The topic of this article is the adaptive generalized predictive control (GPC) applied to the control of the speed of a digital axis. The system is used in CNC machine tools. Usually, the control of digital axes must obey quickly and effectively to changes in the input variable and continuously adapting with the machining conditions, and oppose the influence of external disturbances. However, The Online Recursive Least Squares with Forgetting factor was adopted to estimate in real-time the system parameters and adjust instantaneously GPC controller parameters based on a modeling CARIMA (Controlled AutoRegressive Integrated Moving Average). The results of this control architecture have achieved the desired local performance with good rejection of load disturbances and a good robustness for the parametric variations due to operating point changes