Direct Eigen Control for Induction Machines and Synchronous Motors

Appendix B

Transfer Matrix Calculation

To be able to calculate the transfer matrix in the case of an interior permanent magnet synchronous motor (IPM-SM), we will initially calculate the eigenvectors associated with the eigenvalues of the evolution matrix.

The four row eigenvectors , , and , constitute the 4 × 4 transfer matrix:

(B.1)    

B.1 First Eigenvector Calculation

Equation (3.46), applied to the first eigenvector, is written:

(B.2)    

Developing the matrix relation, we obtain the following equation system:

(B.3)    

The last two system equations are solved by the elimination of p₃₁, one of the two unknowns:

(B.4)    

However , since μ₁ ≠ 0 ∀ ω (cf. equation (3.34)). The only possible solution is ...