Matlab won't solve system of equations

Hi!

I have been working on solving a system of equations symbolically using Matlab, but it won't return a value. I have 6 equations and 6 variables (solvable). I have even tried to simply this system of equations by hand, which gave me 2 equations and 2 unknown variables, but Matlab wouldn't solve that one either. I have the following code:

tau = 8.5; w_r = 1500*pi/30; p = 2; i_sn = 3.1; u_sn = 400*sqrt(2);
w_e = p*w_r; power = tau*w_r;

syms u_sq u_sd i_sq i_sd L_sq L_sd
eq1 = sqrt(w_e^2 * ((L_sd*i_sd)^2 + (L_sq*i_sq)^2)) == u_sn
eq2 =  ((L_sd*i_sd)^2 + (L_sq*i_sq)^2) / (sqrt(w_e^2 * ((L_sd*i_sd)^2 + (L_sq*i_sq)^2))) == 0
eq3 = (3/2)*p*(L_sd - L_sq)*u_sd*u_sq/(w_e^2*L_sd*L_sq) == tau
eq4 = 3*p*u_sd*u_sq*(L_sd - L_sq)/(w_e^3*L_sd*L_sq) == 0
eq5 = i_sq*u_sq + i_sd*u_sd == power
eq6 = i_sq^2 + i_sd^2 == i_sn^2

eqs = [eq1, eq2, eq3, eq4, eq5, eq6];
solveFor = [u_sq, u_sd i_sq i_sd L_sq L_sd];

solution = solve(eqs, solveFor);
solutionL_sq = solution.L_sq
solutionL_sd = solution.L_sd

The results is:

solutionL_sq =

Empty sym: 0-by-1

solutionL_sd =

Empty sym: 0-by-1

Does anyone know what's wrong? I cannot seem to find this online.

Answer 1

[Swatantra Mahato]

Hi,

You may want to recheck the system of equations you want to solve as I can see inconsistencies in eq1-2 and eq3-4

eq1 = sqrt(w_e^2 * ((L_sd*i_sd)^2 + (L_sq*i_sq)^2)) == u_sn 
eq2 =  ((L_sd*i_sd)^2 + (L_sq*i_sq)^2) / (sqrt(w_e^2 * ((L_sd*i_sd)^2 + (L_sq*i_sq)^2))) == 0 

By combining the above equations we get

((L_sd*i_sd)^2 + (L_sq*i_sq)^2) == 0 

Which when substituted back to eq1 gives

sqrt(w_e^2) == u_sn 

which is incorrect.

Similarly, for eq3 and eq4 we get

2*tau/w_e == 0 

which is again false.

Additionally, you can refer the documentation for tips on troubleshooting ‘solve’

https://www.mathworks.com/help/symbolic/troubleshoot-equation-solutions-from-solve-function.html

Hope this helps