how to solve a system of non linear-equations

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?

[Star Strider]

The posted code runs without error. If you are not getting the ‘correct’ results, the only approach I can suggest is to check your derivations and coding. We do not have access to that, so we cannot help with it.

[steven rijns]

Is there maybe another way to solve the set of nonlinear equations(above), since I do not get correct results??

[Star Strider]

I cannot detect any errors. For this sort of problem, solving it symbolically is likely the most appropriate approach.

You have already determined the correct values for the R’s and C’s, so why not just go with those? Were they derived differently? Are they correct?

Beyond that, I have no further suggestions.

[Devineni Aslesha]

Hi Steven,

Could you provide the source from which R1, R2, C1 and C2 values are derived? Or were they solved manually?

Answer 1

[Cameron B]

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);

Answer 2

[Alex Sha]

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