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 E

F and G Matrix Calculations

The transition and the input matrix of the discretized state-space equations for the IPM-SM, must be calculated in the (d, q) reference frame, which turns with the rotor, following the rotor magnetic anisotropy, to allow to:

  • filter measurements made in the (α, β) fixed frame: the two-phase currents and the position of the rotor, generally
  • predict an initial state-space during the control computation.

These two matrices F and G (cf. equations (3.124)) are calculated, from the exponential function of the diagonalized evolution matrix D multiplied by the sampling period T (cf. equation (3.69)), from the input matrix B of the continuous-time state-space equations, and from the transfer matrix and its inverse, calculated in Appendix B and C respectively:

image(E.1)    

In addition, the expression of D− 1 ⋅ (eDTI) ⋅ P− 1B, was already calculated in (3.72).

E.1 Transition Matrix Calculation

We will start by calculating eDTP− 1, by simply creating the product of the two matrices eDT by P− 1, and then we will multiply the result by the matrix P on the left.

(E.2)    image

To reduce the first row of the produced matrix, we then use equations (3.42) and (3.44) and the reduced variable ζd1, defined in (3.49). A new relation is thus obtained:

(E.3)    

To reduce ...

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