Proportional (P)–proportional integral (PI) control parameter design and adjustment for improving cornering accuracies in CNC machine tools with linear motions

The motion axis of a computer numerical control (CNC) machine tool is mainly composed of a permanent-magnet synchronous motor (PMSM), ball screw, and moving table so that the motion axis can be practically modeled as a two-mass mechanical system. However, the proportional (P)–proportional integral (PI) (P–PI) control design, which is extensively used in commercial PMSM drivers, generally considers the motion axis as a single-mass mechanical system, thereby limiting the cornering motion performance of the CNC machine tool. In this study, the motion axis is modeled as a two-mass mechanical system, and the P–PI control parameters are designed and adjusted to reduce cornering errors during linear cornering motions. The two-mass equivalent system is first derived from the motion axis model, and the pole assignment method is used to design the proportional and integral control parameters such that the PMSM velocity responses have short rise times and small overshoots. Thereafter, particle swarm optimization is applied to adjust the proportional control parameter to further reduce the cornering errors using an objective function with weighted errors. The results of experiments performed with a CNC lathe show that the cornering errors of the test path could be reduced by 30%, thus validating the feasibility and performance of the P–PI control parameter design and adjustment method developed herein.