GRA-based approach to PID parameter tuning for closed-loop servo systems

Performances of servo system are the key factors, which determine the best process accuracy and efficiency that computer-numerical-control (CNC) machine tools can reach, and therefore it is absolutely necessary to conduct dynamic simulation and to design a corrector after static design. PID (proportion-integral-differential)-controller as a correction device is adopted. Overshoot of closed-loop servo system of the machine tool remains still as high as 13.27%, after corrected by proportion-integral-differential (PID) controller, whose parameters are tuned only with critical one fourth attenuation curve. Therefore PID controller parameters merely based on critical oscillation are required to be further optimized by grey relational analysis (GRA) combined with orthogonal experiment, in which controllable factor values are assigned according to the single-factor experiment results, and the two examined indexes, overshoot and rise time, are converted into one index through analysis of grey relational grade. In MATLAB software, a simulation model was created, and the simulation results to unit step response are 3.03% in overshoot and 0.1960 second in rise time, reflecting better dynamic performances, both smoothness and rapidity, and showing that the method is effective.