Nonlinear contour tracking of a voice coil motors-driven dual-axis positioning stage using fuzzy fractional PID control with variable orders

This study aims to develop a variable-order fuzzy fractional proportional-integral-differential (VOFFPID) control system for controlling the mover position of a newly designed voice coil motors- (VCMs-) driven dual-axis positioning stage. First, the operation principle and dynamics of the stage are analyzed. After that, the design of a fuzzy fractional proportional-integral-differential (FFPID) control system is introduced on the basis of a fractional calculus and fuzzy logic system. With an additional degree of freedom to the control parameters and fuzzy operation, the FFPID control system can upgrade the contour tracking performance of a conventional proportional-integraldifferential (PID) control system with respect to the specified dynamics of the stage. Moreover, the VOFFPID control system is designed to further improve the tracking responses of the FFPID control system. In this system, the five control parameters are optimized with the cuckoo search algorithm via an adaptive strategy. Lastly, nominal and payload conditions attributed to two nonlinear contour demands are provided to evaluate the contouring performance of the PID, FFPID, and VOFFPID control systems. The experimental results subjected to different performance measures demonstrate that the proposed VOFFPID controller outperforms PID and FFPID controllers in terms of the designed VCMs-driven dual-axis positioning stage under both conditions.