Identifying force coefficients of a linear system

Hello

I have to develop an algorithim to identify the correct force coefficients of a cutting process. Cutting forces are generated using a synthetic model with the coefficients as shown after which their FFT is taken:

f =  [480.772081733469;250.888548275570]; % FFT of force values for zeroeth order
x = [800000000;200000000;10000;10000;]  ; % coefficients of force

Then I have developed a numerical fourier force model to approximate the FFT of cutting forces, which it is doing quite good.

x = [800000000;200000000;10000;10000;] 
A  = 3*[-1.14591559026165e-07 -1.40073764644624e-07  -0.00233909040370103  -0.00190985931710274;1.40073764644624e-07  -1.14591559026165e-07  0.00190985931710274  -0.00233909040370103];

c = (A*x)

The answer I get is

c =
                 
 -486.5325
  254.5452
  

Now I have to do the inverse process, I have to identify the force coefficients (x) using the matrix A ( it is the matrix of fourier coefficients like cos(thetha) and sin(thetha) ) and force vector, for this I have the system of equations that I have is Ax =f, where f is the forces.

I am solving the system using the mldivide. here is my code

  f = [480.772081733469;250.888548275570];
A  = 3*[-1.14591559026165e-07 -1.40073764644624e-07  -0.00233909040370103  -0.00190985931710274;1.40073764644624e-07  -1.14591559026165e-07  0.00190985931710274  -0.00233909040370103];

x = A\f ;

d = (A*x);

The results for d and x_1 are :

d =

  480.7721   % correct results for d
  250.8885
  
x =

   1.0e+04 *  % incorrect results for x

         0
         0
   -2.3592
   -5.5016
  

Is there any way I can develop an algorithim to correctly identify the force coefficients?

Do I have to include more values in matrix A, maybe also for 1st order and 2nd order.

Or there could be some other way?

Answer 1

[Rishabh Mishra]

Hi,

While performing the inverse process to calculate ‘x’. Use the code below:

>> x = inv(A)*f

Or

>> x = A^ (-1)

Instead of:

>> x = A/f

The ‘inv()’ function evaluates inverse of matrix A.

For more information on calculating inverse of matrices, refer the following link.