5. Mathematical models for converters powering machines

The mathematical modeling of inverter-machine assemblies for numerical control is an important step in control synthesis, as it is very often from the system equations that controls are selected and calculated. Electrical engineering has long since established equations for the machines themselves (at least within the framework of classical assumptions, such as the linearity of relations between fluxes and currents), but converters pose specific problems because their operation is, in all rigor, non-linear and sampled. Because of the difficulty of establishing and using these models, we usually settle for approximate models, either linear and continuous, or linear and sampled, but approximate. In certain special cases, more rigorous models are sought.

In this section, we limit ourselves to the simplest case, that of converters feeding DC motors. These models are...