$H_2$ Control for Head Positioning in Axial and Radial Dimensions for Self-Servo Track Writing

The self-servo track writing (SSTW) process for hard disk drives (HDDs) consists of axial (or time) and radial (or track) dimensions and is described by using a 2-D model. Within the 2-D system framework, the error propagation containment problem of the SSTW is formulated as a 2-D stabilization problem, and the position error minimization problem is formulated as a 2-D H control problem. The adopted 2-D controller is designed with the easily implemented linear matrix inequality (LMI) approach. With the stored error information of the preceding track, the 2-D control scheme is realizable. The simulation results demonstrate that the error propagation is prevented by the 2-D control scheme and the positioning accuracy is remarkably improved by the 2-D H control scheme. Also, servo performance is evaluated with the 1-D controller in time dimension, obtained from the designed 2-D controller.