The hypergravity centrifugal shaking table (HCST) is the most effective means for studying the disaster effects of rock and soil earthquakes, and the accurate control of acceleration waveform recurrence is the critical problem. This paper compares the dynamic characteristics of the normal gravity shaking table (NGST) and the HCST, highlighting the latter’s particularities, and analyzes the limitations of the existing control strategy. Meanwhile, a hypergravity unidirectional airborne shaking table (HUAST) is designed, and a data-driven iterative learning control and two-degree-of-freedom control-based acceleration waveform reproduction strategy is proposed and experimentally verified.