An Innovative Discrete-Time dq-Axis Model Considering Phase Discretization Error for High-Speed IM Drive and Its Analysis

The field-oriented control (FOC)-based auto current regulators (ACRs) are commonly designed under the ideal assumption that the phase is obtained continuously when performing the Park transformation, but the current regulators are always discretely implemented. It will inevitably introduce non-negligible phase discretization errors with the increase of fundamental-to-switching(control) frequency ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\left(f_{e} / f_{s}\right)$</tex>. Therefore, an innovative discrete-time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d q$</tex>-axis model for AC motor considering the Park transformation phase discretization error is proposed and the corresponding ACR is designed. Then, the decoupling performance and stability of the proposed closedloop current system are theoretically analyzed using complex vector method. Furthermore, the proposed discretization method is subsequently performed on an induction motor (IM) and verified through simulations and experiments. Eventually, the Padé approximant order of the discrete control matrix is discussed.