A smart monitoring system for superconducting cable test is proposed with an adaptive current control of a superconducting transformer secondary. The design, based on Fuzzy Gain Scheduling, allows the controller parameters to adapt continuously, and finely, to the working variations arising from transformer nonlinear dynamics. The control system is integrated in a fully digital control loop, with all the related benefits, i.e., high noise rejection, ease of implementation/modification, and so on. In particular, an accurate model of the system, controlled by a Fuzzy Gain Scheduler of the superconducting transformer, was achieved by an experimental campaign through the working domain at several current ramp rates. The model performance was characterized by simulation, under all the main operating conditions, in order to guide the controller design. Finally, the proposed monitoring system was experimentally validated at European Organization for Nuclear Research (CERN) in comparison to the state-of-the-art control system [P. Arpaia, L. Bottura, G. Montenero, and S. Le Naour, "Performance improvement of a measurement station for superconducting cable test," Rev. Sci. Instrum. 83, 095111 (2012)] of the Facility for the Research on Superconducting Cables, achieving a significant performance improvement: a reduction in the system overshoot by 50%, with a related attenuation of the corresponding dynamic residual error (both absolute and RMS) up to 52%.