Modeling of inertial and compliance parametric uncertainties in Port-Hamiltonian Systems using LFR
Doubly-fed induction machines (DFIMs) have been proposed in the literature, among other applications, for high-performance storage systems, wind turbine generators or hybrid engines (see  for and extended literature survey and discussion). The attractiveness of the DFIM stems primarily from its ability to handle large-speed variations around the synchronous speed. Furthermore, this induction machine require an small power electronic equipment for control purposes (instead of the classical induction machines). The DFIM is a three-phase induction machine whit both stator and rotor windings accessible, and the rotor side is used for control. A DFIM can be used as a generator or motor. In this work we present a controller for a motor mode, and the goals are to regulate the mechanical speed while keeping the power factor close to one. Under the assumption that the machine is symmetric (all windings are equal), the cross inductances are smooth, sinusoidal functions of θ (rotor position), and the three-phase system is balanced, this mathematical transformation can be used to decouple variables (reduce the system dimension) and to facilitate the solution of equations with time-varying coefficients. Then, the original θ-depending model is simplified, and also, for control purposes, the dq, or Park, transformation  allows to describe a tracking problem as a regulation one, which can be solved with IDA-PBC (Interconnection and Damping Assignment–Passivity-based Control) techniques .