How to find the expression for theta1?

    theta1=2*atan((2*tan(theta2/2)*tan(gama/2 - theta2/2) + (4*tan(theta2/2)^2 - 4*M^2*tan(theta2/2)^2 - 4*M^2*tan(gama/2 - theta2/2)^2 - M^2*gama^2*l^2 - 8*M^2*tan(theta2/2)*tan(gama/2 - theta2/2) - 4*M^2*gama*l*tan(theta2/2) - 4*M^2*gama*l*tan(gama/2 - theta2/2) - M^2*gama^2*l^2*tan(theta2/2)^2*tan(gama/2 - theta2/2)^2 + 2*M^2*gama^2*l^2*tan(theta2/2)*tan(gama/2 - theta2/2) + 4*M^2*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)^2 + 4*M^2*gama*l*tan(theta2/2)^2*tan(gama/2 - theta2/2) + 4)^(1/2) - 2)/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)) - (2*tan(theta2/2)*tan(gama/2 - theta2/2))/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)))

Can anyone help me to find an expression for theta1 in terms of thetac where

    theta2=thetac-theta1

[Manuela Gräfe]

Hi, umme mumtahina.

I see you are working with the LLC converter and the IEEE document (Optimal design methodology for LLC Resonant Converter... by Zhijian Fang etc.).

I am looking for the same solution at the moment for my bachelor thesis and I was wondering if you could provide me your MATLAB code? So I 'don't have to annoy Walter Roberson with the same issues. Please contact me via private message.

Answer 1

[John D'Errico]

Nope. Wanting magic to happen is not sufficient. I am quite confident that there is no way to untangle the implicit function you will get when you eliminate theta2.

Having theta1 inside and out of all of those terms will make it impossible to solve.

If you have values for all of the other variables, then you can use a root finder, but expect multiple solutions to exist.

I'd suggest rethinking your problem.

[safi58]

I have the values for thetac and all other variables except theta2. When I was trying to get the value of theta1 numerically, MATLAB is not allowing me to do so because this expression has theta1 in it.

[Walter Roberson]

You will probably need to work numerically, using fzero() or fsolve() or vpasolve()

[safi58]

k1=0.423;
k_1=0.423;
F=1.05;
gama=pi/F
thetac=2.98;
theta2=thetac-theta1;
l=0.218;
M=0.95;

Can you please tell me how can I find theta1 using these values?

[Walter Roberson]

syms theta1 theta2 gama M l
eqn = theta1 == 2*atan((2*tan(theta2/2)*tan(gama/2 - theta2/2) + (4*tan(theta2/2)^2 - 4*M^2*tan(theta2/2)^2 - 4*M^2*tan(gama/2 - theta2/2)^2 - M^2*gama^2*l^2 - 8*M^2*tan(theta2/2)*tan(gama/2 - theta2/2) - 4*M^2*gama*l*tan(theta2/2) - 4*M^2*gama*l*tan(gama/2 - theta2/2) - M^2*gama^2*l^2*tan(theta2/2)^2*tan(gama/2 - theta2/2)^2 + 2*M^2*gama^2*l^2*tan(theta2/2)*tan(gama/2 - theta2/2) + 4*M^2*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)^2 + 4*M^2*gama*l*tan(theta2/2)^2*tan(gama/2 - theta2/2) + 4)^(1/2) - 2)/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)) - (2*tan(theta2/2)*tan(gama/2 - theta2/2))/(2*tan(theta2/2) + 2*M*tan(gama/2 - theta2/2) + 2*M*tan(theta2/2) + M*gama*l - M*gama*l*tan(theta2/2)*tan(gama/2 - theta2/2)));

F=1.05;
gama=pi/F
thetac=2.98;
theta2=thetac-theta1;
l=0.218;
M=0.95;

seqn = subs(eqn);
sol = vpasolve(seqn);

or

F=1.05;
gama=pi/F
thetac=2.98;
l=0.218;
M=0.95;

eqn = @(theta1) (2*atan((-2*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)+(4*tan(-(1/2)*thetac+(1/2)*theta1)^2-4*M^2*tan(-(1/2)*thetac+(1/2)*theta1)^2-4*M^2*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)^2-M^2*gama^2*l^2+8*M^2*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)+4*M^2*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)-4*M^2*gama*l*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)-M^2*gama^2*l^2*tan(-(1/2)*thetac+(1/2)*theta1)^2*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)^2-2*M^2*gama^2*l^2*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)-4*M^2*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)^2+4*M^2*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)^2*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)+4)^(1/2)-2)/(-2*tan(-(1/2)*thetac+(1/2)*theta1)+2*M*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)-2*M*tan(-(1/2)*thetac+(1/2)*theta1)+M*gama*l+M*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1))+2*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)/(-2*tan(-(1/2)*thetac+(1/2)*theta1)+2*M*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)-2*M*tan(-(1/2)*thetac+(1/2)*theta1)+M*gama*l+M*gama*l*tan(-(1/2)*thetac+(1/2)*theta1)*tan((1/2)*gama-(1/2)*thetac+(1/2)*theta1)))) - theta1;

sol = fzero(eqn, rand())

Answer 2

[Manuela Gräfe]

Hi, umme mumtahina.

I see you are working with the LLC converter and the IEEE document (Optimal design methodology for LLC Resonant Converter... by Zhijian Fang etc.).

I am looking for the same solution at the moment for my bachelor thesis and I was wondering if you could provide me your MATLAB code? So I 'don't have to annoy Walter Roberson with the same issues. Please contact me via private message.