from, but it seems as if they've been rounded off, and maybe this is the reason we are unable to converge on an answer. I get close to the answers (a1, a2, b1, b2) when using your expected values, but there is still a little bit off.
syms R1 R2 C1 C2 positive
h = 60;
Ts = 60;
b0 = 0.009229;
R0 = b0;
a1 = (Ts/(R1*C1)) + (Ts/(R2*C2)) -2 == -1.817;
a2 = 1 - (Ts/(R1*C1)) - (Ts/(R2*C2)) + ((Ts^2)/(R1*C1*R2*C2)) == 0.8168;
b1 = (Ts/C1) + (Ts/C2) + ((Ts*R0)/(R1*C1)) + ((Ts*R0)/(R2*C2)) - (2*R0) == -0.01419;
b2 = R0 + ((Ts^2)/(R1*C1*C2)) + ((Ts^2)/(R2*C1*C2)) + (((Ts^2)*R0)/(R1*R2*C1*C2)) - (Ts/C1) - (Ts/C2) - ((Ts*R0)/(R1*C1)) - ((Ts*R0)/(R2*C2)) == 0.004967;
sol = solve([a1, a2, b1, b2], [R1 R2 C1 C2], 'Real', true);
R1sol = sol.R1;
R2sol = sol.R2;
C1sol = sol.C1;
C2sol = sol.C2;
R1sol = vpa(R1sol);
R2sol = vpa(R2sol);
C1sol = vpa(C1sol);
C2sol = vpa(C2sol);
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Alex Sha 2020 年 1 月 31 日
Hi, I get the solutions below:
1:
r1: 0.0136978624480164
r2: -0.0529268624480211
c1: 23794.5028958407
c2: 1043438.64860562
Fevl:
f1= 2.22044604925031E-16
f2= -3.33066907387547E-16
f3= 1.73472347597681E-18
f4= -8.67361737988404E-19
2:
r1: -0.052926862448011
r2: 0.0136978624480164
c1: 1043438.64860548
c2: 23794.5028958408
Fevl:
f1= -8.88178419700125E-16
f2= 7.7715611723761E-16
f3= -1.21430643318376E-17
f4= 1.12757025938492E-17

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