Stability and performance of a variable gain controller with application to a dvd storage drive

Abstract

This paper deals with the control design for optical storage drives. A nonlinear design is suggested to overcome the tradeoff between disturbance rejection, in the sense of tracking error reduction during low-frequency shock and vibration, and playability, in the sense of sensor noise tracking during high-frequency disc surface defects. Based on a variable gain control design, it is shown that improvements in disturbance rejection can be obtained without unnecessarily affecting playability. With this design, additional control is applied beyond a pre-defined error level. Accordingly, it is shown that large vibrations induce additional control effort giving improved disturbance rejection while, at the same time, small vibrations hardly induce any additional control effort thus leaving the playability properties unaffected. The variable gain strategy is studied regarding closed-loop stability and regarding performance. Closed-loop stability is derived on the basis of absolute stability theory. Performance is quantified using a measure derived from the linear sensitivity function. Based on the amplitude of the linear sensitivity function, the maximum absolute values of the periodic nonlinear response subjected to harmonic excitation are computed within a frequency range of interest. Experiments are performed on an industrial setup to validate the numerical results, and to illustrate the applicability of the nonlinear control design in a dvd application.