O'Reilly logo

Direct Eigen Control for Induction Machines and Synchronous Motors by Jean Claude Alacoque

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Appendix C

Transfer Matrix Inversion

To invert one matrix P, the various steps are as follows:

  • calculate its determinant det(P)
  • calculate the cofactor pij of each element, starting from the determinant of the corresponding minor matrix P{ij} of P, i.e. the matrix P, in which one removes the row i and the column j:

(C.1)    image

  • constitute the cofactor matrix, or the matrix of the cofactors:

(C.2)    image

  • calculate the transpose cofactor matrix com(P)T, adjugate of P
  • calculate the inverse of P by:

(C.3)    image

These algebraic calculations are heavy, rather than complex. We will, however, carry them out for the IPM-SM, for inverting the transfer matrix P (equation (B.37)); this result is indeed necessary to calculate the control vector.

The following calculations will not detail the intermediate calculation of the coefficients cij of the adjugate of the P matrix, since it is enough to:

  • calculate the 3 × 3 determinants of the minor matrices of P, using Cramer’s rules
  • give to the determinants, the corresponding sign (−1)i + j
  • invert the subscripts i and j to create the coefficients cpij, of the adjugate matrix:

(C.4)    

To calculate the inverse matrix P− 1, we will thus calculate firstly the determinant of the transfer ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required