dq Synchronous Reference Frame Model of A Series-Series Tuned Inductive Power Transfer System

A control-oriented circuit model of an inductive power transfer system is needed to design a high-performance controller. In this article, a dq synchronous reference frame model of a series-series tuned resonant inductive power transfer system is proposed. A single-phase dq modeling technique for a resonant converter is used to derive the model. The proposed control-oriented model clearly demonstrates the cross- and mutual-coupling between the state variables of the wireless power transfer system. It is interesting to note that the proposed model is similar to a dq synchronous reference frame model of a three-phase induction motor. The well-known controller design methods, such as proportional-integral controller design, manipulated input decoupling, disturbance input decoupling, state observers, and disturbance observers, etc. can be extended to the inductive power systems with the proposed model. The large- and small-signal responses of the transmitter current versus its input voltage are identified. Considering the frequency response, a new transmitter current controller that has a control bandwidth of 500 Hz is designed to show the validity of the proposed model. The proposed model and the controller are evaluated using simulated and experimental results. The simulated open- and closed-loop frequency responses of the model agree well with the theoretical bode plots of them. Also, the experimental results show that the proportional-integral with feedforward input controller regulates the transmitter current within 1 ms for three conditions: a step change of the reference, a step change of the load, and a step change of the mutual-coupling.