MATLAB: How to solve this equation Numerically [VPASOLVE]

equationnumerical equationsolvesymbolicsymsvpasolve

Hi there,
When i try to numerically solve my equation i got the following error :
Error using mupadengine/feval_internal (line 172)
More equations than variables is only supported for polynomial systems.
I simplified the equation to give you an example, and here is the equation example (the matlab code):
syms Idn
%%data
    Ism=200;
    Wb=1500;
    speedend=6000;
    Vsm=100;
    Ws=Wb:15:speedend;
    
    Eq2=Idn==sqrt(Idn)+(((2.4*10.^(-5))*(Idn).^2-0.013*(Idn+3.3)*10^(-3)))*Ws/Vsm %%The equation
    Idn=vpasolve(Eq2,Idn)
Can anyone help me to solve this kind of equation?

Best Answer

You can solve it numerically using fzero.
Ism=200;
Wb=1500;
speedend=6000;
Ws=Wb:15:speedend;
Idn = zeros(size(Ws));
Idn0 = 1;
for i = 1:numel(Ws)
Idn(i) = fzero(@f,Idn0,[],Ws(i));
end
plot(Ws,Idn),grid
xlabel('Ws'),ylabel('Idn')
function  F = f(Idn,Ws)
    Vsm=100;
    F = sqrt(Idn)+(((2.4*10.^(-5))*(Idn).^2-0.013*(Idn+3.3)*10^(-3)))*Ws/Vsm-Idn; %%The equation
 end
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