Stability of the frequency adaptive control technique and its application to compact disk drives

This paper presents the stability and implementation of the frequency adaptive control technique (FACT) for periodic disturbance cancellation in compact disk drives. The compact disk drive operates at various rotating speeds and modes, which causes periodic disturbances with different fundamental frequencies. To solve this, FACT provides a suitable framework for periodic disturbance rejection in the cases where the fundamental frequencies of the disturbance are alterable. This paper shows that the convergence property of parameters in the proposed adaptive algorithm is exponentially stable. The FACT controller is also shown to be equivalent to a linear time-invariant controller, and the upper bound of adaptation gains is determined according to system dynamics for the attenuation of periodic disturbances. These results are verified by experiments using the track-following system of a high speed CD-ROM drive. It is found that the stable limits of the adaptation gains match well between analytic and experimental results. The results significantly enhance the ability to design and analyze the FACT controller for a variety of applications where periodic disturbances with various fundamental frequencies are encountered.