Plumb-line alignment can affect the sensors of precise scientific instruments. When its effect is one of the main contributors to the measurement uncertainty, the deviation from the true vertical must be continuously monitored or compensated. This paper describes a digital control system designed and tested for an autoleveling platform. Best performances are obtained with an adaptive digital compensator based on a convolution of the error signal. Although accuracy and resolution of the leveling transducer limit the ultimate sensitivity, laboratory tests showed that the controller kept for several hours the base-plate top within ±1 μrad. These performances are suitable for maintaining the alignment of relative spring gravimeters used by volcanologists in long-term gravity measurements.