Optimization sol. of sys. of nonlinear trigonometric funct.

trigonometric optimization

Dear All,

I'm working on an inverter and to eliminate harmonics in output voltage and current i have to optimize a solution of a system of nonlinear trigonometric functions and i don't know how, Newton-Raphson iteration method is too difficult with this...so I really need your help.

here's an example for what i want to solve:

I want to eliminate 3rd, 5th, 7th, 9th and 11th harmonics so i have to optimize a solution for the next functions by solving them together at every value of m:

cos(x)+cos+cos(z)+cos(w)+cos(h)=m

cos(3x)+cos(3y)+cos(3z)+cos(3w)+cos(3h)=0

cos(5x)+cos(5y)+cos(5z)+cos(5w)+cos(5h)=0

cos(7x)+cos(7y)+cos(7z)+cos(7w)+cos(7h)=0

cos(9x)+cos(9y)+cos(9z)+cos(9w)+cos(9h)=0

cos(11x)+cos(11y)+cos(11z)+cos(11w)+cos(11h)=0

where: x,y,z,w & h are angels less than Π/2
0<x<Π/10
Π/10<y<Π/8
Π/8<z<Π/6
Π/6<w<Π/4
Π/4<h<Π/2
m = variable varies with 0.1 step & 0<m<1 & i.e. m = 0.1 , 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8,0.9


Note:
This method to eliminate the harmonics is called "Selective Harmonic Elimination Method of Multi-Level Inverter"

I hope i could explain my problem...and if you may ask me about specific thing will help in to solve this problem...that will be great.

Thanks in advance
Ahmed