PID control and multi-loop control schemes are widely used in machine-tool computer numerical control servo systems. However, fast and efficient tuning methods for solving mismatches are uncommon. Servo mismatch is an important source of error owing to its effect on positioning accuracy. A circular test using a double ball-bar is used to access such errors. This study proposed a simple, model-free, and inexpensive approach without add-on measurement to solve the servo mismatch system by measurement of simultaneous movements in two axes. Based on the proposed features, our approach is established by iterative tuning using Lagrange interpolation polynomials for the position and velocity loops parameters. The system performance can be improved to iteratively minimize the mismatch of servo systems by tuning the servo parameters of multi-axis feed drive systems. The proposed approach is based on the linear scale signals of iterative circular tests, which avoids using expensive measurement instruments. The experimental results demonstrate the accuracy of feed drive system diagnosis and the performance improvement (mismatch is improved from 0.67 to 0.01ms).
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