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This paper analyzes the dynamics of an LCL-T-based inductive power transfer power supply, and aims to improve its reference tracking performance for dynamic roadway wireless powering applications using a digital PI controller. An approximate small-signal model of the power supply that describes how the power supply reacts to a perturbation in its input is derived using the generalized state-space averaging technique. The model is verified experimentally and shown to capture the supply dynamics. Limitations of the model and their implications are also discussed. Using the small-signal model, a closed-loop digital PI controller is designed to ensure a fast turn-on of a 20 kHz power supply at no-load in approximately 300 μs with no overshoot in the track current.