Method of calculating recovery commands for numerical controlled system

A computer implemented method of calculating recovery commands for a numerical controlled system, the numerical controlled system comprising an upper controller providing position commands to a servo driver to drive a motor, the method comprising:

• (a) providing a memory space to store the position commands;
• (b) reading a position matrix with k-by-1 elements;
• (c) reading a transformation matrix with k-by-k elements;
• (d) calculating a plurality of position coefficients of a position polynomial of degree (k−1);
• and
• (e) calculating a plurality of position interpolations according to the position polynomial and the position coefficients,
• wherein the position polynomial is modified to be a modified position polynomial to synchronize the position commands between the servo driver and a control loop of the upper controller, and the position polynomial is expressed as follows:
• θ(n)=a(k-1)*n(k-1)+a(k-2)*n(k-2)+a(k-3)*n(k-3)+ . . . +a1*n+a0;
• and variable n of the position polynomial is replaced by variable t to acquire the modified position polynomial, and the modified position polynomial is expressed as follows:
• θ(t)=a(k-1)*t(k-1)+a(k-2)*t(k-2+a(k-3)*t(k-3)+ . . . +a1*t+a0
• wherein t=Ta+nxTs-Tc, and
• Ta is the time of the position commands are initially transmitted to the control loop;
• Ts is the time of the position commands are sampled by the control loop;
• and
• Tc is the period of the position commands of the upper controller.