Fractional-Order Fuzzy PID Contouring Control for a VCMs-Based X-Y Motion Stage

The object of this study is to develop a fractional-order fuzzy proportional-integral-derivative (FOFPID) control system for controlling the mover position of a voice coil motors (VCMs)-based x-y motion stage. First, the operating principle and dynamics of the VCMs-based x-y motion stage are analyzed. Then, a design of the fractional-order proportional-integral-derivative (FOPID) control system is introduced on the basis of the fractional calculus. With the additional degree of freedom to the control parameters, the FOPID controller can upgrade the contouring performance levels of the conventional proportional-integral-derivative (PID) controller in transient and steady-state responses with respect to the dynamic of the VCMs-based x-y motion stage. To further improve the control response of the FOPID controller, the FOFPID control system is thus designed by integrating a fuzzy logic controller. Finally, to evaluate and compare the contouring performances of the PID, FOPID, FOFPID control systems, two test conditions are provided which are the nominal condition and payload condition. Experimental results demonstrated that the developed FOFPID controller outperforms conventional PID and FOPID controllers with regard to the VCM-based x-y motion stage under both conditions. The good stability and smoothness against to the parameter variations of the FOFPID can also be observed clearly.