system of equations fails to solve

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Ben J Eells
Ben J Eells 2020-3-5
评论： Ben J Eells 2020-4-8
Matlab refuses to solve this system of equations despite certain other programs finding a single valid solution.
The original script:
syms x r C
eqn1 = 22.6==(x*((r^2+(1/(2*pi*5000*C)^2))^(1/2)))/(x+((r^2+(1/(2*pi*5000*C)^2))^(1/2)))
eqn2 = 19.1==(x*((r^2+(1/(2*pi*50000*C)^2))^(1/2)))/(x+((r^2+(1/(2*pi*50000*C)^2))^(1/2)))
eqn3 = 14.4==(x*((r^2+(1/(2*pi*500000*C)^2))^(1/2)))/(x+((r^2+(1/(2*pi*500000*C)^2))^(1/2)))
assume(C>0)
assume(x>0)
assume(r>0)
sol = solve(eqn1,eqn2,eqn3,x,r,C,'IgnoreAnalyticConstraints',1)
The errors:
Warning: Solutions are parameterized by the symbols: z, z1, z2. To include parameters and conditions in the solution,
specify the 'ReturnConditions' value as 'true'.
> In solve>warnIfParams (line 475)
In solve (line 357)
In failedscript (line 11)
Warning: Solutions are valid under the following conditions: 191/10 - (z*(z1^2 + 1/(10000000000*z2^2*pi^2))^(1/2))/(z
+ (z1^2 + 1/(10000000000*z2^2*pi^2))^(1/2)) == 0 & 0 < z & 0 < z1 & 0 < z2 & 72/5 - (z*(z1^2 +
4611686018427387904/(45515516623913202182151461698081*z2^2))^(1/2))/(z + (z1^2 +
4611686018427387904/(45515516623913202182151461698081*z2^2))^(1/2)) == 0 & 113/5 - (z*(z1^2 +
1/(100000000*z2^2*pi^2))^(1/2))/(z + (z1^2 + 1/(100000000*z2^2*pi^2))^(1/2)) == 0. To include parameters and
conditions in the solution, specify the 'ReturnConditions' value as 'true'.
> In solve>warnIfParams (line 482)
In solve (line 357)
In failedscript (line 11)
sol =
struct with fields:
x: [1×1 sym]
r: [1×1 sym]
C: [1×1 sym]
For simplicity the original equations are here:

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回答（2 个）

Sindhu Karri
Sindhu Karri 2020-3-18
Hii,
It seems like the mathematical equations you code doesn't match with the original set of equations you provided. I urge you to recheck the equation once more. Although I wrote the code with the original equation and it seems to be working for me. You can refer to the following code. Also I recommend you to use vpasolve instead of solve function.
Code:
syms x r C
eq1=x+(1/(((1/r)^2+(2*3.14159*500*C)^2))^1/2)==22.6
eq2=x+(1/(((1/r)^2+(2*3.14159*50000*C)^2))^1/2)==19.1
eq3=x+(1/(((1/r)^2+(2*3.14159*500000*C)^2))^1/2)==14.4
assume(x>0)
assume(r>0)
assume(C>0)
sol=vpasolve(eq1,eq2,eq3,r,x,C)
https://www.mathworks.com/help/symbolic/vpasolve.html
https://www.mathworks.com/help/symbolic/solve-a-system-of-algebraic-equations.html
  1 个评论
Ben J Eells
Ben J Eells 2020-3-18
编辑：Ben J Eells 2020-3-18
My appologies. I've been working with 2 different circuit topologies and I posted a screen clipping of the incorrect equation. I need to solve the equations that were in the original code. Here is a screen clipping of what they should look like.
I should mention I've tried vpasolve and it returns this:
struct with fields:
x: [0×1 sym]
r: [0×1 sym]
C: [0×1 sym]
Where all three components are:
Empty sym: 0-by-1

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Sindhu Karri
Sindhu Karri 2020-3-19
This seems to work
syms x r C
eq1=(x*(((1/r)^2+(2*3.14159*5000*C)^2))^1/2)/(x+((((1/r)^2+(2*3.14159*5000*C)^2))^1/2))==22.6
eq2=(x*((((1/r)^2+(2*3.14159*50000*C)^2))^1/2))/(x+((((1/r)^2+(2*3.14159*5000*C)^2))^1/2))==19.1
eq3=(x*((((1/r)^2+(2*3.14159*500000*C)^2))^1/2))/(x+((((1/r)^2+(2*3.14159*5000*C)^2))^1/2))==14.4
sol=vpasolve(eq1,eq2,eq3,r,x,C)
  1 个评论
Ben J Eells
Ben J Eells 2020-4-8
I'm not sure where you're getting the 1/r term. Either that's an algebraic manipulation I'm just not seeing or a typo.
I've revised the equation a bit further after realizing Matlab may not be interpreting my input the way I had expected. Seen here:
Again there is a 1/r term in both the numerator and denominator so I suspect this is an algebraic manipulation I've forgotten over the years.
My current system of equations script looks like this:
syms x r C
eq1=(x*(sqrt((r^2)+(1/(2i*pi*5000*C))^2)))/(sqrt((x+r)^2+(1/(2i*pi*5000*C))^2))==325.3
eq2=(x*(sqrt((r^2)+(1/(2i*pi*50000*C))^2)))/(sqrt((x+r)^2+(1/(2i*pi*50000*C))^2))==282.3
eq3=(x*(sqrt((r^2)+(1/(2i*pi*500000*C))^2)))/(sqrt((x+r)^2+(1/(2i*pi*500000*C))^2))==231.8
assume(x>0)
assume(r>0)
assume(C>0)
sol=vpasolve([eq1,eq2,eq3],[r,x,C])
Again I'm getting the error:
sol =
struct with fields:
r: [0×1 sym]
x: [0×1 sym]
C: [0×1 sym]

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