Passivity-based control of a class of Blondel-Park transformable electric machines

In this paper we study the viability of extending, to the general rotating electric machine's model, the passivity-based controller method that we have developed for induction motors. In this approach the passivity (energy dissipation) properties of the motor are taken advantage of at two different levels. First, we prove that the motor model can be decomposed as the feedback interconnection of two passive subsystems, which can essentially be identified with the electrical and mechanical dynamics. Then, we design a torque tracking controller that preserves passivity for the electrical subsystem, and leave the mechanical part as a "passive disturbance". In position or speed control applications this procedure naturally leads to the well known cascaded controller structure which is typically analyzed invoking time-scale separation assumptions. A key feature of the new cascaded control paradigm is that the latter arguments are obviated in the stability analysis. Our objective in this paper is to characterize a class of machines for which such a passivity-based controller solves the output feedback torque tracking problem. Roughly speaking, the class consists of machines whose nonactuated dynamics are well damped and whose electrical and mechanical dynamics can be suitably decoupled via a coordinate transformation. The first condition translates into the requirement of approximate knowledge of the rotor resistances to avoid the need of injecting high gain into the loop. The latter condition is known in the electric machines literature as Blondel-Park transformability, and in practical terms it requires that the air-gap magnetomotive force must be suitably approximated by the first harmonic in its Fourier expansion. These conditions, stemming from the construction of the machine, have a clear physical interpretation in terms of the couplings between its electrical, magnetic and mechanical dynamics, and are satisfied by a large number of practical machines. The passivity-based controller presented here reduces to the well known indirect vector controller for current-fed induction machines. Our developments constitute an extension, to voltage-fed machines, of this de facto standard in industrial applications. Furthermore, our analysis provides it with a solid theoretical foundation.