A numerical controller of a processing machine determines corresponding setpoint axis values based on setpoint position values for position-regulated axes operating on machine elements. Before controlling the position-regulated axes, volumes to be occupied by protection bodies associated with the machine elements, a workpiece and a tool are defined and it is checked whether the protection bodies remain disjoint while controlling the position-regulated axes. Depending on the result of the checks, the controller either controls the position-regulated axes in accordance with the setpoint position values or merely executes an error response without control. The controller contains a position error field which specifies for any given setpoint axis value an actual position the tool relative to the workpiece. The position error field is taken into consideration, at least for a subset of the protection bodies, when defining the volumes to be occupied by the protection bodies upon activation of the position-regulated axes.

A learning control system for a nano-precision motion stage comprises a closed-loop feedback section including a motion trajectory generator, a feedback controller, a motion stage, and a first Fourier transformer; and a feedforward section including a second Fourier transformer, a learning controller, an iteration backward shift operator, and a Fourier inverse transformer. An iteration experiment count j is initialized as j=1, and a j-th frequency domain feedforward signal is initialized to 0; the system is run to collect a frequency domain error signal and a frequency domain position measurement signal; a (j+1)-th frequency domain feedforward signal is updated; and an iteration experiment count j is incremented by 1. The present disclosure can effectively suppress the influence of external noise and disturbances, and improve convergence performance. Moreover, the present disclosure requires less computation, achieves simple determination of learning gains and strong robustness, and is convenient for engineering applications.